Question

Solve for the requested variable.

s varies directly as the square of t, and s = 80 when t = 4. Find s when t is 8.

Answer 1

`\huge\boxed{\sf s = 320}`

Explanation:

Given that,

`s \propto t^2`

Converting proportionality into equality and adding a constant.

s = kt² ----------------(1)

Given that, s = 80 when t = 4

Put in Eq. (1)

80 = k(4)²

80 = k(16)

Divide 16 to both sides

80/16 = k

5 = k

k = 5

Now,

Put t = 8 in Eq. (1)

s = (5)(8)²

s = (5)(64)

s = 320

`\rule[225]{225}{2}`