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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.470. (page 741)

If $m$ varies inversely with the square of $n$ , when $m = 4$ and $n = 6$ .
Find $m$ when $n = 2$ .

Short Answer

Expert verified

The solution is $m = 36$ .

Step by step solution

01

Step 1. Given information.

$m$ varies inversely with $n^{2}$ , when $m = 4$ and $n = 6$ .

02

Step 2. Write the formula for inverse variation.

$m = \frac{k}{n^{2}}$

03

Step 3. Substitute the values and find the value of k.

$m = \frac{k}{n^{2}} k = m n^{2} k = 4 脳 {(6)}^{2} 鈥� 鈥� (m = 4, n = 6) k = 144$

04

Step 4. Find the value of m, when k=144 and n=2.

$m = \frac{k}{n^{2}} m = \frac{144}{4} m = 36$

05

Step 5. Simplified answer.

Hence, the value of $m = 36$ .

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