Respuesta :
Answer:
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
Step-by-step explanation:
1)m varies directly as y
[tex]\Rightarrow m \propto y \\\Rightarrow m =ky[/tex]
k is the constant of variation
We are given that m is 6 when y is 36
[tex]\Rightarrow 6=k(36)\\\Rightarrow \frac{6}{36}=k\\\Rightarrow \frac{1}{6}=k[/tex]
Hence the constant of variation is 1/6
2)A varies directly as b.
[tex]\Rightarrow A \propto b\\\Rightarrow A =kb[/tex]
k is the constant of variation
We are given that A = 3 when b = 24
[tex]\Rightarrow 3=k(24)\\\Rightarrow \frac{3}{24}=k\\\Rightarrow \frac{1}{8}=k\\So,A=\frac{1}{8}b[/tex]
Substitute A=10
[tex]10=\frac{1}{8}b[/tex]
80=b
So, b=80 when A=10
3)y varies inversely with x
[tex]\Rightarrow y \propto \frac{1}{x}\\\Rightarrow y = \frac{k}{x}[/tex]
k is the constant of variation
We are given that y = 5 when x = 8
[tex]\Rightarrow 5 = \frac{k}{8}\\\Rightarrow 40=k[/tex]
So, the value of k is 40
4)y varies inversely with x
[tex]\Rightarrow y \propto \frac{1}{x}\\\Rightarrow y = \frac{k}{x}[/tex]
k is the constant of variation
We are given that k=0.32
[tex]\Rightarrow y = \frac{0.32}{x}[/tex]
Substitute y = 10
[tex]\Rightarrow 10 = \frac{0.32}{x}\\\Rightarrow x = 0.032[/tex]
So, x=0.032 when y = 10
