Question

Solve S = 4v2 for v.

Answer 1

I'm assuming the equation is \[\large S = 4v^2\]

Answer 2

yes i was a little confused becasue this is all they gave

Answer 3

you want the equation in the form of
v= _____

Answer 4

yes

Answer 5

First divide both sides by 4 to get

\[\large S = 4v^2\]


\[\large \frac{S}{4} = v^2\]


\[\large v^2 = \frac{S}{4}\]

what's your next step?

Answer 6

next step be square rooting it? im really lost in this whole lesson

Answer 7

good, that undoes the square exponent

Answer 8

keep in mind that if you have something like x^2 = 4

then x = 2 or x = -2 since both are solutions (when you replace x with either value)

Answer 9

so this means

\[\large v^2 = \frac{S}{4}\]

turns into

\[\large v = \pm\sqrt{\frac{S}{4}}\]

after you take the square root of both sides

Answer 10

you can optionally write

\[\large v = \pm\sqrt{\frac{S}{4}}\]

as

\[\large v = \sqrt{\frac{S}{4}} \ \text{ or } \ v = -\sqrt{\frac{S}{4}} \]

but they mean the same thing

Answer 11

the first way is more compact

Answer 12

so it can be either negative or positively written?

Answer 13

yep

Answer 14

ok wow thank u! so much!

Answer 15

because

(2)^2 = 4

and

(-2)^2 = 4

so this shows you that x^2 = 4 has two solutions x = -2 or x = 2, which is really x = plus/minus 2

Answer 16

np

Answer 17

Solve M = 2x + 3y for y
I also have a question like this, think you could help? explaining it helps I do online classes and really do not have any well explaining

Answer 18

how do you undo the +2x

Answer 19

wudnt u have to cancel it out

Answer 20

how would you cancel out 2x on the right side

Answer 21

subtract 2x from the y side also. Im not really sure

Answer 22

good

Answer 23

\[\large M = 2x + 3y\]


\[\large M - 2x = 3y\]


\[\large 3y = M - 2x\]


what's next?

Answer 24

would we add 2, to the 2x to cancel it out and get the y all by itself

Answer 25

3y means 3 times y

we move that 3 over by undoing the "times 3"

what will undo the "times 3"?

Answer 26

wud we do 3x2 to find out what we re multiplying? im not sure

Answer 27

i never no which numbers to fill in to get the rest of the problem

Answer 28

let's say we start with the number 5

then we multiply it by 3 to get 5*3 = 15

how do we undo this and go back to 5?

Answer 29

15-10 wud get us back to 5

Answer 30

true, but what operation undoes multiplication

what is the opposite of multiplication?

Answer 31

division

Answer 32

so if we multiply by 3

to do the complete opposite, we divide by 3

Answer 33

15 divided by 3

Answer 34

good

Answer 35

this means we divide both sides by 3

Answer 36

so the complete step by step picture looks like this

\[\large M = 2x + 3y\]


\[\large M - 2x = 3y\]


\[\large 3y = M - 2x\]


\[\large y = \frac{M - 2x}{3}\]

Answer 37

so at first, we undid the addition of 2x...so we subtracted 2x from both sides

then we undid the multiplication of 3...which means we divided both sides by 3

Answer 38

we subtracted 2x fromthe 2x and 3y
then divided 33 and divided it from 2x?

Answer 39

yes

we go from 2x+3y to just 3y when you subtract off 2x

you must do the same to the other side, which explains how it goes from M to M - 2x

Answer 40

we now have

\[\large 3y = M - 2x\]

then you divide both sides by 3

so

3y divided by 3 = y since the 3s cancel

and dividing the right side by 3 means you can leave it as

\[\large y = \frac{M - 2x}{3}\]

since not much simplification is done anyway

Answer 41

so divide 2x and the 3 thts how we get it

Answer 42

correct and you leave the right side as it is

Answer 43

so this wud be everything after simplifying Y=M-2 over 3

Answer 44

yep

\[\large y = \frac{M - 2x}{3}\]

Answer 45

oh it should be -2x and not just -2

Answer 46

2x ok got it thank u

Answer 47

yw

Answer 48

:)