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- The figure below shows a uniform cross-section of a swimming pool which is 4m wide. The depth of the pool increase gently from 1.5m to...(Solved)
The figure below shows a uniform cross-section of a swimming pool which is 4m wide. The depth of the pool increase gently from 1.5m to 3.0m.
a) How much water in litres does it hold when full?
b) Calculate total internal surface area of the pool.
c) Find the angle at which the bottom of the pool inclines to the horizontal.
Date posted: August 20, 2019. Answers (1)
- The diagram which is not drawn to scale, shows an isosceles triangle XYZ in which XY=YZ. The coordinates of x and y are (5,6) and...(Solved)
The diagram which is not drawn to scale, shows an isosceles triangle XYZ in which XY=YZ. The coordinates of x and y are (5,6) and (0, -4) respectively.
Given that the equation of line YZ is y=3/4x – 4 and that the perpendicular from X to YZ meet YZ at D,
find.
(i) The equation of XD
(ii) The coordinate of D
(iii) The coordinates of Z
(iv) The area of triangle XYZ
Date posted: August 20, 2019. Answers (1)
- Two airports are such that B is 500km due East of A. Two planes P and Q take off from A and B respectively and...(Solved)
Two airports are such that B is 500km due East of A. Two planes P and Q take off from A and B respectively and at the same time. Place P flies at 360km/h on a bearing of 030o. Plane Q flies at 240km/h on a bearing of 315o. The two planes land after 90 minutes. Using a scale of 1:10,000,000:
a) Show the positions of the planes after 90 minutes.
b) Find the distance between the planes after 90 minutes.
c) Find:
(i) The bearing of plane P from plane Q after 90 minutes.
(ii) The bearing of plane Q from plane P after 90 minutes
Date posted: August 20, 2019. Answers (1)
- Mr. Biwott operates two passenger service vehicles along Nakuru- Eldoret route. One is a 16 seater Matatu and the other is 8-seater van. Each vehicle...(Solved)
Mr. Biwott operates two passenger service vehicles along Nakuru- Eldoret route. One is a 16 seater Matatu and the other is 8-seater van. Each vehicle makes one route trip per day and the charges are ksh 250 and ksh 300 per passenger respectively (one way). The matatu uses diesel which costs ksh.48 per litre and the van uses regular petrol which costs ksh.52 per litre. The fuel consumption of the two vehicles is in the ratio of 4:3 respectively.
a) If the matatu uses 80 litres for the round trip, determine the fuel consumption of the van for the round trip.
b) Calculate the daily collection for each vehicle.
c) Determine which vehicle is more profitable (on daily basis) and by how much.
d) If the price of both types of fuel goes up by 20% determine the percentage change in daily collection.
Date posted: August 20, 2019. Answers (1)
- The L.C.M of 15, 18 and a third number is 1260. Find the square of third number.(Solved)
The L.C.M of 15, 18 and a third number is 1260. Find the square of third number.
Date posted: August 20, 2019. Answers (1)
- Solve the following simultaneous equations.
Log2(4y + x) = 3
Log3(4x + y) = 2(Solved)
Solve the following simultaneous equations.
Log2(4y + x) = 3
Log3(4x + y) = 2
Date posted: August 20, 2019. Answers (1)
- The mean age of 4 girls is 15 years. The first and second are aged 13 years and 18 years respectively.
The third girl is 3...(Solved)
The mean age of 4 girls is 15 years. The first and second are aged 13 years and 18 years respectively.
The third girl is 3 years older than the first girl. Find the modal age.
Date posted: August 20, 2019. Answers (1)
- Obenda weighed 120kg before he was taken ill of HIV/AIDs. After sometimes his weight decreased by 10% every week for 5 weeks. He was put...(Solved)
Obenda weighed 120kg before he was taken ill of HIV/AIDs. After sometimes his weight decreased by 10% every week for 5 weeks. He was put on ARVs and his weight increased by 5% every week for 3 weeks. What is his weight at the end of eighth week?
Date posted: August 20, 2019. Answers (1)
- Tap A takes one hour to fill a tank with water. If tap B takes y hours to remove the same water and both taps...(Solved)
Tap A takes one hour to fill a tank with water. If tap B takes y hours to remove the same water and both taps takes 1 ½ hours to fill the tank, find the value of y.
