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Old separable differential equations example | First order differential equations | Khan Academy

Video vocabulary

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

whether

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US / ˈweðə(r) /

UK / ˈhwɛðɚ, ˈwɛð- /

A1
  • conjunction
  • If something will happen or not

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

involve

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US / ɪn'vɒlv /

UK / ɪnˈvɑlv /

A2
  • verb
  • To have or be included as a part of something

sense

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US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

physics

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US / ˈfɪzɪks /

UK / ˈfɪzɪks /

A1
  • other
  • The study of heat, light, and energy on objects

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

reasonable

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US / ˈri:znəbl /

UK / ˈrizənəbəl /

A2
  • adjecitve
  • Being somewhat good, but not great
  • Fair and sensible; appropriate

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

tool

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US / tu:l /

UK / tul /

A2
  • noun
  • Device used to make things, e.g. a hammer
  • verb
  • To provide a workshop with the right equipment

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

integral

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US / ˈɪntɪgrəl /

UK / ˈɪntɪɡrəl, ɪnˈtɛɡrəl /

B1
  • adjecitve
  • Being an essential part of something; necessary

satisfy

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US / ˈsætɪsfaɪ /

UK / ˈsætɪsˌfaɪ /

A2
  • verb
  • To make someone happy because they got their wish
  • To do what is required in order to finish

rid

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US / rɪd /

UK / rɪd /

A2
  • verb
  • To cause to no longer have (pest, problem)

certain

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US / ˈsə:tn /

UK / ˈsɚtn /

A1
  • adjecitve
  • Definite, fixed
  • Referring to an unspecified amount or quantity
  • Being sure about something; without doubt

separate

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US / 'sepəreɪt /

UK / 'sepəreɪt /

A2
  • adjecitve
  • Being different from or unrelated to another
  • verb
  • To divide two things by being in between them
  • To live away from your husband or wife
  • To move things away from each other

science

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US / 'saɪəns /

UK / ˈsaɪəns /

A2
  • noun
  • Study of the physical world, based on facts

day

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US / deɪ /

UK / de /

A1
  • noun
  • A period of 24 hours beginning at midnight
  • The period of time when it is light outside
  • Person's name

complicated

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US / 'kɒmplɪkeɪtɪd /

UK / ˈkɑmplɪˌketɪd /

B1
  • adjecitve
  • Difficult to do, understand or use
  • verb
  • To make more difficult to do, understand or use

integrate

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US / ˈɪntɪgreɪt /

UK / ˈɪntɪˌɡret /

A2
  • verb
  • To combine together; make into one thing

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

new

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US / nju: /

UK / nu, nju /

A1
  • adjecitve
  • Not old, recently born, built or made
  • Being or doing something for the first time
  • Not felt, seen or known previously
  • Having been recently bought or obtained

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

while

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US / waɪl /

UK / hwaɪl, waɪl /

A1
  • conjunction
  • In spite of the fact that; although
  • During the time that; at the same time
  • noun
  • Short amount of time

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

couple

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US / 'kʌpl /

UK / ˈkʌpəl /

A2
  • noun
  • Two people in a romantic relationship
  • Two of something; two people; a pair
  • verb
  • To join something to something else
  • (Two animals) to engage in sexual relations
  • To put two people or things together

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

connection

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US / kəˈnekʃn /

UK / kəˈnɛkʃən /

A2
  • noun
  • Something that joins things together; being joined
  • Person you know who can help you in some way
  • Changing vehicles when traveling

differentiation

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US / ˌdɪfəˌrenʃɪ'eɪʃn /

UK / ˌdɪfəˌrɛnʃiˈeʃən /

B1
  • noun
  • Difference between things different and distinct

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

hopefully

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US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

unsolved

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US / ˌʌnˈsɒlvd /

UK / ˌʌnˈsɑ:lvd /

B1
  • adjecitve
  • (Of problem, etc.) not solved/worked out

large

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US / lɑ:dʒ /

UK / lɑ:rdʒ /

A1
  • adjecitve
  • Big; of great size; broad, tall, wide, or fat

form

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US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

most

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US / məʊst /

UK / most /

A1
  • adverb
  • Very; extremely
  • Greatest possible degree
  • pronoun
  • Nearly all of something

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

exclude

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US / ɪk'sklu:d /

UK / ɪk'sklu:d /

A2
  • verb
  • To prevent someone from taking part in something

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

never

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US / 'nevə(r) /

UK / ˈnɛvɚ /

A1
  • adverb
  • Not ever; not at any time

differential

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US / ˌdɪfəˈrenʃl /

UK / ˌdɪfəˈrɛnʃəl /

B2
  • adjecitve
  • Different, as in treatment; discriminatory
  • noun
  • A gear to let back wheels spin at different speeds

correct

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US / kə'rekt /

UK / kəˈrɛkt /

A2
  • adjecitve
  • Being suitable and appropriate for an occasion
  • True or accurate
  • verb
  • To fix a problem
  • To write marks on a piece of work to show mistakes
  • To punish in order to improve

