It is given that x varies directly as y and inversely as z^(2). If y is decreased by 10% and z is increased by 20%, then x is decreased by __%?

Question

anonymous · Answer

From it equation can be formed as :

$$x = \frac{ky}{z^2}$$

anonymous · Answer

x=0.9yk / 1.44z^(2) ?

anonymous · Answer

If y is decreased by 10 % this means:

$$y' = y - \frac{10}{100}y = \frac{90}{100}y \implies \frac{9}{10}y$$

Similarly:

$$z' = \frac{120}{100}z \implies \frac{6}{5}z$$

anonymous · Answer

Now x has become :

$$\large x = \frac{k \times \frac{9}{10}y}{\frac{36}{25}z^2}$$

anonymous · Answer

*x'

anonymous · Answer

Now just divide both x and x'

anonymous · Answer

(x' - x )/x * 100%

anonymous · Answer

i am problem in calculating ...

anonymous · Answer

You are left with :

$$\frac{x}{x'} = \frac{0.9}{1.44 \times 1.44} = 0.434$$

anonymous · Answer

what??

anonymous · Answer

Just reverse it..

$$\frac{x'}{x} = 2.304$$

anonymous · Answer

Electricity gone, have to log out sorry..

anonymous · Answer

never mind, thanks

goformit100 · Answer

@kryton1212 Well Done :)

anonymous · Answer

i haven't done anything..

anonymous · Answer

$$\frac{ x*z^2 }{ y }=k$$
k is  a constant.. if y decrease %10 then x dectease %10, i z  increase %20, ( it means $$z^{2}$$ incresse %4, and it means x decrease %4 more.. but this %4 is the %90's %4.. in brief %4*%90= %3.6.. ans substract this value from %90, you get %86.4.. this is the last value of x.. it means x decteased (%100-86.4) %13.6 totally..

directrix · Answer

@kryton1212   If you see this, post the question here.

directrix · Answer

>>hey, the openstudy page have loaded a very long time, can i ask you some questions about Maths?  @kryton1212   The OpenStudy site has been down for 8 or more hours. No word given on Facebook on the OS page as to when to expect functionality.