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Given that sin (x + 30) = Cos 3x, find the value of tan (x-45) correct to 4 significant figures.
(Solved)
Given that sin (x + 30) = Cos 3x, find the value of tan (x-45) correct to 4 significant figures.
Date posted:
August 23, 2019
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Answers (1)
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Water is drawn to fill an empty tank whose capacity is 1200litres using two types of buckets. It requires at least 30 type A buckets...
(Solved)
Water is drawn to fill an empty tank whose capacity is 1200litres using two types of buckets. It requires at least 30 type A buckets and 50 type B buckets to fill the tank. Also, two type A buckets are required to fill at most three type B buckets. Each type B bucket has a capacity of not more than 20litres.
a) Taking x litres and y litres to represent the capacity of each type A bucket and each type B bucket respectively; write down 3 inequalities to represent the above information.
b) Use graphical method to determine the capacity of each type of bucket.
Date posted:
August 23, 2019
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Answers (1)
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The figure below represent a kite ABCD, AB = AD = 15cm. The diagonals BD and AC intersect atO. AC = 30cm and AD =...
(Solved)
The figure below represent a kite ABCD, AB = AD = 15cm. The diagonals BD and AC intersect at O. AC = 30cm and AD = 12cm.
Find the area of the kite
Date posted:
August 23, 2019
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Answers (1)
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The velocity V metres per second of a particle at time, t seconds is given by the equation below;
V = 2t2 – 4t + 15
b)...
(Solved)
The velocity V metres per second of a particle at time, t seconds is given by the equation below;
V = 2t2 – 4t + 15
a) Complete the table below for values of V and t
b) On the grid provided, draw the graph of V against t.
c) i) Using the mid-ordinate rule with seven ordinates estimate the distance covered by the particle between t = 1 sec and t = 8sec.
ii) Determine the exact distance covered by the particle between t = 1 sec and t = 8 sec
iii) Find the percentage error in the distance covered by the particle when the mid-ordinate rule is used.
Date posted:
August 23, 2019
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Answers (1)
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The figure below is a solid in which the base ABCD is a rhombus. AC = 16cm, BD = 12cm and CE = 12cm.
Calculate:-
a) the...
(Solved)
The figure below is a solid in which the base ABCD is a rhombus. AC = 16cm, BD = 12cm and CE = 12cm.
Calculate:-
a) the length of line BC
b) the angle between the planes EBD and ABCD
c) the angle between the planes ECB and ECD
d) the length of line AE
Date posted:
August 23, 2019
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Answers (1)
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The table below shows the distribution of wages in a week for a number of employees in a certain factory.
a) Using Kshs. 1049.50 per week...
(Solved)
The table below shows the distribution of wages in a week for a number of employees in a certain factory.
a) Using Kshs. 1049.50 per week as the assumed mean wage, calculate:-
i) the mean for the group wages.
ii) the standard deviation.
b) The week that followed, every employee earned Ksh. 100 as wage increment.Determine:
i) the new mean for the group wage.
ii) the new standard deviation
Date posted:
August 23, 2019
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Answers (1)
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In the figure below AB is parallel to DI and FD is parallel to CB. Angle EAJ = 30º and angle EDC = 63º. Find angle...
(Solved)
In the figure below AB is parallel to DI and FD is parallel to CB. Angle EAJ = 30º and angle EDC = 63º. Find angle ACB.
Date posted:
August 23, 2019
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Answers (1)
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The positions of two towns on the earth’s surface are A (400S, 450W) and B (400S, 1350E)
a) Calculate;
The difference in distance between two towns A...
(Solved)
The positions of two towns on the earth’s surface are A (400S, 450W) and B (400S, 1350E)
a) Calculate;
The difference in distance between two towns A and B along the parallel of latitude and along the great circle. (in Nm).
b) Two planes X and Y left town A at 8.00am flying at 758 knots each towards town B. If plane X flys along the parallel of latitude and plane Y along the great circle; then determine the position of one of the planes when the other lands at town B.
Date posted:
August 23, 2019
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Answers (1)
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The probability that Hilda, Lucy and Caroline will be late for breakfast on any one morning are a quarter , a third and a...