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

fully

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US / 'fʊlɪ /

UK / ˈfʊli /

A1
  • adverb
  • Completely or entirely

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

computer

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US / kəmˈpju:tə(r) /

UK / kəmˈpjutɚ /

A1
  • noun
  • Machine for storing data, accessing the internet

few

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US / fju: /

UK / fju /

A1
  • pronoun
  • Not many, a small number

anyway

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US / ˈeniweɪ /

UK / ˈɛniˌwe /

A1
  • adverb
  • A word used to change the topic of a conversation

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

graph

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US / græf /

UK / ɡræf /

A2
  • noun
  • Image expressing numerical data in lines or shapes
  • verb
  • To show data using images

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

sine

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US / saɪn /

UK / saɪn /

C1
  • noun
  • Angle's ratio of side opposite hypotenuse

toolkit

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US / ˈtuːlkɪt /

UK / ˈtuːlkɪt /

C2
  • noun
  • A set of hand tools, e.g. drivers and spanners

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

dip

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US / dɪp /

UK / dɪp /

B1
  • noun
  • Food or sauce eaten with crackers/raw vegetables
  • Place on surface (e.g. a road) lower than the rest
  • verb
  • To decrease or lower temporarily
  • To put something in and out of a liquid quickly
  • To switch off or lower lights on a car

scratch

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US / skrætʃ /

UK / skrætʃ /

B1
  • noun
  • Action of rubbing your skin when itchy
  • A small cut or mark on a surface
  • verb
  • To rub your skin with your nails to stop an itch
  • To make a small cut or mark on a surface

often

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US / ˈɔfən /

UK / ˈɔfən,ˈɑfən,ˈɔftən,ˈɑf- /

A1
  • adverb
  • Many times; frequently; on many occasions

economic

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US / ˌi:kəˈnɒmɪk /

UK / ˌɛkəˈnɑmɪk, ˌikə- /

A2
  • adjecitve
  • Concerning trade, industry, and money

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

technicality

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US / ˌteknɪˈkæləti /

UK / ˌtɛknɪˈkælɪti /

B1
  • noun
  • Term or point

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

next

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US / nekst /

UK / nɛkst /

A1
  • adverb
  • The one that follows another in time or order
  • At a time or place directly after the present one
  • noun
  • The one that follows after
  • adjecitve
  • Immediately after the previous one
  • First occurrence after the present one

end

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US / end /

UK / ɛnd /

A1
  • noun
  • The point where a process or activity stops
  • A point that marks the limit of something; finish
  • Goal or desired result
  • The tip, edge or limit of something
  • verb
  • To be the last part of something

slightly

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US / ˈslaɪtli /

UK / ˈslaɪtli /

B1
  • adverb
  • Only a little

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

playlist

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US / ˈpleɪlɪst /

UK / ˈpleɪlɪst /

A1
  • noun
  • List of musical selections to be performed

separable

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US / ˈsepərəbl /

UK / ˈsɛpərəbəl, ˈsɛprə- /

B2
  • adjecitve
  • Capable of being divided or parted

numerically

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US / nju:'merɪklɪ /

UK / nuˈmɛrɪkəlɪ /

B2
  • adverb
  • In number; with regard to numbers

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

nice

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US / naɪs /

UK / naɪs /

A1
  • adjecitve
  • Being attractive or of high quality or value
  • Good or enjoyable
  • Being kind or friendly

initial

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US / ɪ'nɪʃl /

UK / ɪˈnɪʃəl /

A2
  • adjecitve
  • Existing or occurring at the beginning
  • noun
  • First letter of your given name
  • verb
  • To authorize something by writing your initials

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

pretty

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US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

derivative

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US / dɪˈrɪvətɪv /

UK / dɪˈrɪvətɪv /

B1
  • adjecitve
  • Not from original ideas; from somewhere else

gut

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US / ɡʌt /

UK / ɡʌt /

B1
  • noun
  • Stomach and internal organs of digestion
  • Guts courage; emotional strength
  • verb
  • To destroy the inside of a building , e.g. by fire
  • To remove the internal parts of an animal or fish

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

theory

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US / ˈθiəri /

UK / ˈθiəri, ˈθɪri /

A2
  • noun
  • Ideas or principles that explain facts or events

general

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US / 'dʒenrəl /

UK / ˈdʒɛnərəl /

A1
  • adjecitve
  • Widespread, normal or usual
  • noun
  • Top ranked officer in the army

