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- The figure below is a square based pyramid, ABCDV, such that AB= 7 cm,and VA=VB= VC = VD= 9cm.
(a) Find the height of the vertex...(Solved)
The figure below is a square based pyramid, ABCDV, such that AB= 7 cm,and VA=VB= VC = VD= 9cm.
(a) Find the height of the vertex V above the centre of the base.
(b) Find the angle between BV and the base ABCD.
(c) Calculate the angle between the planes BVC and BVA.
Date posted: August 26, 2019. Answers (1)
- Solve the following inequalities and represent the solutions on a single number line.(Solved)
Solve the following inequalities 
and represent the solutions on a single number line.
Date posted: August 26, 2019. Answers (1)
- An aeroplane leaves town A (83°N, 155°W) to town B (40°N, 25°E) using the shortest route at a speed of 450 knots. (Take p =...(Solved)
An aeroplane leaves town A (83°N, 155°W) to town B (40°N, 25°E) using the shortest route at a speed of 450 knots. (Take π = 3.142 and radius of the earth R = 6370km).
(a) (i) Calculate the distance between A and B in nautical miles.
(ii) Calculate the time taken to travel from town A to B
(b) From B, the plane flies westwards along the latitude to town C (40°N, 13°W). Calculate the distance BC in kilometers.
(c) From town C, the plane took off at 3:10 pm towards town D (10°N, 13°W), at the same speed. At what time did the plane land at D?
Date posted: August 26, 2019. Answers (1)
- Bag X contains 2 green marbles and 8 yellow marbles. Bag Y contains 4 green marbles and 5 yellow marbles. A bag is selected at...(Solved)
Bag X contains 2 green marbles and 8 yellow marbles. Bag Y contains 4 green marbles and 5 yellow marbles. A bag is selected at random and two marbles drawn one at a time without replacement.
(a) Represent this information on a tree diagram.
(b) Find the probability that:
(i) They are both green.
(ii) They are both yellow and form bag X.
(iii) The second ball is yellow.
Date posted: August 26, 2019. Answers (1)
- A straight line L1 whose equation is y = 3 - 4x meets the y axis at K.
a) Find the coordinates of K.
b)Hence find the...(Solved)
A straight line L1 whose equation is y = 3 - 4x meets the y axis at K.
a) Find the coordinates of K.
b)Hence find the equation of a straight line L2 perpendicular to L1 and passes through K in the form ax + by + c = 0.
Date posted: August 26, 2019. Answers (1)
- A body is moving along a straight line and its acceleration after t seconds is (5 – 2t)ms-2.Its initial velocity Vms-1 is 4ms-1. Find V...(Solved)
A body is moving along a straight line and its acceleration after t seconds is (5 – 2t)ms-2.Its initial velocity Vms-1 is 4ms-1. Find V in terms of t.
Date posted: August 26, 2019. Answers (1)
- Determine the period and amplitude of the function y = 4 sin (2x - 20°)(Solved)
Determine the period and amplitude of the function y = 4 sin (2x - 20°)
Date posted: August 26, 2019. Answers (1)
- Simplify without using tables or calculator.(Solved)
Simplify without using tables or calculator.
Date posted: August 26, 2019. Answers (1)
- In an arithmetic progression, the 20th term is 92 and the sum of the first 20 terms is 890. Calculate;
(a) the first term
(b) the...(Solved)
In an arithmetic progression, the 20th term is 92 and the sum of the first 20 terms is 890. Calculate;
(a) the first term
(b) the common difference
Date posted: August 26, 2019. Answers (1)
- In the figure below PA is 12mm shorter than PD. It is also given that AB = 156mm, CD = 96mm and PA = x...(Solved)
In the figure below PA is 12mm shorter than PD. It is also given that AB = 156mm, CD = 96mm and PA = x mm.
Calculate the value of x.
Date posted: August 26, 2019. Answers (1)
- A two digit number is such that its value equals four times the sum of its digits. If 27 is added to the number the...(Solved)
A two digit number is such that its value equals four times the sum of its digits. If 27 is added to the number the result is equal to the value of the number obtained when the digits are interchanged. What is the number?
Date posted: August 26, 2019. Answers (1)
- Form the three inequalities that satisfy the given region R. Given lines A, B and C.(Solved)
Form the three inequalities that satisfy the given region R. Given lines A, B and C.
Date posted: August 26, 2019. Answers (1)
- Points P, Q and R are on the same horizontal ground such that point P is due south of R and point Q is due...(Solved)
Points P, Q and R are on the same horizontal ground such that point P is due south of R and point Q is due west of point R. S is a point at the top of a tower, 20m vertically above R. The angles of elevation of S from P and Q are 27° and 35° respectfully. Calculate to the nearest degree, the bearing of Q from P.
Date posted: August 26, 2019. Answers (1)
- Without using a calculator or a mathematical table evaluate.(Solved)
Without using a calculator or a mathematical table evaluate.
Date posted: August 26, 2019. Answers (1)
- Solve for x and y in the simultaneous equation below.
xy + 6 = 0
x – 2y = 7(Solved)
Solve for x and y in the simultaneous equation below.
xy + 6 = 0
x – 2y = 7
Date posted: August 26, 2019. Answers (1)
- The line segment BC = 7.5 cm long is one side of triangle ABC.a) Use a ruler and compasses only to complete the construction of...(Solved)
The line segment BC = 7.5 cm long is one side of triangle ABC.
a) Use a ruler and compasses only to complete the construction of triangle ABC in which angle ABC = 45o, AC = 5.6 cm and angle BAC is obtuse.
b) Draw the locus of a point P such that P is equidistant from a point O and passes through the vertices of triangle ABC.
c) Locate point D on the locus of P equidistant from lines BC and BO. Q lies in the region enclosed by lines BD, BO extended and the locus of P. Shade the locus of Q.
Date posted: August 26, 2019. Answers (1)
- The thickness of a mathematics text book is 0.8cm. Eight such books are piled together on a table. Find the limit within which the height...(Solved)
The thickness of a mathematics text book is 0.8cm. Eight such books are piled together on a table. Find the limit within which the height of the pile lies.
Date posted: August 26, 2019. Answers (1)
- Water flows from a pipe at the rate of 250 litres per minute. If the pipe is used to drain a tank full of water measuring...(Solved)
Water flows from a pipe at the rate of 250 litres per minute. If the pipe is used to drain a tank full of water measuring 3.2m by 2.5m by 2m, how many minutes would it take to drain the tank completely?
Date posted: August 26, 2019. Answers (1)
- The data below represent the heights taken to the nearest centimeters of 40 lemon trees in a garden.(Solved)
The data below represent the heights taken to the nearest centimeters of 40 lemon trees in a garden.
a) Complete the table.
b) Using 165.5 as the assumed mean, calculate the mean height.
c) Calculate the standard deviation of the distribution.
Date posted: August 26, 2019. Answers (1)
- Without using tables, solve the equation.
log10(10x + 5) – log10(x - 4) = 2(Solved)
Without using tables, solve the equation.
log10(10x + 5) – log10(x - 4) = 2
Date posted: August 26, 2019. Answers (1)