Question

Can someone please help me with these and explain it ?

Round to at least the thousandths place if needed
1) The variable Z is inversely proportional to X. When X is 5, Z has the value 2.2.
What is the value of Z when X = 12

2)The variable Z is inversely proportional to X. When X is 12, Z has the value 0.25.
What is the value of Z when X = 19

3)The variable Z is directly proportional to X, and inversely proportional to Y. When X is 10 and Y is Z has the value 47.5. What is the value of Z when X = 13, and Y = 10

Answer 1

For the first case inversely proportional means when one increases the other decreases and vice-versa or to be more exact Z=k/X where k is called the constant of proportionality. So in the first case substituting we have 2.2=k/5, solving for k yield k=2.2*5=11. Therefore when x=12 we get z=k/x or substituting z=11/12 or approx 0.917

The second case is identical so Z= k/X so .25=k/12 or k=12*.25=3 therefore Z=3/x for this case or Z=3/19 or approx 0.158

For the final case directly proportional means when one increases the other increases or if only directly proportional Z=k*X but since it is also inversely proportional to Y we get Z=k*X/Y. At this point a bit of a problem, since I can't tell from your question are Y and Z both 47.5, or you may be missing one of them, but anyways the same process at this point as 1 and 2.

Answer 2

sorry I had miss typed the last one.

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 10 and Y is 4, Z has the value 47.5.

What is the value of Z when X = 13, and Y = 10

Answer 3

Ok so finishing up in this case Z=k*X/y so 47.5=k*10/4 so k is 4*47.5/10=19 and so Z=19*X/Y or Z=19*13/10 = 24.7

Answer 4

thank you so much.