Question

Assume varies inversely with . Find the constant of proportionality and the function.

Answer 1

Answer:

$k = 40$ and $y = \frac{40}{x}$

$k = 33$ and  $y = \frac{33}{x}$

$k = 5000$ and $y = \frac{5000}{x}$

Step-by-step explanation:

Given

y varies inversely with x.

This is represented as:

$y =\frac{k}{x}$

Where k is the constant of proportionality.

(a): $y = 8\ when\ x= 5$

This gives:

$8 =\frac{k}{5}$

$k = 8 * 5$

$k = 40$ --  the constant of proportionality.

To calculate the function, substitute 40 for k in $y =\frac{k}{x}$

$y = \frac{40}{x}$

$(b): y= 3\ when\ x = 11$

This gives:

$3 =\frac{k}{11}$

$k = 3 * 11$

$k = 33$ --  the constant of proportionality.

To calculate the function, substitute 33 for k in $y =\frac{k}{x}$

$y = \frac{33}{x}$

$(c): y= 50\ when\ x = 100$

This gives:

$50 =\frac{k}{100}$

$k = 50 * 100$

$k = 5000$ --  the constant of proportionality.

To calculate the function, substitute 5000 for k in $y =\frac{k}{x}$

$y = \frac{5000}{x}$