Date posted: August 20, 2019. Answers (1)
- The position vector of points A and B relative to the origin O are a and b respectively. Given that a = 4i + 3j...(Solved)
The position vector of points A and B relative to the origin O are a and b respectively. Given that a = 4i + 3j and b = i + 2j, find the modulus of the vector a + b
Date posted: August 20, 2019. Answers (1)
- Use reciprocal and cube root tables to evaluate.(Solved)
Use reciprocal and cube root tables to evaluate.
Date posted: August 20, 2019. Answers (1)
- Two points P and Q are found on the earth’s surface. The position of P is (520S, 660W) and Q (520S, 1140E). Using earth’s radius...(Solved)
Two points P and Q are found on the earth’s surface. The position of P is (520S, 660W) and Q (520S, 1140E). Using earth’s radius = 6370km:
(a) Find the difference in longitude between two points P and Q.
(b) Calculate the shortest distance between points P and Q along:-
(i) The Latitude in km (to 1 whole number).
(ii) The Longitude in km (to one whole number).
(c) A plane travelling at 800km/hr leaves point P at 10.00am and sails through South Pole to point Q. Find the local time the plane arrives at point Q to the nearest minutes.
Date posted: August 20, 2019. Answers (1)
- (a) Sketch the graph of the function: y = 4x3 + 2x2 – 5(Solved)
(a) Sketch the graph of the function: y = 4x3 + 2x2 – 5
(b) Find the area under the graph of the function: y = 4x3 + 2x2 – 5 between lines y = 0, x = 1 and x = 3 by:
(i) Using the trapezium method taking intervals of 0.5 of a unit.
(ii) Integration.
(c) Express the error in (b) (i) above as a percentage of the area obtained in (b) (ii) above.
Date posted: August 20, 2019. Answers (1)
- Express the following as fraction.(Solved)
Express the following as fraction.
Date posted: August 20, 2019. Answers (1)
- Evaluate the following expression.(Solved)
Evaluate the following expression.
Date posted: August 20, 2019. Answers (1)
- The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots.(Solved)
The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots. The lengths BE and CD are 100m and 80m respectively. Angle ABE = 300, ACE = 450 and ACD = 1000
(a) Find to four significant figures:
(i) The length of AE.
(ii) The length of AD.
(iii) The perimeter of the piece of land.
(b) The plots are to be fenced with five strands of barbed wire leaving an entrance of 2.8m wide to each plot. The type of barbed wire to be used is sold in rolls of lengths 480m. Calculate the number of rolls of barbed wire that must be bought to complete the fencing of the plots.
Date posted: August 20, 2019. Answers (1)
- A sum of money is divided between three people, Tom, Mary and Lucy in the ratio 5:3:1. If Mary has sh.700 more than Lucy, calculate...(Solved)
A sum of money is divided between three people, Tom, Mary and Lucy in the ratio 5:3:1. If Mary has sh.700 more than Lucy, calculate how much Tom has.
Date posted: August 20, 2019. Answers (1)
- Using logarithms tables evaluate.(Solved)
Using logarithms tables evaluate.
Date posted: August 20, 2019. Answers (1)
- (a) Find the inverse of the matrix:(Solved)
(a) Find the inverse of the matrix:
(b) Rose bought 20 bags of oranges and 15 bags of mangoes for a total of sh. 9,500. Chumo bought 30 bags of oranges and 20 bags of mangoes for a total of sh. 13,500. If the price of a bag of oranges is X and that of mangoes is y:
(i) Form two equations to represent the information above.
(ii) Hence use the matrix A-1 above to find the price of one bag of each item.
(c) The price of each bag of oranges was increased by 10% and that of mangoes reduced by 10%. The businesswomen (Rose and Chumo) bought as many oranges and as many mangoes as they bought earlier. Find by matrix method the total cost of oranges and mangoes that the businesswomen bought after the percentage change.
Date posted: August 20, 2019. Answers (1)
- A watch which looses a half-minute every hour was set to read the correct time at 0545h on Monday. Determine the time, in the 12...(Solved)
A watch which looses a half-minute every hour was set to read the correct time at 0545h on Monday. Determine the time, in the 12 hour system, the watch will show on the following Friday at 1945h.
Date posted: August 20, 2019. Answers (1)