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

log

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US / lɒg /

UK / lɔ:g /

B1
  • noun
  • Detailed account of events and progress on journey
  • Piece of a tree that has fallen or been cut
  • verb
  • To move a certain distance or speed, as recorded
  • To leave a website or computer account
  • To record something in an official account
  • To cut trees down and take the wood to use it

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

prove

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US / pru:v /

UK / pruv /

A2
  • verb
  • To demonstrate truth by providing evidence

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

implicit

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US / ɪm'plɪsɪt /

UK / ɪmˈplɪsɪt /

B1
  • adjecitve
  • Unquestioning and without doubt

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

solution

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US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

reverse

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US / rɪ'vɜ:s /

UK / rɪˈvɚs /

B1
  • noun
  • Setting that makes the vehicle go backward
  • (Drive a vehicle) backward gear of a vehicle
  • Instance of a significant change, for the worse
  • In a backwards order
  • Back part or side of something
  • verb
  • To drive a vehicle backward
  • To change to an opposite state, way or condition
  • To change back to a previous or normal condition
  • To change something to its opposite

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

broad

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US / brɔ:d /

UK / brɔd /

A2
  • adjecitve
  • General; not detailed
  • Wide; from the shorter two sides to the other

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

solvable

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US / 'sɒlvəbl /

UK / 'sɒlvəbəl /

A1
  • adjecitve
  • Capable of being solved

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

whose

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US / hu:z /

UK / huz /

A1
  • pronoun
  • Refers to the person who owns something

hodgepodge

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US / ˈhɔdʒpɔdʒ /

UK / ˈhɑdʒˌpɑdʒ /

A1
  • noun
  • Strange mixture of things

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

below

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US / bɪ'ləʊ /

UK / bɪˈlo /

A1
  • preposition
  • In a lower position, place, or level

natural

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US / ˈnætʃərəl /

UK / ˈnætʃərəl, ˈnætʃrəl /

A1
  • adjecitve
  • Being as one would expect; being usual or normal
  • Not made by humans; without human intervention

encounter

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US / ɪn'kaʊntə(r) /

UK / ɛnˈkaʊntɚ /

B1
  • noun
  • A chance meeting; unexpected or unplanned meeting
  • verb
  • To come up against a problem or trouble; meet
  • To meet someone or something unexpectedly

least

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US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

hard

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US / hɑ:d /

UK / hɑː(r)d /

A1
  • adjecitve
  • Difficult to do; difficult to understand
  • (Of facts) not able to be misunderstood; clear
  • (Of alcohol) strong
  • Involving or requiring lots of work, effort, care
  • Being full of pain, trouble, and problems
  • Strong
  • (Of edge) clear; sharp
  • Difficult to bend, break or cut; solid
  • adverb
  • With lots of force, power, or impact

whenever

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US / wenˈevə(r) /

UK / hwɛnˈɛvɚ /

A1
  • adverb
  • At any or every time that

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

nothing

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US / 'nʌθɪŋ /

UK / ˈnʌθɪŋ /

A1
  • noun
  • Item of little or no value, importance, interest
  • Number or value of zero
  • pronoun
  • Not anything, not a single thing

include

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US / ɪnˈklu:d /

UK / ɪnˈklud /

A1
  • verb
  • To make someone, something part of a group

find

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US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

type

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US / taɪp /

UK / taɪp /

A1
  • noun
  • Printed letters or blocks used for printing them
  • Group of things or people sharing common features
  • verb
  • To identify something belonging to a group
  • To write by touching keys on a keyboard

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

analytically

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US / ˌænə'lɪtɪklɪ /

UK / ˌænə'lɪtɪklɪ /

B2
  • adverb
  • In an analytical manner; with detailed analysis

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

reaction

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US / rɪ'ækʃn /

UK / riˈækʃən /

A2
  • noun
  • Bodily response to a drug or something eaten
  • Feeling or action in response to something

respect

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US / rɪ'spekt /

UK / rɪˈspɛkt /

A2
  • noun
  • Behavior that follows the established rules
  • Admiration for someone
  • Regard or admiration for someone or something
  • verb
  • To follow the established rules
  • To think very highly of another person

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

method

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US / 'meθəd /

UK / ˈmɛθəd /

A2
  • noun
  • (Organized and planned) way of doing something

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

fun

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US / fʌn /

UK / fʌn /

A1
  • adjecitve
  • Amusing and enjoyable
  • noun
  • Enjoyable or amusing quality or feeling

