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A number 0.7 is truncated to 3.sf. Calculate the percentage error due to the truncation.
(Solved)
A number 0.7 is truncated to 3.sf. Calculate the percentage error due to the truncation.
Date posted:
November 7, 2019
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Answers (1)
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Expand (1 + 1/2x)5 upto the term on x³, use the expansion to estimate the value of (1.05)5 correct to 4 significant figures.
(Solved)
Expand (1 + 1/2x)5 upto the term on x³, use the expansion to estimate the value of (1.05)5 correct to 4 significant figures.
Date posted:
November 7, 2019
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Answers (1)
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The equation of a circle is x² + 4x + y² - 5 = 0. Find the centre and the radius of the circle.
(Solved)
The equation of a circle is x² + 4x + y² - 5 = 0. Find the centre and the radius of the circle.
Date posted:
November 7, 2019
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Answers (1)
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In the figure below, P, Q, R and S are points on the circumference of the circle centre O. TP and TR are tangents to...
(Solved)
In the figure below, P, Q, R and S are points on the circumference of the circle centre O. TP and TR are tangents to the circle at P and R respectively. POQ is a diameter of the circle and angle PQR = 64°
Giving reasons in each case, find the size of
a) b) c) d) e)
Date posted:
November 6, 2019
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Answers (1)
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A pirate boat sails from port A on a bearing of 050° at a speed of 112km/h, for 2½ hours to port B. From port...
(Solved)
A pirate boat sails from port A on a bearing of 050° at a speed of 112km/h, for 2½ hours to port B. From port B it changes its course and travelled on a bearing of 170° at a speed of 75km/h for 2 2/3 hours toward part C. From C it travelled to port D. D is on a bearing of 130° and 160km from A.
a) Using a scale of 1cm to represent 40km, Draw a diagram showing the positions of the ports A, B, C and D.
b) Use your drawing to find.
i) The distance CD
ii) The bearing of C from D
c) A marine police patrol leaves port A to intercept the pirate boat at M as it moves from B to C in the shortest time possible.
i) How far from A will the two boats meet at M.
ii) If the boats meets after 2 hours, what is the speed of the marine police boat.
Date posted:
November 6, 2019
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Answers (1)
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A closed cylindrical metal tin has radius r and height h. The capacity of the tin is 250 p litres
a) Express in term of r.
i)...
(Solved)
A closed cylindrical metal tin has radius r and height h. The capacity of the tin is 250 π litres
a) Express in term of r.
i) the height h of the tin.
ii) the total surface area of the tin.
b) i) Find the value of r for which the surface are of the metal used is to be minimum
ii) The minimum area of the metal used to make the cylinder.
Date posted:
November 6, 2019
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Answers (1)
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A truck left town X at 8.45am and traveled toward Y at an average speed of 50km/hr. A car left town X at 11.15am on...
(Solved)
A truck left town X at 8.45am and traveled toward Y at an average speed of 50km/hr. A car left town X at 11.15am on the same day and traveled along the same road at an average speed of 90km/h. The distance between the two town is 420km.
a) Calculate the time of the day when the car overtook the truck.
b) The distance from Y when the car overtook the truck.
c) After overtaking the bus, both vehicles continued towards Y at their original speeds. Find how long the car had to wait at town Y before the truck arrived.
Date posted:
November 6, 2019
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Answers (1)
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The cross-section of a head of a bolt is the form of a regular hexagon as shown below.
Determine the area of the cross-section to 2dp.
(Solved)
The cross-section of a head of a bolt is the form of a regular hexagon as shown below.
Determine the area of the cross-section to 2dp.
Date posted:
November 6, 2019
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Answers (1)
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Two similar blocks have masses of 729g and 216g respectively. If the surface area of the smaller block is 300cm², calculate the surface area of...
(Solved)
Two similar blocks have masses of 729g and 216g respectively. If the surface area of the smaller block is 300cm², calculate the surface area of the larger block.
Date posted:
November 6, 2019
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Answers (1)
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Evaluate without using tables or a calculator.
(Solved)
Evaluate without using tables or a calculator.
Date posted:
November 6, 2019
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Answers (1)
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Find the value of k in the equation.
