Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

Question

asked Apr 7, 2020 208k views

2 Answers

Alexander Hein · Answer 1 · 2020-04-09T11:44:24+0000

Answer:

Final answer is choice B.
y=(4)/(7x^2) ,
y(5)=(4)/(175)

Explanation:

Given that if y varies inversely as square of x, and
y=(4)/(63) when x=3, then we need to find out y-value when x=5.

We also need to find the constant of variation and the equation.

Since y varies inversely as square of x, so we can write equation

y=(k)/(x^2)

where k is constant of variation.

Plug given values
y=(4)/(63) and x=3

y=(k)/(x^2)

(4)/(63) =(k)/(3^2)

(4)/(63) =(k)/(9)

(4)/(63)*9 =k

(4)/(7) =k

Hence constant of variation is
k=(4)/(7)

Now plug the value of k into formula

we get required equation as
y=(4)/(7x^2)

Now plug the value of x=5 into above formula

y=(4)/(7x^2)

y=(4)/(7(5)^2)

y=(4)/(7(25))

y=(4)/(175)

Hence final answer is choice B.
y=(4)/(7x^2) ,
y(5)=(4)/(175)

Pixel · Answer 2 · 2020-04-12T07:48:54+0000

Answer: b.

Explanation:

Based on the information given, you can write the following expression:

y=(k)/(x^2)

Where k is the the constant of variation

If y=4/63 when x=3, then you can substitute these values into the expression and solve for k:

$(4)/(63)=(k)/(3^2)\\k=9*(4)/(63)\\k=(4)/(7)$

Substitute k into the expression. Then the equation is:

y=(4)/(7x^(2))

Substitute x=5 into the equation. Then, y is:

y=(4)/(7(5)^(2))=(4)/(175)}