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- 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)
- In what ratio will coffee grade A costing kshs. 90 per kg be mixed with grade B costing kshs.60 per kg so that a profit...(Solved)
In what ratio will coffee grade A costing kshs. 90 per kg be mixed with grade B costing kshs.60 per kg so that a profit of 25% is realized by selling the mixture at kshs.80 per kg.
Date posted: August 29, 2019. Answers (1)
- Use logarithm table to evaluate.(Solved)
Use logarithm table to evaluate.
Date posted: August 29, 2019. Answers (1)
- a) A carpet measuring (x + 4)m by (x + 1)m is laid down in a rectangular room measuring 2x m by x m leaving...(Solved)
a) A carpet measuring (x + 4)m by (x + 1)m is laid down in a rectangular room measuring 2x m by x m leaving out uncovered floor near the walls all round the room. If the carpet is 36m2, calculate the area of the uncarpeted floor.
b) If 20cm square tiles were used to carpet the uncarpeted section of the floor in (a) above, calculate the cost of carpeting the whole floor if the carpet costs sh300 per metre square and each tile costs sh100.
Date posted: August 29, 2019. Answers (1)
- The probability of a couple getting a baby girl is 0.55 and that of a baby boy is 0.45. The couple intend to have two...(Solved)
The probability of a couple getting a baby girl is 0.55 and that of a baby boy is 0.45. The couple intend to have two children. Find the probability that they will be of different sexes.
Date posted: August 29, 2019. Answers (1)
- Three business partners Denga, Nyamita and cobe agreed to share shs. 1800 gained after a sale of property. For every shs. 1 that Denga gets,...(Solved)
Three business partners Denga, Nyamita and cobe agreed to share shs. 1800 gained after a sale of property. For every shs. 1 that Denga gets, Nyamita gets 50cts and for every shs 2 that Nyamita’s gets cobe gets shs. 3. Find Nyamita’s share.
Date posted: August 29, 2019. Answers (1)
- Expand (1 + 2x)7 upto the term in x3. Use your expansion to estimate (1.02)7to 4dp.(Solved)
Expand (1 + 2x)7 upto the term in x3. Use your expansion to estimate (1.02)7to 4dp.
Date posted: August 29, 2019. Answers (1)
- A point P divides the line RT in the ratio -2:5. Find the coordinates of P given R(3,1) and T(6,-5)(Solved)
A point P divides the line RT in the ratio -2:5. Find the coordinates of P given R(3,1) and T(6,-5)
Date posted: August 29, 2019. Answers (1)