Question

y varies directly as the square of x. When x = 5, y = 100. Find y when x = 6.

y = 105

y = 120

y = 144

y = 150

Answer 1

What's the square of \(x\) when \(x = 5\)?

Answer 2

um...........idk

Answer 3

What's the square of 5?

Answer 4

25?

Answer 5

Yeah, but let's leave that for a minute.\[y \text{ varies directly with }x^2 \implies y = kx^2\]

Answer 6

We have to find \(k\), and we can do that by substituting \(x = 5\) and \(y = 100\).\[100 = k(5^2) \]\[100=25k\]\[ k = 4\]Does that make sense?

Answer 7

yes

Answer 8

Now you have to find \(y \) when \(x = 6\). Recall our equation\[ y = kx^2\]We already know that k = 4 and x = 6. Substituting,\[y = 4(6^2) \]\[ \implies 4(36)\]\[\implies\cdots \]

Answer 9

What is 4(36)?

Answer 10

144

Answer 11

Right, and that is it.

Answer 12

thanks!!