Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;
Variation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.
The required answers to the given questions are:
1. y [tex]\alpha[/tex] x
 ⇒ y = kx
where k is the constant of proportionality.
Given that, y = 5 and x =3, then;
5 = 3x
x = [tex]\frac{5}{3}[/tex]
Thus,
y = [tex]\frac{5}{3}[/tex] x
2. v [tex]\alpha[/tex] w
 v = kw
Given: v = 21, w = 8
Then,
21 = 8k
k = [tex]\frac{21}{8}[/tex]
Thus,
v = [tex]\frac{21}{8}[/tex]w
3. Â q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]
 y = [tex]\frac{k}{q}[/tex]
Given: q = 5, q = 6
Then,
5 = [tex]\frac{k}{6}[/tex]
k = 5 x 6
k = 30
Thus,
p = [tex]\frac{30}{q}[/tex]
4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]
 y = [tex]\frac{k}{x}[/tex]
Given: y = 11, x = 3
Then,
11 = [tex]\frac{k}{3}[/tex]
k = 11 x 3
k = 33
Thus,
y = [tex]\frac{33}{x}[/tex]
5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]
F = [tex]\frac{k}{l}[/tex]
Given; F = 20 pounds, l = 1.5 ft
20 = [tex]\frac{k}{1.5}[/tex]
k = 20 x 1.5
k = 30
F = [tex]\frac{30}{l}[/tex]
When l = 6 ft, then;
F = [tex]\frac{30}{6}[/tex]
F Â = 5 pounds
The amount of force required is 5 pounds.
For more clarifications on variation, visit: https://brainly.com/question/21139235
#SPJ1
