Question

1.If m varies directly as y and m is 6 when y is 36, find the constant of variation.

2. A varies directly as b. If A = 3 when b = 24, find b when A = 10.







3. If y varies inversely with x, and y = 5 when x = 8, what is k?







4. If y varies inversely with x and k = 0.32, what is x when y = 10?

Answer 1

1) the constant of variation is 1/6

2) b=80 when A=10

3)the value of k is 40

4) x=0.032 when y = 10

Explanation:

1)m varies directly as y

`\Rightarrow m \propto y \\\Rightarrow m =ky`

k is the constant of variation

We are given that m is 6 when y is 36

`\Rightarrow 6=k(36)\\\Rightarrow (6)/(36)=k\\\Rightarrow (1)/(6)=k`

Hence the constant of variation is 1/6

2)A varies directly as b.

`\Rightarrow A \propto b\\\Rightarrow A =kb`

k is the constant of variation

We are given that A = 3 when b = 24

`\Rightarrow 3=k(24)\\\Rightarrow (3)/(24)=k\\\Rightarrow (1)/(8)=k\\So,A=(1)/(8)b`

Substitute A=10

`10=(1)/(8)b`

80=b

So, b=80 when A=10

3)y varies inversely with x

`\Rightarrow y \propto (1)/(x)\\\Rightarrow y = (k)/(x)`

k is the constant of variation

We are given that y = 5 when x = 8

`\Rightarrow 5 = (k)/(8)\\\Rightarrow 40=k`

So, the value of k is 40

4)y varies inversely with x

`\Rightarrow y \propto (1)/(x)\\\Rightarrow y = (k)/(x)`

k is the constant of variation

We are given that k=0.32

`\Rightarrow y = (0.32)/(x)`

Substitute y = 10

`\Rightarrow 10 = (0.32)/(x)\\\Rightarrow x = 0.032`

So, x=0.032 when y = 10