Question

1.Solve S = 4v2 for v.

Show your work

Answer 1

Wel, first isolate the term for v^2

Answer 2

*first isolate v^2

Answer 3

(divide by 4, if you don't know)

Answer 4

ok

Answer 5

S/4=v^2

Answer 6

ok

Answer 7

Then, take the plus-minus square root of both sides.

Answer 8

You know how to simplify
\(\Huge \pm\sqrt\frac{S}{4}\) right?

Answer 9

ok im following you

Answer 10

Let me show you the whole thing. ONe sec, this may take a minute or two.

Answer 11

ok im waiting :)

Answer 12

S = 4v2
\(\Large S=4v^2\) ->Isolate the "\(v^2\)"
\(\Large \frac{S}{4}=v^2\) Take the positive negative square root of both sides
\(\huge \pm\sqrt{\frac{S}{4}}=v\)
\(\huge \pm\frac{\sqrt{S}}{\sqrt{4}}=v\)
Can you try from here?

Answer 13

@brittany_lundgren ?

Answer 14

I can try........ I dont remember how to do any of ths... I'm sooo lost!

Answer 15

Alright, it's ok. Just tell me which steps you don't understand :)

Answer 16

I honestly need help with the whole problem, im soooo confused! :'(

Answer 17

Ok, so, from step one, right?
Which parts of step one do you not understand? Or is it the problem itself?

Answer 18

It's the problem itself, I just don't understand :'(

Answer 19

Ok, what they do is give you an equation. What they want you to do is to "solve for v" This means they want you to put v on one side, and everything else on the other.

Answer 20

Note that v can ONLY be on one side. If you have v on both sides, it's a mistake.

Answer 21

okay, im following you so far!

Answer 22

Good. :)

Answer 23

i have solved it before - not is clearly there ?

Answer 24

Now, do you remember how we move things around?

Answer 25

Like, combine like terms, move things from one side to the other, and take square roots?

Answer 26

ok well can you show me how? Like the steps ??

Answer 27

Ok. In general, or just for this equation?

Answer 28

just the steps on how to solve this problem... The problem told me to show my work.......

Answer 29

Okk.

Answer 30

Remember, we want to put "v" on one side, and everything else on the other. The first step is to get rid of what's in front of v.

Answer 31

okay so what would I do then?

Answer 32

What's in front of v?

Answer 33

1.Solve S = 4v2 for v.

Answer 34

I mean, what's in front of "v^2"?

Answer 35

4

Answer 36

So, how do we move the 4 to the other side?

Answer 37

-4(4-4)=-2(2v-1)

Answer 38

Not that complicated. Just divide both sides by 4 :)

Answer 39

Is the answer to the question v=2?

Answer 40

Well, we can't actually solve for an exact value of v. We can only express it in terms of "s".

Answer 41

okay, I'm sooo confused!!! :'(

Answer 42

Ok. We can't always solve for v (in terms of a number, like 3, or -2). But, we can move everything over to one side and leave v on the other.

Answer 43

OMG!!! dumb right now :(

Answer 44

Ok. If you have the equation x-2y=0 you can't find x, because you don't know y.

Answer 45

okay, I understand that, I just don''t understand on how to solve this problem!

Answer 46

Ok. Solve for v doesn't mean "get a number value for v".
It means, "put just v on one side, and everything else without v on the other"

Answer 47

ok,im following so far.

Answer 48

Alright. Since we just want to move everything to the other side, we divide both sides by 4 to get rid of what's in front of v.

Answer 49

ok so S/4=4v^2/4

Answer 50

Ok. Now simplify the rigt side.

Answer 51

S=v^2

Answer 52

Careful, you can't cancel out the left side...

Answer 53

S/4=v^2

Answer 54

yess.

Answer 55

Now, what do we do to get rid of v^2? (turn it into v)

Answer 56

S/4=v

Answer 57

Careful. You have to take the square root of BOTH sides.

Answer 58

I got confused, just now. I beeen following this whole time and i just now got lost!!! :'(

Answer 59

That's ok.

Answer 60

S/4=4v^2/4
-> \(\huge \frac{S}{4}=\frac{(4v^2)}{4}\)

Answer 61

Then
\(\Huge \frac{S}{4}=v^2\)

Answer 62

Now, here's the part you got lost. Let me show it in more detail.

Answer 63

\(\Huge \pm\sqrt{\frac{S}{4}}=\sqrt{v^2}\)

Answer 64

There's a lot going on right here.

Answer 65

Does everything make sense?

Answer 66

ima little lost there

Answer 67

Ok.
Do you know why we have the plus minus sign?

Answer 68

nope, im confused whole step.......

Answer 69

I'm really sorry, but I have to go to bed. I'll try to make sure I get people here to help you.
(I have to take some tests myself tomorrow, and I can't afford to miss them)
@nbouscal , would you be so kind as to help out? THanks.

Answer 70

damn, what time is it there?

Answer 71

2:00 AM. I have to go to sleep and get done before 2:00PM, but I have two tests around 1 hour each, :S

Answer 72

dang........

Answer 73

ACtually, I'm going to take both right now. No chances.

Answer 74

Time for a cup of coffee. thanks, @nbouscal .

Answer 75

Okay, if you have \(v^2=\frac{S}{4}\), and you want to know what \(v\) is, you have to take the square root of both sides. That's the only way to get the left side to just have \(v\) by itself. The problem is, when you square root something, you always have to put a \(\pm\) sign in front, because you don't know whether it's positive or negative. For example, \(2^2=4, (-2)^2=4\), so the square root of 4 could be either 2 or -2. So, we take the square root of both sides and we add a plus-or-minus, and we get \[
v=\pm\sqrt{\frac{S}{4}}
\]

Answer 76

@nbouscal brb imma go get something to drink

Answer 77

ok, im following so far.

Answer 78

Brittany, I can help too, becaues I just realized I only have one test.

Answer 79

\(\huge v=\pm\frac{\sqrt{S}}{\sqrt{4}}\)

Answer 80

Remember,
\(\Huge \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\)

Answer 81

Now, what's the square root of 4?

Answer 82

(@nbouscal , I'm going to go ahead and take my scantron before the coffee wears off)

Answer 83

2

Answer 84

@inkyvoyd @nbouscal

Answer 85

Ok, then, what do we get?

Answer 86

(use draw if you have to)

Answer 87

\(v=\pm\dfrac{\sqrt{S}}{\sqrt{4}}\), \(\sqrt{4}=2\), so \(v=?\)

Answer 88

@brittany_lundgren , do you get it?