Answer:
[tex]k = 40[/tex] and [tex]y = \frac{40}{x}[/tex]
[tex]k = 33[/tex] and [tex]y = \frac{33}{x}[/tex]
[tex]k = 5000[/tex] and [tex]y = \frac{5000}{x}[/tex]
Step-by-step explanation:
Given
y varies inversely with x.
This is represented as:
[tex]y =\frac{k}{x}[/tex]
Where k is the constant of proportionality.
(a): [tex]y = 8\ when\ x= 5[/tex]
This gives:
[tex]8 =\frac{k}{5}[/tex]
[tex]k = 8 * 5[/tex]
[tex]k = 40[/tex] -- the constant of proportionality.
To calculate the function, substitute 40 for k in [tex]y =\frac{k}{x}[/tex]
[tex]y = \frac{40}{x}[/tex]
[tex](b): y= 3\ when\ x = 11[/tex]
This gives:
[tex]3 =\frac{k}{11}[/tex]
[tex]k = 3 * 11[/tex]
[tex]k = 33[/tex] -- the constant of proportionality.
To calculate the function, substitute 33 for k in [tex]y =\frac{k}{x}[/tex]
[tex]y = \frac{33}{x}[/tex]
[tex](c): y= 50\ when\ x = 100[/tex]
This gives:
[tex]50 =\frac{k}{100}[/tex]
[tex]k = 50 * 100[/tex]
[tex]k = 5000[/tex] -- the constant of proportionality.
To calculate the function, substitute 5000 for k in [tex]y =\frac{k}{x}[/tex]
[tex]y = \frac{5000}{x}[/tex]
