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- A line L1 passes through the points (-2, 3) and (-1, 6) and is perpendicular to L2 at (-1, 6).(Solved)
A line L1 passes through the points (-2, 3) and (-1, 6) and is perpendicular to L2 at (-1, 6).
a) Find the equation of L1.
b) Find the equation of L2 in the form ax + by - c = 0 where a, b and c are constants.
c) Given that another line L3 is parallel to L1 and passes through point (1,2) , find the x and y intercepts of L3 .
d) Find the point of intersection of L2 and L3.
Date posted: November 8, 2019. Answers (1)
- The diagram represents a solid frustum with base radius 21cm and top radius 14cm. The frustum is
22.5cm high and is made of a metal whose...(Solved)
The diagram represents a solid frustum with base radius 21cm and top radius 14cm. The frustum is
22.5cm high and is made of a metal whose density is 3 πβππ3. (Take π = 22/7)
a) Calculate
(i) The volume of the metal in the frustum.
(ii) The mass of the frustum in kg.
b) The frustum is melted down and recast into a solid cube. In the process 20% of the metal is lost.
Calculate to 2 decimal places the length of each side of the cube.
Date posted: November 8, 2019. Answers (1)
- A number m is such that if its reciprocal is added to three times itself the result is 4. Form an equation in m and...(Solved)
A number m is such that if its reciprocal is added to three times itself the result is 4. Form an equation in m and solve it.
Date posted: November 8, 2019. Answers (1)
- At the end of his stay in Kenya, a French tourist had 3 420 French francs which he decided to change
into Euros. Given the exchange...(Solved)
At the end of his stay in Kenya, a French tourist had 3 420 French francs which he decided to change
into Euros. Given the exchange rate was;
1 French franc = Ksh. 11.25
1 Euro = Ksh. 72.50
Calculate the number of Euros he received if the bank charged him 2% commission.
Date posted: November 8, 2019. Answers (1)
- Expand and simplify (1 - 4x)6 up to the expansion of the term in x3.(Solved)
Expand and simplify (1 - 4x)6 up to the expansion of the term in x3.
Date posted: November 8, 2019. Answers (1)
- Solve the equations below using matrix method.
x + y = 8
2y - 3x = 1(Solved)
Solve the equations below using matrix method.
π₯ + π¦ = 8
2π¦ β 3π₯ = 1
Date posted: November 8, 2019. Answers (1)
- Find the area of the shaded region in the figure below given that AD = 15 cm, BE = 3 cm, AB = 3 cm,
???????...(Solved)
Find the area of the shaded region in the figure below given that AD = 15 cm, BE = 3 cm, AB = 3 cm,
β π·π΄π΅ = β πΈπ΅πΆ = 90Β°.
Date posted: November 8, 2019. Answers (1)
- A man sets off by bus on a journey of 130 km. after the bus has traveled 119 km at an average speed of 42...(Solved)
A man sets off by bus on a journey of 130 km. after the bus has traveled 119 km at an average speed of 42 ππ/βπ, it breaks down and he is immediately given a lift by a passing cyclist who takes him to his destination at average speed of 66 km/h.
Calculate;
a) The time taken for the whole journey.
b) His average speed for the whole journey.
Date posted: November 8, 2019. Answers (1)
- The position vectors of A and B are respectively. Find the magnitude of the vector AB.(Solved)
The position vectors of A and B are 
respectively. Find the magnitude of the vector AB.
Date posted: November 8, 2019. Answers (1)
- (a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm,
angle ABC = 30Β° and angle ACB = 45Β°...(Solved)
(a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm,
angle ABC = 30Β° and angle ACB = 45Β° .
(b) At A drop a perpendicular to meet BC at D and measure AD.
Date posted: November 8, 2019. Answers (1)
- The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed...(Solved)
The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed of 50 km/h between A and B and 60 km/h between B and C, it takes 3 hours to travel from A to C. If it maintains 60 km/h between A and B and 50 km/h between B and C, the journey takes 8 minutes less.
What is the distance from A to C via B?
Date posted: November 8, 2019. Answers (1)
- A cylindrical tank of diameter 1.4 m and height 1.2 m is two β thirds full of water. The tank if filled using a cylindrical...(Solved)
A cylindrical tank of diameter 1.4 m and height 1.2 m is two β thirds full of water. The tank if filled using a cylindrical bucket of diameter 35 cm and diameter 20 cm. Find the number of buckets required to fill the tank.