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

absolute

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US / ˈæbsəlu:t /

UK / ˈæbsəˌlut /

A2
  • adjecitve
  • Complete; total; pure; not limited in any way
  • noun
  • Something that is complete, total, pure, certain

hit

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US / hɪt /

UK / hɪt /

A1
  • noun
  • A planned killing, usually for money
  • Song, movie etc. that is successful
  • When someone strikes someone or something
  • Time when a player makes contact with the ball
  • Time when a website is accessed
  • verb
  • To have a negative impact on a person/place/thing
  • To press something, such as a button or switch
  • To suddenly realize the importance of something
  • To move your hand, a bat, etc. against with force
  • To fight, attack or damage something or someone
  • To arrive at a specific place, level, or goal
  • To make contact with the ball in a game or sport

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon
  • Subtitles section
  • I think it's reasonable to do one more separable differential equations problem, so let's do it.
  • The derivative of y with respect to x is equal to y cosine of x divided by 1 plus 2y squared, and they give us an initial condition that y of 0 is equal to 1.
  • Or when x is equal to 0, y is equal to 1.
  • And I know we did a couple already, but another way to think about separable differential equations is really, all you're doing is implicit differentiation in reverse.
  • Or another way to think about it is whenever you took an implicit derivative, the end product was a separable differential equation.
  • And so, this hopefully forms a little bit of a connection.
  • Anyway, let's just do this.
  • We have to separate the y's from the x's.
  • Let's multiply both sides times 1 plus 2y squared.
  • We get 1 plus 2y squared times dy dx is equal to y cosine of x.
  • We still haven't fully separated the y's and the x's.
  • Let's divide both sides of this by y, and then let's see.
  • We get 1 over y plus 2y squared divided by y, that's just 2y, times dy dx is equal to cosine of x.
  • I can just multiply both sides by dx.
  • 1 over y plus 2y times dy is equal to cosine of x dx.
  • And now we can integrate both sides.
  • So what's the integral of 1 over y with respect to y?
  • I know your gut reaction is the natural log of y, which is correct, but there's actually a slightly broader function than that, whose derivative is actually 1 over y, and that's the natural log of the absolute value of y.
  • And this is just a slightly broader function, because it's domain includes positive and negative numbers, it just excludes 0.
  • While natural log of y only includes numbers larger than 0.
  • So natural log of absolute value of y is nice, and it's actually true that at all points other than 0, its derivative is 1 over y.
  • It's just a slightly broader function.
  • So that's the antiderivative of 1 over y, and we proved that, or at least we proved that the derivative of natural log of y is 1 over y.
  • Plus, what's the antiderivative of 2y with respect to y?
  • Well, it's y squared, is equal to-- I'll do the plus c on this side.
  • Whose derivative is cosine of x?
  • Well, it's sine of x.
  • And then we could add the plus c.
  • We could add that plus c there.
  • And what was our initial condition? y of 0 is equal to 1.
  • So when x is equal to 0, y is equal to 1.
  • So ln of the absolute value of 1 plus 1 squared is equal to sine of 0 plus c.
  • The natural log of one, e to the what power is 1?
  • Well, 0, plus 1 is-- sine of 0 is 0 --is equal to C.
  • So we get c is equal to 1.
  • So the solution to this differential equation up here is, I don't even have to rewrite it, we figured out c is equal to 1, so we can just scratch this out, and we could put a 1.
  • The natural log of the absolute value of y plus y squared is equal to sine of x plus 1.
  • And actually, if you were to graph this, you would see that y never actually dips below or even hits the x-axis.
  • So you can actually get rid of that absolute value function there.
  • But anyway, that's just a little technicality.
  • But this is the implicit form of the solution to this differential equation.
  • That makes sense, because the separable differential equations are really just implicit derivatives backwards.
  • And in general, one thing that's kind of fun about differential equations, but kind of not as satisfying about differential equations, is it really is just a whole hodgepodge of tools to solve different types of equations.
  • There isn't just one tool or one theory that will solve all differential equations.
  • There are few that will solve a certain class of differential equations, but there's not just one consistent way to solve all of them.
  • And even today, there are unsolved differential equations, where the only way that we know how to get solutions is using a computer numerically.
  • And one day I'll do videos on that.
  • And actually, you'll find that in most applications, that's what you end up doing anyway, because most differential equations you encounter in science or with any kind of science, whether it's economics, or physics, or engineering, that they often are unsolveable, because they might have a second or third derivative involved, and they're going to multiply.
  • I mean, they're just going to be really complicated, very hard to solve analytically.
  • And actually, you are going to solve them numerically, which is often much easier.
  • But anyway, hopefully at this point you have a pretty good sense of separable equations.
  • They're just implicit differentiation backwards, and it's really nothing new.
  • Our next thing we'll learn is exact differential equations, and then we'll go off into more and more methods.
  • And then hopefully, by the end of this playlist, you'll have a nice toolkit of all the different ways to solve at least the solvable differential equations.
  • See you in the next video.