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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.303. (page 742)

If $y$ varies inversely with the square of $x$ and $x = 3$ when $y = 9$ , find $y$ when $x = 4$ .

Short Answer

Expert verified

The solution is $y = \frac{81}{16}$ .

Step by step solution

01

Step 1. Given information.

$y 伪 \frac{1}{x^{2}}$ and $x = 3$ when $y = 9$ .

02

Step 2. Write the equation.

The required equation is $y = \frac{k}{x^{2}}$ .

03

Step 3. Find the value of k, if x=3 and y=9.

$y = \frac{k}{x^{2}} 9 = \frac{k}{3^{2}} k = 9 脳 9 k = 81$

04

Step 4. Now, find the value of y, when k=81 and x=16.

$y = \frac{k}{x^{2}} y = \frac{81}{4^{2}} y = \frac{81}{16}$

05

Step 5. Simplified answer.

Hence, the required solution is $y = \frac{81}{16}$ .

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