a. A boy stands at the point M on the same horizontal level as the foot, T of a vertical building. He observes an object on the top, P of the building at an angle of elevation of 66°. He moves directly backward to a new point C and observes the same object at an angle of 53°. if | MT | = 50 m:
Illustrate the information in a diagram;
bi. Calculate and correct to one decimal place: the height of the building;
bii. Calculate and correct to one decimal place: LINE MC.
a. M = {n: 2n - 3 ≤ 37} Where n is a counting number. i). write down all the elements in M.
ii. If a number is selected at random from M what is the probability that it is a:
(α) multiple of 3;
(β) factor of 10.
b. A shop owner gave an end-of-year bonus to two of his attendees, Kontor and Gapson in the ratio of their ages. Gapson's age is one and a half times that of Kontor who is 20 years old. if Kontor received Le 200,000.00, find: i). Find the total amount shared.
ii. Find Gapson's share.
a. The sum of three numbers is 81. The second number is twice the first. given that the third number is 6 more than the second, find the numbers.
b. Give me the points P(3, 5) and Q(-5, 7) on the Cartesian plane such that R (x, y) is the midpoint of PQ, find the equation of the line that passes through R and perpendicular to line PQ.
a. Copy and complete the tables of values of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 17 | -4 |
b. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 unit on the y-axis, draw the graph of y = \(2x^2 - x - 4\) for -3 ≤ x ≤ 3.
ci. Use the graph to find: the roots of the equation \(2x^2 - x - 4\)
ii. Use the graph to find the: values of x for which y increases as x increases;
iii. Use the graph to find the: minimum point of y.
a. The table shows the height of teak trees harvested by a farmer: Find the median height.
| Height(m) | 3 | 4 | 5 | 6 | 7 | 8 |
| number of trees | 4 | 6 | 4 | 5 | 6 | 2 |
b. calculate and correct to one decimal place the: i. mean; ii. standard deviation.
