Suppose that y varies directly as the 4th power of x, and that y=10 when x=7. What is y when x=6? Round your answer to two decimal places if necessary.

Question

I need help. I need so much help. I can never understand how to set these up. Then I just get overwhelmed

Answer 1

When y varies directly with x you can frame the relationship as y=some constant( I will call it k)times x So

y=kx

In this example y=k(x^4) so need to solve for k

we know that y=10 when x=7 so 10= k(7^)4 k= 10/(7^4) so when x=6

y=(10)/(7^4) x 6^4

y= 5.40