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- The positions of three towns on the earth’s surface are given as P (600N, 550W), Q (200S, 550W) S (600N, 1250E) respectively (Take R =...(Solved)
The positions of three towns on the earth’s surface are given as P (600N, 550W), Q (200S, 550W) S (600N, 1250E) respectively (Take R = 6370km and π = 22/7)
a) Calculate the distance:
i. PQ in nautical miles.
ii. PS along the parallel of latitude in km.
iii. The shortest distance between P and S.
b) A plane leaves town T (840S, 100E) and flies westwards for 6 ½ hrs at a speed of 268 knots and reaches town R (840S, X0). Find the longitude X, give your answer to the nearest degree.
Date posted: November 20, 2019. Answers (1)
- A transformation whose matrix is maps a quadrilateral ABCD onto another quadrilateral A’B’C’D’ whose area is 540????2. Find the area of the quadrilateral ABCD.(Solved)
A transformation whose matrix is 
maps a quadrilateral ABCD onto another quadrilateral A’B’C’D’ whose area is 540𝑐𝑚2. Find the area of the quadrilateral ABCD.
Date posted: November 20, 2019. Answers (1)
- Two machines M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5%...(Solved)
Two machines M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of items produced by machine M are defective while 3% of the items produced by machine N are defective. If an item is selected at random from the factory, find the probability that it is defective.
Date posted: November 20, 2019. Answers (1)
- Trains A and B are moving in opposite directions on parallel tracks. Train A is 56 metres long and is moving at a speed of...(Solved)
Trains A and B are moving in opposite directions on parallel tracks. Train A is 56 metres long and is moving at a speed of 63km/h. Train B is 90 metres long and is moving at a speed of 45km/h. The two trains are about to start passing each other. Calculate the time, to the nearest second, that they will take to completely pass each other.
Date posted: November 20, 2019. Answers (1)
- ABCD and MNPQ in the figure below are two shutters of a window. The shutters are identical and square in shape. Both shutters are opened...(Solved)
ABCD and MNPQ in the figure below are two shutters of a window. The shutters are identical and square in shape. Both shutters are opened through an angle of 58°.
If each edge of the shutter is 70cm long, find the shortest distance from C to M.
Date posted: November 20, 2019. Answers (1)
- In the figure below, ABC is a tangent to the circle BDEF at B. BC = 17cm, DC = 10cm and BG = 15cm. chord...(Solved)
In the figure below, ABC is a tangent to the circle BDEF at B. BC = 17cm, DC = 10cm and BG = 15cm. chord FD intersects chord BE at G and FG: GD = 1: 5
Find the length of;
a) GD
b) GE
Date posted: November 20, 2019. Answers (1)
- Using matrices solve the following pair of simultaneous equations
6y - 2x + 20 = 0
3x - 7y - 26 = 0(Solved)
Using matrices solve the following pair of simultaneous equations
6y − 2x + 20 = 0
3x − 7y − 26 = 0
Date posted: November 20, 2019. Answers (1)
- Two taps, A and B, when opened at the same time can fill a tank in 3 hours 36 minutes. Tap A working alone takes...(Solved)
Two taps, A and B, when opened at the same time can fill a tank in 3 hours 36 minutes. Tap A working alone takes 3 hours longer than Tap B to fill the tank. How many hours does it take Tap A alone to fill the tank?
Date posted: November 20, 2019. Answers (1)
- Point M is the midpoint of a straight line XY. If the position vectors of Y and M are 3i + 4j - 2k and...(Solved)
Point M is the midpoint of a straight line XY. If the position vectors of Y and M are 3i + 4j − 2k and 3j − 0.5k respectively. Find the position vector of X, hence the magnitude of XY.
