Question

Suppose that a and b vary inversely and that b=5/4 when a=8. Write a function that models the inverse variation and find b when a =15.

Answer 1

@mukushla @mathmale @e.mccormick

Answer 2

well a vary inversely with variations of b, that means you can write:\[a =\frac{k}{b}\]is it clear?

Answer 3

Yes, it is.

Answer 4

can you find constant \(k\)

Answer 5

Don't you do a*b=k?

Answer 6

use the fact that b=5/4 when a=8 :-) and find \(k\)

Answer 7

Ok thank you! So would it be 10? would K equal 10?

Answer 8

Oh wait, did I do this right?

Answer 9

@mukushla ?

Answer 10

@ganeshie8 @Hero ?

Answer 11

ab = k

8(5/4) = k
10 = k

Yes, 10 is correct so far.

Answer 12

Ok then do I plug in 15 for a?

Answer 13

Basically, from here you use formula

ab = k again

This time, k = 10 (still), but a = 15. Input those values then solve for b

Answer 14

Okay thank you, this clears it all up!

Answer 15

You're welcome

Answer 16

So I got b=5/4a

Answer 17

This is when I simplified it, it's just that its asking me to write a function.

Answer 18

You input

15(b) = 10

and ended up with

b = 5/4a?

How?

Answer 19

It's looking for the function.

Answer 20

At some point though, you got confused.

Answer 21

Oh... that makes sense.

Answer 22

Basically you're suggesting that

b = 5/4a is the same as ab = 5/4

You're suggesting that 5/4 = k which isn't true.

Answer 23

The only consistent value is k = 10. You want to include that in your formula. But one thing I notice is, you never solved for b

Answer 24

I didn't?

Answer 25

No.

You were supposed to take

ab = k (the formula for inverse variation)

then input a = 15 and k = 10
15b = 10

Then solve for b

Just try doing that please.

Answer 26

So that would mean it's b=10/a! @Hero

Answer 27

Yes, but you still haven't solved for b. That's the formula though

Answer 28

Thank you :) I got .666

Answer 29

b needs to be in fraction form

Answer 30

10/15

Answer 31

b=10/15

Answer 32

In simplified fraction form

Answer 33

Oh! 1/3

Answer 34

Wups 2/3

Answer 35

How did you get from 10/15 to 1/3? Show your work

Answer 36

Yes, correct b = 2/3 and the formula is ab = 10

Answer 37

Simplified by 5, okay thanks for clearing this up @Hero

Answer 38

For some reason this particular topic confuses 90% of students

Answer 39

It's not even that hard

Answer 40

But for some reason I get a little confused sometimes

Answer 41

Thanks again :)

Answer 42

yw