help!

Question

If a certain industry, production index x is directly proportional to
the square of e¢ ciency index y, and indirectly proportional to
investment index z. If a business in this industry halves its
investment index, which of the following is closest to the percent
change in the businesss e¢ ciency index required to keep the
production index the same?
(A) 100% increase
(B) 50% increase
(C) 30% increase
(D) 30% decrease
(E) 50% decrease

n2739178 · Answer

in the image provided with this question, which explains the answer, I don't understand why
 If x is proportional to the square of y and indirectly pro-
portional to z, it is proportional to:
 y^2
---
 z

how did they come up with that answer?

fluke · Answer

The explanation is really good. I don't think I can convey any better. But, here it;

Initially,
x = y^2/z

Now, they halved the z; so z becomes z/2

x= y^2/(z/2)

But, we want x=y^2/z as it was before. The question is asking what we should multiply with y so that we get
x= y^2/z back again

Now;
y^2/(z/2)=2y^2/z

If we double y; y becomes 2y
thus, x becomes 2(2y)^2/z=4y^2/x, which is 4 times y^2/x(we don't want 4 times, we want approximately 1 time the previous)

Answer says; 0.7; let's try that

2(0.7*y)^2/z=2*0.49*y^2/z=0.98*y^2/z

Thus, by multiplying 0.7 with y, we got the same expression.
0.7y is same as saying 30% decrease in y.

KarishmaB · Answer

If x is directly proportional to y, we say x = ky  (k is a constant)
If x is inversely proportional to z, we say  x = \frac{k}{z}  (k is a constant)
Now, in case of joint variation i.e. when both these relations hold, we say  x = \frac{ky}{z}  
This is the concept of Joint Variation.

See if this makes sense.
Say,  x = \frac{ky}{z} 
Here, when z and k are constants, x is directly proportional to y.
When y and k are constants, x is inversely proportional to z.
Hence, both relations are satisfied.
That is the reason we say, "Keeping all else constant, x is directly proportional to y." What we mean is that if x varies with any other variables, keep them all constant. Then relation between x and y is of direct variation.

Anonymous · Answer

Does indirectly proportional means inversely proportional??

Here it says X is indirectly proportional to Z...what does that mean??

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