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Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x - 8
The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?
A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4 cm deep. Calculate its volume.
Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7
If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.
A chord of a circle subtends an angle of 120° degrees at the centre of a circle of diameter 4√3 cm. Calculate the area of the major sector.
If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)
The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is
The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2 * (3 * 4).
If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.
The inverse function f(x) = 3x + 4 is
Make r subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.
Find the maximum value of y in the equation y = 1 - 2x - 3x\(^2\)
Find the range of values of x for which \(\frac{(x+2)}{4}\) -\(\frac{2x-3}{3}\) < 4
The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?
Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0
If \(y = x^2 - \frac{1}{x}\). find dy/dx
A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?
Evaluate \(\int \sin 3x \mathrm d x\)