Date posted: November 8, 2019. Answers (1)
- Solve for x in the equation 125-x Γ 52(x-2) = 25(x+2)(Solved)
Solve for x in the equation 125-x Γ 52(x-2) = 25(x+2)
Date posted: November 8, 2019. Answers (1)
- a) Complete the table given below by filling the blank spaces.
b) On the grid provided draw on the same axes, the graph of y=4 cos2x...(Solved)
a) Complete the table given below by filling the blank spaces.
b) On the grid provided draw on the same axes, the graph of y=4 cos2x and y=2 sin (2x +30o ) for OO β€ X β€180O . Take the scale 1cm for 15o on the x βaxis and 1cm for 1 unit on the y-axis.
c) From your graph
i) State the amplitude of y= 4cos 2x.
ii) Find the period of y=2sin(2x +30o )
d) Use your graph to solve 4cos 2x β 2sin (2x + 30o ) = 0
Date posted: November 8, 2019. Answers (1)
- a) The first term of a geometric progression is 36. The sum of the first three terms is 27.
Calculate the common ratio and the value...(Solved)
a) The first term of a geometric progression is 36. The sum of the first three terms is 27.
Calculate the common ratio and the value of the second term.
b) The first term of an AP is 2. The first term of a geometric sequence is also 2 and its common ratio
equals the common difference of the arithmetic sequence. The square of the fifth term of arithmetic
sequence exceeds the third term of the geometric sequence by 2. Find the common difference and the
sum of the first 50 terms of AP.
Date posted: November 8, 2019. Answers (1)
- The table below shows the income tax brackets for a certain year.
Mr.Bundi earns a monthly salary of ksh.45, 000. He gets a house allowance of...(Solved)
The table below shows the income tax brackets for a certain year.
Mr.Bundi earns a monthly salary of ksh.45, 000. He gets a house allowance of ksh.13, 000 and a
commuter allowance of ksh.6, 000. He is entitled to a family relief of ksh.1, 166 per month. Find
a) Mr.Bundiβs taxable income in ksh per month.
b) Total tax payable per month in ksh. by Mr.Bundi.
c) Mr.Bundiβs net salary per month if the following deductions are also made monthly.
NHIF βksh. 1500
Wcps 2% of basic salary.
Date posted: November 8, 2019. Answers (1)
- Two towns on latitude 30oS are 3000km apart. Find the longitude different of the two towns(Solved)
(a) Two towns on latitude 30oS are 3000km apart. Find the longitude different of the two towns
(Take 
and the radius of the earth to be 6370km)
(b) The positions of airport P and Q are (60oN,45oN) and Q(60oN,KoE). It takes a plane 5 hrs to travel due east from P to Q at an average speed of 600 knots
(i) Calculate the value of K
(ii) The local time at P is 10.45am, what is the local time at Q when the plane reaches where?
(c) Calculate the shortest distance between (30oS,36oE) and (30oS,144oW) in nautical miles
Date posted: November 8, 2019. Answers (1)
- The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared...(Solved)
The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared the balance in 24 equal monthly installments each of Sh.2,250
(a) Find the amount of interest paid under hire purchase plan
(b) Ken took a loan from a financial institution and bought the camera with cash. He repaid the loan in two years at 18% interest compound semi-annualy. Find the total interest paid by Ken
(c) The cash price is taken as the value of the Camera. If the camera depreciated at a rate of 15% in the first year after buying and at P% p.a for rest of the time, calculate the value of p if the value of the camera after 5 years was Sh.23,534
Date posted: November 8, 2019. Answers (1)
- (a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed...(Solved)
(a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed after adding the first three terms of the sequences are 14,34 and 78 respectively. Given that the first term of the A.P is a and the first term of the G.P is b, and that the common ratio of the G.P is 3; Find the first term of the AP and G.P and the common difference of the A.P
(b)The second and third terms of a geometric progression are 24 and 12(x+1) respectively. Given that the sum of the first three terms of the progression is 76, find the whole number value of x and hence the first term
Date posted: November 8, 2019. Answers (1)
- The points A1B1 and C1 are the images of A(4,1), B(0,-2) and C(-2,4)(Solved)
(a) The points A1B1 and C1 are the images of A(4,1), B(0,-2) and C(-2,4) respectively under transformation represented by the matrix M= 
write down the coordinates of A1B1C1
(b) A11B11C11 are the images of A1B1C1 under another transformation whose matrix is 
write down the coordinates of A11B11C11
(c) Transformation m followed by N can be represented by a single transformation P. Determine the
matrix for P
(d) Another transformation has the matrix T = 
Determine the matrix for transformation m followed by N and T in that order
Date posted: November 8, 2019. Answers (1)