Point of intersection is got by solving the two equations
Simultaneously
2x – 3y = -29
3(3x + y) = 17)
2x – 3y = -29
9x + 3y = 51
Add the two equations
11x = 22; x = 2
Substitute x = 2 in
2(2) – 3y = -29; 4 – 3y = -29
-3y = -33 y = 11
Centre of the circle is (2,11)
And radius = 5 units
Equation of the circle is
(x - 2) 2 + (y - 11) )2 = 5)2
x2 - 4x + 4 + y)2 - 22y + 121 = 25
x2 - 4x + 4 + y)2 - 22y + 125 = 25
x2 - 4x + 4 + y)2 - 22y + 100 = 0
johnmulu answered the question on March 8, 2017 at 09:36
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A ship leaves an island (5o, 45oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots
(Solved)
A ship leaves an island (5o, 45oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots
a) Calculate the distance between the two islands
i) in nautical miles
ii) in kilometres
b) Calculate the speed of the ship in kilometres per hour
c) Find the position of the second island. (Take 1 nm to be 1.853 km and the radius of the earth to be 6370 km)
Date posted:
March 8, 2017
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Answers (1)
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A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t2.
Find
(Solved)
A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t2.
Find
i) The height above the ground after 2 seconds
ii) The velocity after 1 second
iii) The instant at which the stone is 30 m high
Date posted:
March 8, 2017
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Answers (1)
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A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere
(Solved)
A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere
Date posted:
March 8, 2017
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Answers (1)
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Solve the simultaneous equations
x2 + y2 = 26
x + y = 4
(Solved)
Solve the simultaneous equations
x2 + y2 = 26
x + y = 4
Date posted:
March 8, 2017
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Answers (1)
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A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio
(Solved)
A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio
Date posted:
March 8, 2017
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Answers (1)
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The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter
(Solved)
The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter correct to 2 decimal places
Date posted:
March 7, 2017
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Answers (1)
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The equation of a curve is
y = 3x2 -4x + 1, Find the gradient function of the curve and its value when x = 2
(Solved)
The equation of a curve is
y = 3x2 -4x + 1
a) Find the gradient function of the curve and its value when x = 2
b) Determine the equation of the tangent to the curve at(2,5)
Date posted:
March 7, 2017
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Answers (1)
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a) The nth term of a sequence is given as 3(m + 1) - 2m.
(Solved)
a) The nth term of a sequence is given as 3(m + 1) - 2m. Find the 5th term of the sequence
b) Atieno was employed by NGO on contract for a certain number of years. Her basic annual salary for the first year was sh 580 000 and her last basic annual salary was sh 630 400. By end of contract she had earned a total basic salary of sh 4 841 600. If the annual increment was constant, calculate
i) The period of the contract
ii) The annual increment
iii) The annual basic salary in the third year of contract
Date posted:
March 7, 2017
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Answers (1)
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Find the radius of the circum-circle of a triangle in which angle A = 69o and a = 3.95 cm.
(Solved)
Find the radius of the circum-circle of a triangle in which angle A = 69o and a = 3.95 cm. Give your answer to four significant figures
Date posted:
March 7, 2017
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Answers (1)
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Evaluate$\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$
(Solved)
Given that
$\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$
where a and b are rational numbers. Find the values of a and b
Date posted:
March 7, 2017
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Answers (1)
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For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x
(Solved)
For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x
Date posted:
March 7, 2017
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Answers (1)
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A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount
(Solved)
A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount
Date posted:
March 7, 2017
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Answers (1)
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The equation of the line L1 is 5y + 2x + 8 = 0 and L2 passes through the points (-5,0) and(5, -4).
(Solved)
The equation of the line L1 is 5y + 2x + 8 = 0 and L2 passes through the points (-5,0) and(5, -4). Without drawing the lines L1 and L2, show that the lines are parallel to each other
Date posted:
March 7, 2017
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Answers (1)
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A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr.
(Solved)
A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr. At 8.30 a.m a car left Kisumu towards Nairobi at an average speed of 120 km/hr. Given that the distance between Nairobi and Kisumu is 400 km, calculate.
a) The time the car arrived in Nairobi
b) The time the two vehicles met
c) The distance from Nairobi to the meeting point
Date posted:
March 7, 2017
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Answers (1)
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Determine the amplitude and the period for the graph of
(Solved)
Determine the amplitude and the period for the graph of
6 sin ($\frac{x}{2} - 90^o$)
Date posted:
March 7, 2017
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Answers (1)
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A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially,
(Solved)
A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially, how much money will he have deposited in 12 months
Date posted:
March 7, 2017
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Answers (1)
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In the expression (x + 2)x, the sum of the first two terms is 768. Find the value x
(Solved)
In the expression (x + 2)x, the sum of the first two terms is 768. Find the value x
Date posted:
March 7, 2017
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Answers (1)
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A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.
(Solved)
A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.
Date posted:
March 7, 2017
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Answers (1)
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A quantity T is partly constant and partly varies as the square root of S.
a) Using k and m as the constants, write down an equation connecting T and S
(Solved)
A quantity T is partly constant and partly varies as the square root of S.
a) Using k and m as the constants, write down an equation connecting T and S
b) If S = 16 when T = 24 and S = 36 when T = 32, find the value of the constants
Date posted:
March 7, 2017
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Answers (1)
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$\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form
(Solved)
$\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form
i) Write down the conjugate of the denominator in its simplest form
ii) Hence use the conjugate in (i) above to rationalize the denominator in the expression above
Date posted:
March 7, 2017
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Answers (1)