Which formula shows a joint variation?

Question

asked Jul 21, 2019 215k views

2 Answers

Vinod Srivastav · Answer 1 · 2019-07-23T22:14:23+0000

Answer : I, II and III

To find volume formula that shows joint variation we analyze each option

Joint variation always depends on atleast two dependent variables

for example y = kxy

The variable y depends on x and y and k is constant of proportionality

V= lwh

It means volume depends on length , width and height. 1 is the constant of proportionality .

$v=(1)/(3) \pi r^2h$

V depends on radius r and height h. Here 1/3 pi is the constant of proportionality

V= BH

V depend on base b and height h . 1 is the constant of proportionality .

So answer is I, II , III

Rebecca Scott · Answer 2 · 2019-07-25T21:27:15+0000

The answer is the first option: I, II and III.

The explanation is shown below:

1. By definition, there is a joint variation when a variable depends on two or more different variables. Therefore, you can express it as following:

y=kxz

Where
x,y and
are the variables and
is the constant of proportionality.

As you can see,
is directly proportional to
and
.

2. Keeping the information above, you have:

I)
V=lwh (
varies jointly with
,
and
.

II)
$V=(1)/(3)r^(2)h\pi$ (If
$(\pi)/(3)$ is the constant of proportionality,
varies jointly with
r^(2) and
).

III)
V=Bh (
varies jointly with
and
.