a. In the diagram above, PQR is an equilateral triangle of side 18 cm. M is the midpoint of QR. An arc of a circle with center P touches QR at M and meets PQ at A and PR at B. Calculate, correct to two decimal places, the area of the shaded region. (take \(\pi = \frac{22}{7})\)

a. In the diagram above, P, Q, R, and S are points on the circle with centre K. KR is a bisector of angle ∠SRQ, ∠KSP = 41°, and ∠SKR = 80°. Find:
∠RQP;

b. Find ∠SPQ

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.