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- 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)
- Find all the integral values of x which satisfy the inequality
3 (1 + x) < 5x – 11 < x + 45(Solved)
Find all the integral values of x which satisfy the inequality
3 (1 + x) < 5x – 11 < x + 45
Date posted: August 20, 2019. Answers (1)
- Coast bus left Nairobi at 8.00a.m. and traveled towards Mombasa at an average speed of 80km/hr.(Solved)
Coast bus left Nairobi at 8.00a.m. and traveled towards Mombasa at an average speed of 80km/hr. At 8.30am, Lamu bus left Mombasa towards Nairobi at an average speed of 120km/h. Given that the distance between Nairobi and Mombasa is 400km; determine:
(i) The time Lamu Bus arrived in Nairobi.
(ii) The time the two buses met.
(iii) The distance from Nairobi to the point where the buses met.
(iv) How far Coast Bus is from Mombasa when Lamu bus arrives in Nairobi.
Date posted: August 20, 2019. Answers (1)
- The diagram below, not drawn to scale, is a regular pentagon circumscribed in a circle of radius 10cm at centre O
Find
(a) The length of any...(Solved)
The diagram below, not drawn to scale, is a regular pentagon circumscribed in a circle of radius 10cm at centre O
Find
(a) The length of any side of the pentagon
(b) The area of the shaded region
Date posted: August 20, 2019. Answers (1)
- The table below shows how income tax was charged on income earned in a certain year.(Solved)
The table below shows how income tax was charged on income earned in a certain year.
Mr. Gideon is an employee of a certain company and earns a salary of Ksh. 15,200 per month. He is housed by the company and pays a nominal rent of Ksh. 1050 per month. He is married and is entitled to a family relief of Kshs. 450 per month.
(i) Calculate his taxable income in k£ p.a.
(ii) Calculate his gross tax per month.
(iii) Calculate his net tax per month.
(iv) Calculate his net salary per month.
Date posted: August 20, 2019. Answers (1)
- A group of 10 soldiers set off with enough food to last 7 days. After 4 soldiers deserted,(Solved)
A group of 10 soldiers set off with enough food to last 7 days. After 4 soldiers deserted, how many more days will the food last for the remaining soldiers?
Date posted: August 20, 2019. Answers (1)
- Below is a net of a model of a solid. The lengths AB = BC = AC = 6.0cm and lengths AF = FB =...(Solved)
Below is a net of a model of a solid. The lengths AB = BC = AC = 6.0cm and lengths AF = FB = BD = CD = CE = AE = 8.0cm.
a).Sketch the solid of the net by taking ABC as the base and the height 5cm.
b) State the name of the figure sketched:
Date posted: August 20, 2019. Answers (1)
- The masses of two similar bars of soap are 343g and 1331g. If the surface area of the smaller bar is 196cm2. Calculate the surface...(Solved)
The masses of two similar bars of soap are 343g and 1331g. If the surface area of the smaller bar is 196cm2. Calculate the surface area of the larger bar.
Date posted: August 20, 2019. Answers (1)
- Evaluate the expression below
(Solved)
Evaluate the expression below
Date posted: August 20, 2019. Answers (1)
- Mrs. Tabut bought 4 spoons and 6 plates for Kshs. 660 and Mrs. Koross bought 2 spoons and 1 plate less than Mrs. Tabut for...(Solved)
Mrs. Tabut bought 4 spoons and 6 plates for Kshs. 660 and Mrs. Koross bought 2 spoons and 1 plate less than Mrs. Tabut for Kshs. 510.
(i) Find the price of each item.
(ii) Mrs. Lagat spent Kshs. 2280 to buy the same type of spoons and plates. If the number of plates she bought were 4 more than the number of spoons, find the number of spoons bought by Mrs. Lagat.
Date posted: August 20, 2019. Answers (1)