Question

W is directly proportional to t² and inversely proportional to z³. When t=8 and z=11, find w.

A) 4
B) 7
C) 10
D) 14

Answer 1

The value of w is 14

Therefore, correct answer is D) 14

Step-by-step explanation:

The direct and inverse proportionality relationship is expressed as
`\( W \propto (t^2)/(z^3) \)`. To find the constant of proportionality, substitute the given values for t and z when W = k , where k is the constant. Solving for k , we get
`\( k = W * z^3/t^2 \).` Now, plug in t = 8 and z = 11 to find k . Finally, substitute k , t = 8 , and z = 11 into the original equation to find W.

Understanding direct and inverse proportionality is fundamental in various mathematical applications. These relationships often model real-world scenarios, and the ability to manipulate these proportions is crucial in solving problems in physics, engineering, and other scientific fields.

Therefore, correct answer is D) 14