Answer:
[tex] y = 163.84 [/tex]
Step-by-step explanation:
When a variable y varies inversely as the n-th power of another variable x , it can be expressed as:
[tex]\Large\boxed{\boxed{ y = \dfrac{k}{x^n} }}[/tex]
where
k is the constant of variation.
In this case, y varies inversely as the 4th power of x .
so
n = 4 .
Given that y = 25 when x = 8 , we can substitute these values into the equation to find k :
[tex] 25 = \dfrac{k}{8^4} [/tex]
Now, solve for k :
[tex] k = 25 \cdot 8^4 [/tex]
Once you have k , we can find y when x = 5 by plugging it into the equation:
[tex] y = \dfrac{k}{5^4} [/tex]
Now, calculate k and find y :
[tex] k = 25 \cdot 8^4 \\\\ = 25 \cdot 4096 \\\\ = 102400 [/tex]
Now substitute k into the equation for y when x = 5 :
[tex] y = \dfrac{102400}{5^4} [/tex]
[tex] y = \dfrac{102400}{625} [/tex]
[tex] y = 163.84 \textsf{(rounded to two decimal places)}[/tex]
Therefore, when x = 5 , y is approximately 163.84.
