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If b varies inversely as h and b =8 ,when h = 5, find b when h =4​

User Startuprob
by
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2 Answers

1 vote

Answer:

b = 10

Explanation:

When two quantities vary inversely, one quantity increases as the other decreases, and their product remains constant.

Therefore, if b varies inversely with h, then:


b \propto (1)/(h) \implies b=(k)/(h)

where k is the constant of proportionality.

Given b = 8 when h = 5, then:


8=(k)/(5)

Solve for k:


\begin{aligned}8\cdot 5&=(k)/(5)\cdot 5\\\\40&=k\end{aligned}

Therefore, the equation that links h to b is:


b=(40)/(h)

To find the value of b when h = 4, substitute h = 4 into the equation:


\begin{aligned}b&=(40)/(4)\\\\b&=10\end{aligned}

Therefore, the value of b when h = 4 is:


\huge\boxed{\boxed{b=10}}

User Andrei RRR
by
7.3k points
12 votes

Here given that


\\ \sf\longmapsto b\propto (1)/(h)

  • b_1=8
  • b_2=?
  • h_1=5
  • h_2=4


\\ \sf\longmapsto b_1h_1=b_2h_2


\\ \sf\longmapsto 8(5)=4b_2


\\ \sf\longmapsto 4b_2=40


\\ \sf\longmapsto b_2=10

User Caleb Kleveter
by
8.2k points

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