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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. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- A certain volume of methlylated spirit has a mass of 2.2kg. Given that the density of methlylated spirit is 0.8g/cm³ calculate the volume of the...(Solved)
A certain volume of methlylated spirit has a mass of 2.2kg. Given that the density of methlylated spirit is 0.8g/cm³ calculate the volume of the methylated spirit in litres.
Date posted: November 6, 2019. Answers (1)
- A truck left Kisumu to Mombasa a distance of 1000 km at 11.30 am on Monday at a speed of 60km/hr. On the way it...(Solved)
A truck left Kisumu to Mombasa a distance of 1000 km at 11.30 am on Monday at a speed of 60km/hr. On the way it stopped for 2 1/3 hours. At what time did it reach Mombasa.
Date posted: November 6, 2019. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- Evaluate without using tables or a calculator.(Solved)
Evaluate without using tables or a calculator.
Date posted: November 6, 2019. Answers (1)
- 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. Answers (1)
- Find the value of x given that is a singular matrix.(Solved)
Find the value of x given that 
is a singular matrix.
Date posted: November 6, 2019. Answers (1)
- 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. Answers (1)
- If cos a = 15/17 , find without using tables or calculator
Tan (180- a)(Solved)
If cos α = 15/17 , find without using tables or calculator
Tan (180- α)
Date posted: November 6, 2019. Answers (1)
- 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. Answers (1)
- 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. Answers (1)
- Using logarithms tables: Evaluate.(Solved)
Using logarithms tables: Evaluate.
Date posted: November 6, 2019. Answers (1)
- A shopkeeper sells two types of chewing gum. Big G and Orbit. Each big G costs sh. 3 and each orbit costs sh. 4. The...(Solved)
A shopkeeper sells two types of chewing gum. Big G and Orbit. Each big G costs sh. 3 and each orbit costs sh. 4. The shopkeeper has put aside sh. 300 for the purchase of gums. He needs at least twice as many Big G as Orbit and there must be at least 50 Big G and at least 20 orbit. Let x represent the number of Big G and y the number of orbit the shopkeeper purchases.
(a) Write down all the inequalities representing the information
(b) Represents the inequalities in (a) graphically
(c) The shopkeeper makes a profit of sh. 1.00 on each big G and sh. 1.50 on each orbit.
(i) Find the number of gums of each type that would give him maximum profit
(ii) Hence find the maximum profit
Date posted: November 6, 2019. Answers (1)
- The table below shows income tax rates
Mr. Kiprono is employed and housed by a company. For which he pays a normal rent of Sh. 2000....(Solved)
The table below shows income tax rates
Mr. Kiprono is employed and housed by a company. For which he pays a normal rent of Sh. 2000. He earns a basic salary of Ksh. 32,000 pm. He is also given taxable allowances amounting to ksh. 8480.
(a) Calculate his taxable income in K£
(b) Determine his total income tax in Ksh.
(c) If he pays a monthly water bill of Ksh. 350, electricity bill of Ksh. 400 and is a member of a cooperative
and pays Ksh. 2500 pm. Determine his net monthly income.
Date posted: November 6, 2019. Answers (1)
- Mr. Karanja owns a bicycle which he sometimes rides to go to work. Out of the 21 working days in a
month, he only rides to...(Solved)
Mr. Karanja owns a bicycle which he sometimes rides to go to work. Out of the 21 working days in a
month, he only rides to work for 18 days. If he rides to work, the probability that he is bitten by a
rabid dog is 4/15 otherwise its only 1/13. When he is bitten by the dog, the probability that he will get
treatment is 4/5 and if he does not get treatment the probability that he will get rabies is 5/7.
(a) Draw a tree diagram to show the events
(b) Using the tree diagram in (a) above, determine the probability that
(i) Karanja will not be bitten by a rabid dog
(ii) He will get rabies
(iii) He will not get rabies if he does not get treatment
Date posted: November 6, 2019. Answers (1)
- 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. Answers (1)
- Solve for x in the equation.
6sin2 x - cos x – 5 = 0
for 00 = x = 360(Solved)
Solve for x in the equation.
6sin2 x - cos x – 5 = 0
for 00 ≤ x ≤ 360
Date posted: November 6, 2019. Answers (1)