(Solved)
The probability that Hilda, Lucy and Caroline will be late for breakfast on any one morning are a quarter , a third and a fifth respectively on any one morning.
a) Using a probability tree diagram find the probability that:-
i) none of them will be late
ii) Only one of them will be late
iii) at least one of them will be late
iv) at most one of them will be late
Date posted:
August 23, 2019
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Answers (1)
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A plug is made up of hemisphere cup of radius 4.9cm and a cylinder of diameter 42cm and height 6cm as shown in the diagram...
(Solved)
A plug is made up of hemisphere cup of radius 4.9cm and a cylinder of diameter 42cm and height 6cm as shown in the diagram alongside. Calculate the volume of the plug.
Date posted:
August 23, 2019
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Answers (1)
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A line segment joining two points P(0,7) and S (2, 3.8) is divided externally by point Q in the ratio 7:3. Find the co-ordinates of...
(Solved)
A line segment joining two points P(0,7) and S (2, 3.8) is divided externally by point Q in the ratio 7:3. Find the co-ordinates of point Q.
Date posted:
August 23, 2019
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Answers (1)
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A two digit number is such that the square of the unit digit is equal to one less than the tens digit and that the...
(Solved)
A two digit number is such that the square of the unit digit is equal to one less than the tens digit and that the unit digit raised to power four and add three times the tens digit is equal to seven.Find the number.
Date posted:
August 23, 2019
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Answers (1)
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A ball is dropped from the top of a building and its height h, metres above the ground at any time t, seconds is given...
(Solved)
A ball is dropped from the top of a building and its height h, metres above the ground at any time t, seconds is given by h = 350 + 65t – t2.
i) Find the velocity of the ball when t = 2 secs.
ii) State the time when the ball hits the ground.
Date posted:
August 23, 2019
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Answers (1)
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Mrs. Nandi bought a television set on hire purchase by paying a down payment of Ksh. 5000 and Monthly installments of Ksh. 1250 for 2...
(Solved)
Mrs. Nandi bought a television set on hire purchase by paying a down payment of Ksh. 5000 and Monthly installments of Ksh. 1250 for 2 years. If the interest rate charged was 12% p.a what is the carrying change to the nearest hundreds?
Date posted:
August 23, 2019
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Answers (1)
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Draw a line PQ = 7.2cm and on one side of the line, use a ruler and pair of compasses only to draw the locus...
(Solved)
Draw a line PQ = 7.2cm and on one side of the line, use a ruler and pair of compasses only to draw the locus of a point A such that 0 and on it mark point A such that PA = QA.
Date posted:
August 23, 2019
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Answers (1)
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The table below shows heights of 50 students
(Solved)
The table below shows heights of 50 students
a) Sate the modal class.
b) Calculate the median.
Date posted:
August 23, 2019
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Answers (1)
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For a lifting machine, the effort E required to lift a load L is partly constant and partly varies as L. Given that L =...
(Solved)
For a lifting machine, the effort E required to lift a load L is partly constant and partly varies as L. Given that L = 2 when E = 5.5 and L = 6 when E = 6.5, Write an equation connecting E and L.
Date posted:
August 23, 2019
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Answers (1)
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Given the calculation 8.70 x 2.4, Ronoh obtains an approximate value by rounding off the given values to the nearest whole number. Determine the percentage...
(Solved)
Given the calculation 8.70 x 2.4, Ronoh obtains an approximate value by rounding off the given values to the nearest whole number. Determine the percentage error in the calculation arising from the approximation.
Date posted:
August 23, 2019
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Answers (1)
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In the figure below, O is the centre of the circle and TA and TB are tangents to the circle at A and B respectively....
(Solved)
In the figure below, O is the centre of the circle and TA and TB are tangents to the circle at A and B respectively. Given that angle ATO = 390; calculate angle TBX.
Date posted:
August 23, 2019
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Answers (1)
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Evaluate leaving your answer in surd form.
(Solved)
Evaluate leaving your answer in surd form.
Date posted:
August 23, 2019
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Answers (1)