4. Z varies jointly as D and the square of T a) fZ-4 when D- 10 and T- 4, find t

Question

4. Z varies jointly as D and the square of T a) fZ-4 when D- 10 and T- 4, find the variation constant and write the variation equation b) Use the equation in part (a) to find Z when D-4 and T 6 Find the variation constant and write the variation equation and determine the quantity indicated. The volume of a gas, V, varies inversely as its pressure, P. If the volume of the gas is 6400 cubic centimeters when the pressure is 25 millimeters of mercury, determine the volume when the pressure is 200 millimeters of mercury. 5.

Explanation / Answer

4 a) Z is proportional to 'D' and 'T2'
so let's introduce a proportionality constant =k such that
Z= k D T2
if Z=4, D= 10 and T=4 then
4 = k 10 * 42
k = 4/160 = 1/40;
Thus, the equation becomes Z = D T2 / 40;

b) when D=4 and T=6;
Z = 4 * 62 / 40 = 36/10 = 3.6;
Thus, when D= 4 and T=6, Z is = 3.6;

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