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Published byEustațiu Nistor Modified over 6 years ago
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Week 3 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
Differentiate with respect to x (𝑥−3) 𝑥 Solve the equation 9x – 3(3x+1) = 0 Solve the equation for 0⁰ < x < 360⁰ sinx = 1 - 2cos2x Find the area of the finite region enclosed by the curve y = 4x – x2 and the x-axis
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1 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
4y = 6x y2 = 9x2 + 6x + 1 9x2 – 9x2 – 6x – 1 + 9x – 6x – 2 = 1 -3x = 4 x = − y = − 3 2 CLICK FOR SOLUTION NEXT QUESTION
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2 Differentiate with respect to x (𝑥−3) 2 3 𝑥 𝑦= (𝑥−3) 2 3 𝑥
(𝑥−3) 𝑥 𝑦= (𝑥−3) 𝑥 = 𝑥 2 −6𝑥+9 3 𝑥 Y = 𝑥 − 2𝑥 𝑥 − 1 2 𝑑𝑦 𝑑𝑥 = 𝑥 − 1 𝑥 − 𝑥 3 CLICK FOR SOLUTION NEXT QUESTION
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3 Solve the equation for 9x – 3(3x+1) = 0 9x – 3(3x+1) = 0
Let y = 3x y2 – 9y = 0 y(y – 9) = 0 y = 0 and y = 9 3x = 0 or 3x = 9 x = 2 CLICK FOR SOLUTION NEXT QUESTION
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4 Solve the equation for 0⁰ < x < 360⁰ sinx = 1 - 2cos2x
sin x = 1 – 2(1 - sin2x) 2sin2x – sin x - 1 = 0 sin x = 1 or sin x = -½ x = 90⁰, 210⁰, 330⁰ CLICK FOR SOLUTION NEXT QUESTION
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5 Find the area of the finite region enclosed by the curve
y = 4x – x2 and the x-axis 4x – x2 = 0 x = 0 or x = 4 0 4 4𝑥− 𝑥 2 𝑑𝑥= 2 𝑥 2 − 1 3 𝑥 3 = CLICK FOR SOLUTION CLICK FOR SOLUTION
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Week 3 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
Differentiate with respect to x (𝑥−3) 𝑥 1 2 𝑥 − 1 𝑥 − 𝑥 3 Solve the equation 9x – 3(3x+1) = 0 x = 2 Solve the equation for 0⁰ < x < 360⁰ sinx = 1 - 2cos2x x = 90⁰, 210⁰, 330⁰ Find the area of the finite region enclosed by the curve y = 4x – x2 and the x-axis 10 2 3
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