Expand and simplify (1 - 4x)⁶ up to the expansion of the term in x³.

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Kavungya answered the question on November 8, 2019 at 12:33

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Solve the equations below using matrix method. x + y = 8 2y - 3x = 1(Solved)
Solve the equations below using matrix method.
𝑥 + 𝑦 = 8
2𝑦 − 3𝑥 = 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,
∠𝐷𝐴𝐵 = ∠𝐸𝐵𝐶 = 90°.

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 𝑘𝑚/ℎ𝑟, 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 = 30° and angle ACB = 45°...(Solved)
(a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm,
angle ABC = 30° and angle ACB = 45° .
(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 – 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 – 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 × 5^2(x-2) = 25^(x+2)(Solved)
Solve for x in the equation 125^-x × 5^2(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 +30^o ) for O^O ≤ X ≤180^O . Take the scale 1cm for 15^o on the x –axis 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 +30^o )
d) Use your graph to solve 4cos 2x – 2sin (2x + 30^o ) = 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.Bundi’s taxable income in ksh per month.
b) Total tax payable per month in ksh. by Mr.Bundi.
c) Mr.Bundi’s net salary per month if the following deductions are also made monthly.
NHIF –ksh. 1500
Wcps 2% of basic salary.

Date posted: November 8, 2019. Answers (1)
Two towns on latitude 30^oS are 3000km apart. Find the longitude different of the two towns(Solved)
(a) Two towns on latitude 30^oS 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 (60^oN,45^oN) and Q(60^oN,K^oE). 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 (30^oS,36^oE) and (30^oS,144^oW) 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)
The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR(Solved)
The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR

Find
(a)(i) the length PR
(ii) the height of the pyramid

(b)(i) the angle between VR and the base PQRS
(ii) the angle between PM and the base PQRS
(iii) the angle between the planes QVR and PQRS

Date posted: November 8, 2019. Answers (1)
Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.(Solved)
Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.

Date posted: November 8, 2019. Answers (1)
Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300^o from Y. Calculate...(Solved)
Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300^o from Y. Calculate the angle XZY given that XZ is 70km.

Date posted: November 8, 2019. Answers (1)
A transformation matrix maps an object of area 21cm² to an image of area 42cm². Determine the value of p.(Solved)
A transformation matrix maps an object of area 21cm² to an image of area 42cm². Determine the value of p.

Date posted: November 8, 2019. Answers (1)
The points P and Q are 7.4cm apart. By construction locate the locus R such that PR=2.5cm and angle PRQ=90^o.(Solved)
The points P and Q are 7.4cm apart. By construction locate the locus R such that PR=2.5cm and angle PRQ=90^o.

Date posted: November 8, 2019. Answers (1)