If (x = frac{y}{2}),evaluate(left(frac{x^{3}}{y^{3}}+frac{1}{2}right) div left(frac{1}{2} – frac{x^{2}}{y^{2}}right)) A. 5/8 B. 5/2 C. 5/32 D. 5/16 Correct Answer:…

Given that (p = 1 + sqrt{2}) and (q = 1 – sqrt{2}), evaluate (frac{p^{2} – q^{2}}{2pq}). A.…

Simplify ((sqrt[3]{64a^{3}})^{-1}) A. 4a B. 1/8a C. 8a D. 1/4a Correct Answer: Option D Explanation ((sqrt[3]{64a^{3}})^{-1} = (sqrt[3]{(4a)^{3}})^{-1})…

Evaluate 21.05347 – 1.6324 x 0.43 to 3 decimal places A. 20.980 B. 20.351 C. 20.981 D. 20.352…

The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x…

A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?…

In how many ways can a delegation of 3 be chosen from among 5 men and 3 women,…

Given that the various faces of a fair dice 1, 2, 3, 4, 5, 6 appeared 30, 43,…

If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation. A.…

If the volume of a hemisphere is increasing at a steady rate of 18π m(^{3}) s(^{-1}), at what…