Question

(a) if y varies inversely with x^7 and y = 118 when x = 4, find an equation to represent this relationship. y = \frac{472}{x} × (b) find y if x = 7. (round your answer to two decimal places.) y = 67.42 × suggested tutorial: learn it solve a basic problem involving direct or inverse variation resources read it

Explanation:

Step1: Write the inverse - variation formula

The formula for inverse variation is $y=\frac{k}{x^{7}}$, where $k$ is the constant of variation.

Step2: Find the value of $k$

Substitute $x = 4$ and $y=118$ into the formula $y=\frac{k}{x^{7}}$. So, $118=\frac{k}{4^{7}}$. Then $k = 118\times4^{7}=118\times16384 = 1933312$.

Step3: Write the equation

The equation representing the relationship is $y=\frac{1933312}{x^{7}}$.

Step4: Find $y$ when $x = 7$

Substitute $x = 7$ into the equation $y=\frac{1933312}{x^{7}}$. Then $y=\frac{1933312}{7^{7}}=\frac{1933312}{823543}\approx2.35$.

Answer:

(a) $y=\frac{1933312}{x^{7}}$
(b) $y\approx2.35$