help in mathhh!!!!?

Question

w varies jointly as x and y varies inversely as the square of z. If w=225 when x=500, y=15, and z=10, find w when x=20, y=80,and z=5 and please explain how you get this answer i also need the steps to be able to work other problems similar to these out.

Answer 1

"varies jointly" means the same as "varies directly with more than one quantity". This means that one quantity is equal to the product of the others and a constant of variation, k. "varies invesely" means that one quantity is equal to the quotient of a constant of variation (k) and another quantity. So the statement

w varies jointly as x and y and varies inversely as the square of z

can be interpreted algebraically as follows:

w=(k*x*y)/z^2

Plugging in the first set of values (w=225 when x=500, y=15, z=10) we get the value for k:

225=(k*500*15)/10^2
225=k*7500/100
225=k*75
k=225/75
k=3

Now place that value for k into the original expression and use the second set of values (x=20, y=80,and z=5) to find the missing value (w):

w=(3*x*y)/z^2
w=(3*20*80)/25
w=192

In general, anything w varies directly or jointly with will lead to an expression involving the product of k and the other variables, ex: w=k*x*y*z*m*p, etc. Anything w varies inversely with will lead to an expression involving the quotient of k and the other variables, ex: w=k/(x*y*z*m*p), etc.

After setting up the appropriate expression you have to use the values given that constitute a full set of values (everything except k) and solve for k. Once you have k, plce it into the expression you found and put the second set of values into the expression to solve for the missing one.

Answer 2

w varies jointly as x: w=kx; 225=k500, k=225/500


y varies inversely as the square of z: y=c/(z^2), 15 = c/(10^2), c=1500.

find w when x=20: w =(225/500)*20 = 9

Answer 3

Well square 10 and 5 and you have z = 100 and z = 25

Answer 4

w= K1x ; y = K2/sqrt(z) ;
225 = K1 500, so K1 = 225/500 = .45, so w= 0.45x
15= K2/sqrt(10), so K2 = 15sqrt(10), so y= 15sqrt(10)/sqrt(z).
when x = 20, w = .45(20) = 9
when z = 5, y = 15sqrt(10)/sqrt(10) = 15