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- Mr. Karambu is a civil servant in a ministry. He earns a monthly salary of sh.N and allowance of sh.1271.all taxable. He is entitled to...(Solved)
Mr. Karambu is a civil servant in a ministry. He earns a monthly salary of sh.N and allowance of sh.1271.all taxable. He is entitled to a monthly relief of sh.1056. The table below shows the rates of taxation.
When his salary was increased by 50% the net tax increased by 66.25 % to sh.9036 per month.
(a) What was his net tax in K£ p.a before the salary increase
(b) Calculate his salary before the increase
(c) Calculate the percentage increase in his net pay after the salary increase
Date posted: August 29, 2019. Answers (1)
- Obtain the expansion of (1 + 3x)6 up to the term with x4, hence estimate (1.03)6 correct to 4 decimal places.(Solved)
Obtain the expansion of (1 + 3x)6 up to the term with x4, hence estimate (1.03)6 correct to 4 decimal places.
Date posted: August 29, 2019. Answers (1)
- Two straight lines x + 2y = -1 and 2x + 3y = 3 intersects at a point R. Find the equation of the circle,...(Solved)
Two straight lines x + 2y = -1 and 2x + 3y = 3 intersects at a point R. Find the equation of the circle, centre R, radius 5 units, giving your answer in the form x2 + y2 + g x + fy + c = 0
Date posted: August 29, 2019. Answers (1)
- A school’s environmental club consists of 7 boys and 5 girls. Three members are to be randomly chosen to be officials of the club. Use...(Solved)
A school’s environmental club consists of 7 boys and 5 girls. Three members are to be randomly chosen to be officials of the club. Use a tree diagram to find the probability that:
(a) All the officials are boys
(b) One official is a girl
Date posted: August 29, 2019. Answers (1)
- Express S in terms of a, q and P given that(Solved)
Express S in terms of a, q and P given that
Date posted: August 29, 2019. Answers (1)
- Use mathematical tables to evaluate(Solved)
Use mathematical tables to evaluate
Date posted: August 29, 2019. Answers (1)
- Mr. Olik a drapper in Muhoroni town is required to supply two types of shirts, type A and type B to Muhoroni Secondary School. The...(Solved)
Mr. Olik a drapper in Muhoroni town is required to supply two types of shirts, type A and type B to Muhoroni Secondary School. The total number of shirts must not be more than 400. He has to supply more of type A than type B shirts. However the number of type A shirts must not be more than 300 and the number of type B shirts must not be less than 80 let x be number of type A shirts and y be the number of type B shirts.
(a) Write down in terms of x and y all the linear inequalities representing the information above.
(b) On the grid provided, draw the inequalities and shade the unwanted regions.
(c) Mr. Olik made profit of kshs. 600 per shirt of type A and shs. 400 per shirt of type B.
(i) Use the graph to determine the number of shirts of each type that should be made to maximize the profit.
(ii) Calculate the maximum possible profit.
Date posted: August 29, 2019. Answers (1)
- The diagram below represents a Cuboid ABCDEFGH in which FG =4.5cm, GH =8cm HC=6cm(a) Calculate the length FC(b) (i) The size of the angle between...(Solved)
The diagram below represents a Cuboid ABCDEFGH in which FG =4.5cm, GH =8cm HC=6cm
(a) Calculate the length FC
(b) (i) The size of the angle between the lines FC and FH
(ii) Size of the angle between the line AB and FH.
(c) The size of the angle between the planes ABHE and the plane FGHE.
(d) The total surface area of the cuboid (closed)
Date posted: August 29, 2019. Answers (1)
- Water is flowing through a cylindrical pipe at the speed of 1.2m/s. If the pipe has an internal radius of 1.4cm, Calculate
(a) The volume of...(Solved)
Water is flowing through a cylindrical pipe at the speed of 1.2m/s. If the pipe has an internal radius of 1.4cm, Calculate
(a) The volume of water delivered by the pipe per second in cm3 (Take pi = 22/7)
(b) The depth to which the pipe fills a rectangular tank of base dimensions 1.5m x 2m in one hour to the nearest 0.1cm.
(c) The time taken, to the nearest second for the pipe to fill a 50 litre bath tub (initially empty) which has a hole at the base that drains the tub at the rate of 3 litres per minute.
