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A level Maths question - The graph of y=2sin(2x)+1 is rotated 360 degrees about the x-axis to form a solid. Find the volume enclosed by the curve, the co-ordinate axes and the line x=pi/2

First, recall that the formula for finding such a volume is pi times the integral from 0 to pi/2 of y^2 with respect to x. This leads to pi times the integral from 0 to pi/2 of 4sin^2(2x) + 4sin(2x) + 1 (thi...
RK
Answered by Robbie K. • Maths tutor
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Prove the identity: (cos θ + sin θ)/(cosθ-sinθ) ≡ sec 2θ + tan 2θ

First rewrite right hand side in terms of sinθ and cosθ, because those are the terms we'll be dealing with on the left hand side: sec2θ+tan2θ = 1/cos2θ + sin2θ/cos2θ, so RHS = (1+sin2θ)/cos2θNow look at the ...
MM
Answered by Margot M. • Maths tutor
8565 Views

Simplify the following quadratic equation: 3x^2 + 20x - 500 = 0.

x = −b ± √(b 2 − 4ac) / 2a x = −20 ± √(20 2 − 4(3)(-500)) / 2(3) x = (3x + 50) (x - 10)
AS
Answered by Aarnav S. • Maths tutor
1791 Views

How would I go about solving 3(x-2) = x+7?

First of all, you want to try and get rid of the brackets so the equation is easier to simplify in the next steps. So you multiply the whole bracket by 3. So it is 3x-6 = x+7. Secondly, in order to solve the...
FA
Answered by Finn A. • Maths tutor
8941 Views

A farmer has a garden shaped into an isosceles triangle. Its side is 7m. He needs to enclose the perimeter, using copper wires, in order to avoid undesirable incidents. Each meter of copper wire cost 2£. How much does he need to pay to secure his garden?

Each side of the triangle is 7 meters, because it is an isosceles triangle. P= perimeterP = 7 +7 +7 P= 21 meters Each meter of copper wire costs 2 £ so, Total cost= Perimeter in meters * Cost per meterTotal ...
ID
Answered by Iosif D. • Maths tutor
3574 Views