Assume varies inversely with . Find the constant of proportionality and the function. 1. = 8 when = 5 2. = 3 when = 11 3. = 50 when = 100

Question

asked Mar 20, 2022 228k views

1 Answer

Hiraku · Answer 1 · 2022-03-27T00:12:21+0000

Answer:

k = 40 and
y = (40)/(x)

k = 33 and
y = (33)/(x)

k = 5000 and
y = (5000)/(x)

Explanation:

Given

y varies inversely with x.

This is represented as:

y =(k)/(x)

Where k is the constant of proportionality.

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

This gives:

8 =(k)/(5)

k = 8 * 5

k = 40 -- the constant of proportionality.

To calculate the function, substitute 40 for k in
y =(k)/(x)

y = (40)/(x)

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

This gives:

3 =(k)/(11)

k = 3 * 11

k = 33 -- the constant of proportionality.

To calculate the function, substitute 33 for k in
y =(k)/(x)

y = (33)/(x)

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

This gives:

50 =(k)/(100)

k = 50 * 100

k = 5000 -- the constant of proportionality.

To calculate the function, substitute 5000 for k in
y =(k)/(x)

y = (5000)/(x)