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Calculate, correct to three significant figures, the length AB in the diagram above.
The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building's height.
Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is
The locus of a point equidistant from two intersecting lines is
What is the general term of the sequence 3, 8, 13, 18, ...?
Solve the following quadratic inequality: \(x^2 - x\) - 4 ≤ 2
Let a binary operation '*' be defined on a set A. The operation will be commutative if
If \(-2x^3 + 6x^2 + 17x\) - 21 is divided by \((x + 1)\), then the remainder is
How many students scored at least 25%
Find the matrix A
A \(\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}\)
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 median.
A bag contains 8 red balls and some white balls. If the probability of drawing a white ball is half of the probability of drawing a red ball then find the probability of drawing a red ball and a white ball if the balls are drawn without replacement.
If A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find (A – B) ⋃ (B – A).
Factorize: \(16x^4 - y^4\)
In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
Find the value of y, if log (y + 8) + log (y - 8) = 2log 3 + 2log 5
Find the value of y if \(402_y = 102_{ten}\)
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 = \(\sqrt[3]{x^2}(2x - x^2)\)