Find the integral values of \(x\) and \(y\) satisfying the inequality \(3y + 5x \le 15\), given that \(y > 0\), \(y < 3\) and \(x > 0\).

Evaluate ∫2(2x-3)2/3dx

Differentiate (2x+5)2(x-4) with respect to x.

A cylindrical tank has a capacity of 3080 m3. What is the depth of the tank if the diameter of its base is 14 m? (Take pi = 22/7)

The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.

Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k.

If the gradient of the curve y = 2kx2 + x + 1 at x = 1 is 9, find k.

P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.

The bearings of P and Q from a common point N are 020° and 300° respectively. If P and Q are also equidistant from N, find the bearing of P from Q.