Question

Help! I fan and give medals!! :)
V varies inversely with T and V = 14 when T = 7. Which equation shows this relationship?
A.v=2/t
B.v=98/t
C.v=2t
D.v=98t

Answer 1

@ParthKohli :) Sorry I'm such a bother....:)

Answer 2

I have a feeling it might be a or b.:)

Answer 3

So, if V varies inversely with T, that means that the relationship is of the form:
\[V = \frac{k}{T}\]where \(k\) is the constant of variation. We know values for both \(V\) and \(T\) , so we can work out the value of \(k\) that makes the equation work.

Answer 4

Your feeling is correct, as C and D are both examples of V varying directly with T:\[V = kT\]

Answer 5

ok so can you help me work this out?

Answer 6

So, for all the marbles, can you find the value of \(k\) and choose correctly between A and B?

Answer 7

Hint: you can :-)

Answer 8

B.? *crosses fingers*

Answer 9

Here's the formula once again:
\[V = \frac{k}{T}\]
and the problem says "V = 14 when T = 7"

Answer 10

No guessing allowed. You can get the answer with 100% certainty!

Answer 11

oh hang on a sec.

Answer 12

so plug V=14 and T = 7 into that equation and solve for \(k\)

Answer 13

14 divieded by 7 is 2 so my answer is a?

Answer 14

*divided I was multiplying!

Answer 15

Slow down and think this through carefully.

\[V = \frac{k}{T}\]\[V=14\]\[T=7\]\[14=\frac{k}{7}\]If we want to solve for the value of \(k\), what do we do?

Answer 16

multiply?

Answer 17

Multiply both sides by 7:
\[14=\frac{k}{7}\]\[14*7 = 7*\frac{k}{7}\]\[98=k\]
So our full equation to relate \(V\) and \(T\) at any value is...

Answer 18

B.?

Answer 19

As my old math teacher used to say, "is that an answer, or a prayer?" :-)

Answer 20

your answer should be "it's B, of course!" :-)

Answer 21

haha do you mind helping me on more?

Answer 22

Your a great teacher:)

Answer 23

I'm serious — you should be able to do these and be confident in your answers. Just takes a little practice.

What's the next one?

Answer 24

If x varies inversely with y and x = 8 when y = 10, find y when x = 6.



A.




B.




C.




D.


If x varies inversely with y and x = 8 when y = 10, find y when x = 6.



A.




B.




C.




D.

Answer 25

ahhh I typed it twice!!!

Answer 26

A.y=3/20
B.y=4.8
C.y=7.5
D.y=40/3

Answer 27

Okay, so this is exactly like the one we just did. Give it a shot and I'll guide you if you go astray

Answer 28

"x varies inversely with y" means \[x = \frac{k}{y}\]

Answer 29

plug in the known values of \(x\) and \(y\) to find the value of \(k\)

Answer 30

ok so what was the formula again?

Answer 31

urgh I suck at math so bad!

Answer 32

6=k/10

Answer 33

then I multiply each side by 10?

Answer 34

okay, " x = 8 when y = 10" so plug those two into the formula and solve for \(k\)

Answer 35

8=k/10

Answer 36

formula is \[x=\frac{k}{y}\]

Answer 37

right, so know we solve \[8 = k/10\] for \(k\) by multiplying each side by 10 as you suggested

Answer 38

then I multiply each side by k/10 to get 80?

Answer 39

close. multiply each side by 10, which will give us:
\[8 = \frac{k}{10}\]\[8*10 = 10*\frac{k}{10}\]\[80=k\]

Answer 40

then what?

Answer 41

Now we plug the new value of \(x\) in to the equation along with \(k = 80\) to find the value of \(y\) when \(x = 6\) as requested

Answer 42

we're just going one step further than we did in the previous problem.

Answer 43

so then 6=k/10?

Answer 44

then I multiply each side by 10?

Answer 45

okay, we worked out the value of \(k\), right? what was it?

Answer 46

oh duh 80.

Answer 47

so 6=80/10

Answer 48

so our formula is \[x = \frac{80}{y}\]

Answer 49

Then I just plug in

Answer 50

right. but be careful — it's asking for the value of \(y\) not \(x\) so we need to do a bit of algebra

Answer 51

Wait so how do I do that? :)

Answer 52

#1 secret to success in doing math problems is reading the problem carefully :-)

Answer 53

6=80/k

Answer 54

so we know that we want to find the value of \(y\) when \(x = 6\), and that our formula relating \(x\) and \(y\) is \[x = \frac{80}{y}\]We plug in the value of \(x = 6\):
\[6 = \frac{80}{y}\] Now we need to solve for \(y\). What do you get if you multiply both sides of the equation by \(y\)?

Answer 55

I have no idea

Answer 56

6y and 80y?

Answer 57

sure you do.

\[6 * y = \frac{80}{\cancel{y}}*\cancel{y}\]\[6y=80\]

Answer 58

Now can you solve that for the value of \(y\)?

Answer 59

then divide each side by 6?

Answer 60

Exactamundo!!!

Answer 61

13.333333

Answer 62

Right, but probably better to keep it as a fraction, given our answer choices

Answer 63

Which is D.? :)

Answer 64

80/6 = 40/3 so D is correct.

Answer 65

Thanks so very much if I need help later could you possibly help my blonde head become a little smarter I already know I will. :)

Answer 66

Sure, just shoot me a message and I'll respond next time I'm online

Answer 67

Ok thanks I appreciate it alot!

Answer 68

So to recap what we did:

1) write down the skeleton of the variation formula:

x varies directly with y: \(x = ky\)
x varies indirectly with y: \(x = \dfrac{k}{y}\)

2) Plug in known values of \(x, y\) to find \(k\)

3) (if needed) use completed formula with new value of \(x\) or \(y\) to find corresponding value of the other

Answer 69

Thanks again!!!!