Question

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

Answer 1

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}}`

Answer 2

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`