Question

q is inversely proportional to the square of r.

q=4 when r=5

(A) Find the formula for q in terms of r

(B) Work out the value of q when r=15

Answer 1

y is directly proportional to x:
\(y = kx\)

y is inversely proportional to x:
\(y = \dfrac{k}{x}\)

Answer 2

In your case, start with the second formula above.
If you had q is inversely proportional to r, you'd have

\(q = \dfrac{k}{r} \),

but you have q is inversely proportional to the "square of r," so we much account for the "square of r" part:

\(q = \dfrac{k}{r^2} \)

Answer 3

okkkkkkkkkkk

Answer 4

Now you need to find k.
To do that, use the last equation above, and enter the known point, q = 4 when r = 5, and find k. That answers part (A).
For part (B), use the formula with the value of k you find to find the value of q when r = 15.

Answer 5

Could you go into more detail about finding k?

Answer 6

Sure.
Start with

\(q = \dfrac{k}{r^2}\)

Now substitute into that equation the given values of r and q.

\(4 = \dfrac{k}{5^2}\)

Now can you solve for k?

Answer 7

do i do opposite to divide so times?

Answer 8

Square the 5 first.
The multiply both sides by the square of 5.

Answer 9

What is 5^2 = ?

Answer 10

ok thanks!!!!!!!

Answer 11

25

Answer 12

so 4 times 25?

Answer 13

Good.
Now multiply both sides by 25 to get rid of the 25 in the denominator.
Yes.

Answer 14

k = 25 * 4

Answer 15

thank you so much!! you have actually explained it so that i get it, better than my maths teacher lol

Answer 16

You're welcome.
I hope you got k = 100, right?

Answer 17

ok is that what i write for answer a?

Answer 18

k=100

Answer 19

Now that you know what k is, you rewrite the formula

\(q = \dfrac{k}{r^2} \)

with 100 instead of k.

That is the answer to part (A).

Answer 20

ohhhh thanks!

Answer 21

(A) \(q = \dfrac{100}{r^2} \)

Answer 22

thankyou!!!!!!!!!!!!

Answer 23

Now you know what the equation for the inverse proportion is.
To solve part (B), just use that formula, and substitute r with 15, and solve for q.