- A straight road is northwards along the top of a vertical cliff of height 40m. A man at the top of the cliff spots a stationary...(Solved)
A straight road is northwards along the top of a vertical cliff of height 40m. A man at the top of the cliff spots a stationary boat on a bearing of 900 from the foot of the cliff and at an angle of depression of 300. He walks northwards and after one minute views the stationary boat on a bearing of 1100 from the foot of the cliff as he moves at a constant speed.
(a) Make a sketch to represent the position of the man and the boat.
(b) Calculate the distance of the boat from the foot of the cliff.
(c) Find the shortest distance from the position of the man to the stationary boat after 1 minute
(d) Calculate the speed of the man in meters per second.
Date posted: August 9, 2019. Answers (1)
- The ends of the roof of a workshop are segment of a circle of radius 10m. The roof is 20m long . The angle of...(Solved)
The ends of the roof of a workshop are segment of a circle of radius 10m. The roof is 20m long . The angle of the centre is 1200 as shown in the figure below
(a) Calculate:
(i) The area of one end of the roof.
(ii) The area of the curve surface of the roof.
(b) What would be cost to the nearest shilling of covering the two ends and the curved surface with galvanized iron sheet costing sh.80 per square meter.
Date posted: August 9, 2019. Answers (1)
- Draw the net of the solid below given that is a right pyramid and that AB = 4cm = BC = CD = AD and...(Solved)
Draw the net of the solid below given that is a right pyramid and that AB = 4cm = BC = CD = AD and BE= 6cm
Date posted: August 9, 2019. Answers (1)
- Solve for x in the equation
2 log x + log 5 = 1 + 3 log 2.(Solved)
Solve for x in the equation
2 log x + log 5 = 1 + 3 log 2.
Date posted: August 9, 2019. Answers (1)
- A sales woman earns a monthly wage of ksh. 3000 and gets a commission for the goods she sells. In a certain month she sells...(Solved)
A sales woman earns a monthly wage of ksh. 3000 and gets a commission for the goods she sells. In a certain month she sells goods worth ksh. 16,000 and her earning was ksh. 16,000 and her total earning was ksh.4,280.Determine the rate of the commission.
Date posted: August 9, 2019. Answers (1)
- Three towns A, B, and C are situated such that B is 50 km on a bearing of 1500 from town B
(a) Draw a sketch...(Solved)
Three towns A, B, and C are situated such that B is 50 km on a bearing of 1500 from town B
(a) Draw a sketch showing the positions of towns A, B and C.
(b) Calculate;
(i) The size of Angle ABC
(ii)The distance of C and A
Date posted: August 9, 2019. Answers (1)
- The angle of elevation of the top of a tree from a point P is 22.60. From another point Q which is 12m from the...(Solved)
The angle of elevation of the top of a tree from a point P is 22.60. From another point Q which is 12m from the base of the tree, the angle of elevation of the top of the tree is 47.50
(a) The height of the tree
(b) The distance between P and Q
Date posted: August 9, 2019. Answers (1)
- The length of a rectangle is increased by 25% while its width is decreased by 5%. Determine the percentage increase in the area of the...(Solved)
The length of a rectangle is increased by 25% while its width is decreased by 5%. Determine the percentage increase in the area of the rectangle.
Date posted: August 9, 2019. Answers (1)
- A straight line passing through the points P(4,5) also passes through the origin and makes an acute angle theta with the x – axis. Calculate...(Solved)
A straight line passing through the points P(4,5) also passes through the origin and makes an acute angle theta with the x – axis. Calculate to 2 decimal places the sizes of angle theta.
Date posted: August 9, 2019. Answers (1)
- The figure below shows a circle centre O and AOB is a sector of the circle and angle AOB = 720 as shown. Given that the...(Solved)
The figure below shows a circle centre O and AOB is a sector of the circle and angle AOB = 720 as shown. Given that the area of a sector AOB is 5pi cm2, find the radius of the circle and hence calculate the area of the shaded part.
Date posted: August 9, 2019. Answers (1)
- Simplify the expression below(Solved)
Simplify the expression below
Date posted: August 9, 2019. Answers (1)
- Evaluate without using mathematical table or calculator.(Solved)
Evaluate without using mathematical table or calculator.
Date posted: August 9, 2019. Answers (1)
- Given the coordinates of P, Q and R as (2, -1), (3, 4) and (6, 2) respectively,(Solved)
Given the coordinates of P, Q and R as (2, -1), (3, 4) and (6, 2) respectively, find the coordinates
of P1, Q1 and R1 the images of P, Q and R under a transformation represented by the matrix
Date posted: August 9, 2019. Answers (1)
- Point T is the midpoint of a straight line AB. Given that the position vectors of A and T are(Solved)
Point T is the midpoint of a straight line AB. Given that the position vectors of A and T are
Date posted: August 9, 2019. Answers (1)
- In the diagram below find the length of EC if BC = 12 cm.(Solved)
a) In the diagram below find the length of EC if BC = 12 cm.
(b) Given that the area of triangle DCE is 27 cm2, find the area of ABECD.
Date posted: August 9, 2019. Answers (1)
- If each interior angle of a regular polygon is 1500, how many sides does the polygon have?(Solved)
If each interior angle of a regular polygon is 1500, how many sides does the polygon have?
Date posted: August 9, 2019. Answers (1)
- In 2007 parliamentary election, only 55% of the voters in a constituency of 85,000 cast their votes.(Solved)
In 2007 parliamentary election, only 55% of the voters in a constituency of 85,000 cast their votes. Of the votes cast, A received 48%, B received 32% and C received the remainder. How many votes did C receive?
Date posted: August 9, 2019. Answers (1)
- A swimming pool is 20m by 12m and it slopes gently from a depth of 1m at the shallow end to a depth of 3m...(Solved)
A swimming pool is 20m by 12m and it slopes gently from a depth of 1m at the shallow end to a depth of 3m at the deep end.
(a) Calculate the volume of water in the swimming pool (in m3) when it is full.
(b) If the swimming pool is to be drained by a pump which removes water at the rate of 2.5m3 per minute, how long will it take this pump to drain the swimming pool if it was full?
(c) If the sides of the swimming pool and its floor are to be covered with square tiles of side 20cm, find to the nearest 100 the number of tiles required.
Date posted: August 9, 2019. Answers (1)
- Solve the simultaneous equations(Solved)
Solve the simultaneous equations
Date posted: August 9, 2019. Answers (1)
- Solve for n in(Solved)
Solve for n in
Date posted: August 9, 2019. Answers (1)