125k+1 + 53k = 630
(Solved)
Find the value of k in the equation.
125k+1 + 53k = 630
Date posted:
November 6, 2019
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Answers (1)
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The difference between two positive integers is 5 and the sum of their squares is 73. Find the integers.
(Solved)
The difference between two positive integers is 5 and the sum of their squares is 73. Find the integers.
Date posted:
November 6, 2019
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Answers (1)
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The cost of mass production of cars is partly constant and partly varies as the number of cars produced. The total cost of making 400...
(Solved)
The cost of mass production of cars is partly constant and partly varies as the number of cars produced. The total cost of making 400 cars is sh 3,740,000 and that of making 1000 cars is sh 7,100,000. Find the cost of making 2500 cars.
Date posted:
November 6, 2019
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Answers (1)
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Solve the inequality below. Hence represent the solution on a number line.
x < 2x + 7 = - 1/3x + 14
(Solved)
Solve the inequality below. Hence represent the solution on a number line.
x < 2x + 7 ≤ - 1/3x + 14
Date posted:
November 6, 2019
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Answers (1)
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Machine A can complete some work in 8 hours while machine B can complete the same work in 10 hours. The two machines were set...
(Solved)
Machine A can complete some work in 8 hours while machine B can complete the same work in 10 hours. The two machines were set to do the work at the same time. After 3 hours, machine B broke down. Determine the time taken by machine A to complete the remaining piece of work.
Date posted:
November 6, 2019
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Answers (1)
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PQ is a diameter of a circle is such that the co-ordinates of P and Q are (-6, -2) and (4, -2)
respectively. Find the equation...
(Solved)
PQ is a diameter of a circle is such that the co-ordinates of P and Q are (-6, -2) and (4, -2)
respectively. Find the equation of the circle in the form ax2 + by2 + cx + dy + e = 0 where a,b,c,d and
e are constants.
Date posted:
November 6, 2019
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Answers (1)
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Three variables P,Q and R are such that P varies directly as the cube of Q and inversely as the square root of R. If...
(Solved)
Three variables P,Q and R are such that P varies directly as the cube of Q and inversely as the square root of R. If Q is increased by 20% and R is decreased by 10%, Find the percentage change in P.
Date posted:
November 6, 2019
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Answers (1)
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Given that A = 5i + 4j + K and B = 8i – 5j – 5k and P divides AB externally in the ratio...
(Solved)
Given that A = 5i + 4j + K and B = 8i – 5j – 5k and P divides AB externally in the ratio 5:2. Find
the:-
(a) Position vector of P
(b) The magnitude of OP
Date posted:
November 5, 2019
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Answers (1)
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Town B is 180km on a bearing 0500 from town A. Another town C is on a bearing of 1100 from town A and on...
(Solved)
Town B is 180km on a bearing 0500 from town A. Another town C is on a bearing of 1100 from town A and on a bearing of 1500 from town B. A fourth town D is 240 km on a bearing of 3200 from A. Using scale drawing, such that 1cm rep 30km,
(a) Show the relative position of the towns
(b) Using the diagram, find
(i) Distance AC
(ii) Distance CD
(iii) Compass bearing of C from D
Date posted:
November 5, 2019
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Answers (1)
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Nairobi and Eldoret are 600km apart. At 9.20a.m. a lorry leaves Eldoret for Nairobi at a speed of 60km/hr. At 10.00a.m. a car leaves Eldoret...
(Solved)
Nairobi and Eldoret are 600km apart. At 9.20a.m. a lorry leaves Eldoret for Nairobi at a speed of 60km/hr. At 10.00a.m. a car leaves Eldoret for Nairobi at a speed of 120km/hr. After 20 minutes of travel, the car develops a mechanical problem which takes 20 minutes to repair. The car then proceeds with the journey at the same speed.
(a) Calculate the time the lorry arrived in Nairobi
(b) Find the time when the car overtakes the lorry
(c) Find the distance from Nairobi at the overtaking point
(d) Calculate how far the lorry was from Eldoret when the car reached Nairobi
Date posted:
November 5, 2019
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Answers (1)