Date posted: August 29, 2019. Answers (1)
- The figure below shows a direct –belt drive system consisting of two pulleys of radii 40cm and 25cm. The centres of the pulleys x and...(Solved)
The figure below shows a direct –belt drive system consisting of two pulleys of radii 40cm and 25cm. The centres of the pulleys x and y are 86cm apart. Calculate the total length of the belt to4 s.f.
Date posted: August 29, 2019. Answers (1)
- In the figure below RY is the diameter with O as the centre. If angle PRZ = 108o(Solved)
In the figure below RY is the diameter with O as the centre. If angle PRZ = 108o, angle RPZ = 24o, angle PQZ = 8o and PQ is a tangent to the circle. ZNQ is a straight line.
Calculate the following angles;
a) angle XRP
b) angle RPX
c) angle PXY
d) angle YZN
e) angle ZYN
Date posted: August 29, 2019. Answers (1)
- Draw a line AB 6cm. P is a variable point in the plane of the paper above AB such that angle APB =600 and...(Solved)
Draw a line AB 6cm. P is a variable point in the plane of the paper above AB such that angle APB =600 and the area of the triangle APB = 12.5cm2. By accurate construction locate the locus of P.
Date posted: August 29, 2019. Answers (1)
- The bearing of towns P and Q on a horizontal ground from a tower are 050o and 142o respectively.(Solved)
The bearing of towns P and Q on a horizontal ground from a tower are 050o and 142o respectively. The angle of elevation of the top of the tower from town P is 34o. Given that P is 200m from the top of the tower and Q is 120m from the base of the tower. Determine,
a) The height of the tower.
b) The angle of elevation of the top of the tower from Q.
c) The distance between the two towns P and Q.
Date posted: August 29, 2019. Answers (1)
- Two planes P and Q are at (360N 1250W) and (360N 550E) respectively. Calculate the distance in nautical mile between P and Q measured along...(Solved)
Two planes P and Q are at (360N 1250W) and (360N 550E) respectively. Calculate the distance in nautical mile between P and Q measured along the circle through the North Pole.
Date posted: August 29, 2019. Answers (1)
- Find the amplitude period and phase angle of the given curve without sketching the graph.(Solved)
Find the amplitude period and phase angle of the given curve without sketching the graph.
Date posted: August 29, 2019. Answers (1)
- Given that the area of an image is four times the area of the object under a transformation whose matrix is(Solved)
Given that the area of an image is four times the area of the object under a transformation whose matrix is
Find the value of x.
Date posted: August 29, 2019. Answers (1)
- A cylindrical water tank can be filled to a depth of 2.8m by a pipe A in 2 hours.(Solved)
A cylindrical water tank can be filled to a depth of 2.8m by a pipe A in 2 hours. Pipe B takes 8 hours to fill the tank to the same depth. Pipe C can empty this amount in 6 hours.
a) Starting with tank empty and pipe A running alone in one hour, find the depth of water it fills.
b) If pipe A is turned off and pipe C left open for one hour, what will be the new depth of water?
c) If the tank is initially empty and pipe A and B are both running while pipe C is left open, after how long will the depth of water reach 2m?
Date posted: August 29, 2019. Answers (1)
- Given that the position vector of A, B and C are 3i – 2j, -6i +4j and -9i – 3j respectively.(Solved)
Given that the position vector of A, B and C are 3i – 2j, -6i +4j and -9i – 3j respectively.
a) State the column vectors,
i) AB
ii) CB
b) Find the distance from A to C through B
c) Find the co-ordinates of the midpoint of AC
d) If point C1 is the image of C under translation vector 
, find the co-ordinates of C1.
Date posted: August 29, 2019. Answers (1)
- Solve the simultaneous equations
Log ( x - 1) + 2 log y = 2 log 3
Log x + log y = log 6(Solved)
Solve the simultaneous equations
Log ( x - 1) + 2 log y = 2 log 3
Log x + log y = log 6
Date posted: August 29, 2019. Answers (1)
- h varies directly as v and inversely as the square of r. Find the percentage change in h if v is increased by 20% and...(Solved)
h varies directly as v and inversely as the square of r. Find the percentage change in h if v is increased by 20% and at the same time r is increased by 50%.
Date posted: August 29, 2019. Answers (1)