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Determine the area of the region bounded by y = \(2x^2\) + 10 and Y = \(4x + 16\).
Calculate the mean deviation of the first five prime numbers.
Differentiate the function y = \(\sqrt[3]{x^2}(2x - x^2)\)
Find the equation of straight line passing through (2, 3) and perpendicular to the line \(3x + 2y + 4 = 0\)
A coin is thrown 3 times. What is the probability that atleast one head is obtained?
A boat sails 8 km north from P to Q and then sails 6 km west from Q to R. Calculate the bearing of R from P. Give your answer to the nearest degree.
If D = \(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)
Find |D|
A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?
The ages of students in a small primary school were recorded in the table below.
| Age | 5 - 6 | 7 - 8 | 9 -10 |
| Frequency | 29 | 40 | 38 |
Estimate the mean
Evaluate the following limit: \(lim_{x\to2} \frac {x^2 + 4x - 12}{x^2 - 2x}\)
At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?
Find the value of t, if the distance between the points P(–3, –14) and Q(t, –5) is 9 units.
If \(\frac {3 - \sqrt 3}{2 + \sqrt 3} = a + b\sqrt 3\), what are the values a and b?
Divide 1101001\(_{two}\) by 101\(_{two}\)
If a car runs at a constant speed and takes 4.5 hrs to run a distance of 225 km, what time will it take to run 150 km?
The diagram above is a circle with centre C. P, Q and S are points on the circumference. PS and SR are tangents to the circle. ∠PSR = 36\(^o\). Find ∠PQR
Solve for x: 3(x – 1) ≤ 2 (x – 3)
Make x the subject of the formula: y = \(\frac {3x - 9c}{4x + 5d}\)
The area A of a circle is increasing at a constant rate of 1.5 cm\(^2s^{-1}\). Find, to 3 significant figures, the rate at which the radius r of the circle is increasing when the area of the circle is 2 cm\(^2\).
The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.