Date posted: November 20, 2019. Answers (1)
- Without using mathematical tables or calculators, simplify(Solved)
Without using mathematical tables or calculators, simplify
Date posted: November 20, 2019. Answers (1)
- Expand (1 + p)5 in ascending powers of ??. Hence use the expansion to estimate 1.045 giving your answer correct to 4 decimal places.(Solved)
Expand (1 + p)5 in ascending powers of 𝑝. Hence use the expansion to estimate 1.045 giving your answer correct to 4 decimal places.
Date posted: November 20, 2019. Answers (1)
- Given that A = make ?? the subject of the formula.(Solved)
Given that A = 
make 𝑐 the subject of the formula.
Date posted: November 20, 2019. Answers (1)
- Each side of a regular heptagon measures 11.2cm. What is the percentage error in calculating the heptagon’s perimeter?(Solved)
Each side of a regular heptagon measures 11.2cm. What is the percentage error in calculating the heptagon’s perimeter?
Date posted: November 19, 2019. Answers (1)
- Using completing the square method, solve
10x2 - 11x - 6 = 0(Solved)
Using completing the square method, solve
10x2 − 11x − 6 = 0
Date posted: November 19, 2019. Answers (1)
- The figure shows a water tank which consists of a hemispherical part surmounted on top of a cylindrical part. The two parts have the same...(Solved)
The figure shows a water tank which consists of a hemispherical part surmounted on top of a cylindrical part. The two parts have the same diameter of 2.1 M and the cylindrical part is 1.5 m high as shown. All surfaces of the tank are made of iron sheets. (Take π = 22/7)
(a) Allowing for 15% wastage in overlapping, calculate to 2d.p the area of iron sheets required.
(b) Ironsheet costs sh.400 per square meter while labour and other. Materials amountsto 50% of the cost of ironsheets. Find the cost of constructing the tank.
(c) Calculate the (i) volume of the tank in m3
(ii) capacity of the tank in litres.
Date posted: November 19, 2019. Answers (1)
- Lines L1 is given by equation y = -2x +4 and L2 is 3x- y=1 intersect at T.
(a) Determine the co-ordinates of T.
(b) Another...(Solved)
Lines L1 is given by equation y = -2x +4 and L2 is 3x- y=1 intersect at T.
(a) Determine the co-ordinates of T.
(b) Another line, L3 is perpendicular to line L2 and passes through point N(5,8).Determine its equation and leave the answer in the form of ax + by=c where a, b, and c are integers.
(c) Determine the equation of a perpendicular bisector of a line segment passing through points T and N.
Date posted: November 19, 2019. Answers (1)
- Three towns PQR are such that Q is 20km in the bearing of 045° from P while R is 27.5 km in the bearing of...(Solved)
Three towns PQR are such that Q is 20km in the bearing of 045° from P while R is 27.5 km in the bearing of S20°E from Q.Using the scale of 1cm rep 5km.
(a) Determine the actual distance between P and R.
(b) State the true bearing of P from R.
(c) Show a point x which is equidistant from the three towns.
(d) Determine the actual distance from x to town R.
Date posted: November 19, 2019. Answers (1)
- On a certain map, an estate is represented by an area of 48cm2. If the actual area of the estate is 1200Ha, find the scale...(Solved)
On a certain map, an estate is represented by an area of 48cm2. If the actual area of the estate is 1200Ha, find the scale of the map in the form 1: n.
Date posted: November 19, 2019. Answers (1)
- The following data was obtained from a Form IV examination results.
Complete the table above(Solved)
The following data was obtained from a Form IV examination results.
Complete the table above
Date posted: November 19, 2019. Answers (1)
- A Kenyan family intended to spent a holiday in France where Ksh 90,000 was exchanged into Francs.
Currency conversation rate is as follows
KES ...(Solved)
A Kenyan family intended to spent a holiday in France where Ksh 90,000 was exchanged into Francs.
Currency conversation rate is as follows
KES Buying (Francs) Selling (Francs)
Ksh 100 53.50 55.75
The family spent 37, 0000 Franc and changed the rest into Kenya shillings. How much did the holiday cost?
Date posted: November 19, 2019. Answers (1)