Question

T is directly proportional to the square root of z and t = 35 when z = 100. Find t when z = 625.

Answer 1

t = 87.5

Explanation:

Let's change our proportion sign (∝) into an (=) to make it easier.

t = k *
`√(z)` ----------------- (Where K is our constant)

35 = k *
`√(100)` ------------------ (Now simplify the square root)

35 = k * 10

35 = 10k

We now want to divide both sides by 10 to isolate K

`(35)/(10)` =
`(k)/(10)`

3.5 = K

Now we have our constant, lets insert it into our next line of working out.

t =
`√(625\\)` * 3.5 (Now simplify the square root)

t = 25 * 3.5

t = 87.5