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Find the exact gradient of the curve y = ln(1-cos 2x) at the point with x-coordinate π/6.

The gradient to the curve is given by the derivative of the function y = f(x) = ln(1 - cos 2x). This function is a composition of two other functions so we need to use the chain rule to find the derivativ...

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Answered by Archie R. Maths tutor
6244 Views

How do I integrate tan^2 x?

Firstly, use the trigonometric formula tan2x = sec2x - 1, which you can easily derive from sin

JC
Answered by Jakub C. Maths tutor
7930 Views

A quarter circle has a radius of 8, calculate the area giving your answer in terms of pi

area of a circle = pi x radius^2
64pi/4 = 16pi
Student must be aware of the equation for the area of a circle and that they must divide by 4 to get the answer here

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Answered by Sam D. Maths tutor
7350 Views

2435 units of gas used in November, costing 4.12p per unit. The gas company also charge 9.43p per day. The total cost has an additional 5% in VAT. What is the gas bill for the month of November?

30 days in November; (30 X 9.43) = 282.9p (2435 X 4.12) = 10032.2p (10032.2 + 282.9) = 10315.1p 5% in VAT so total price is 105% of 10032.2p Convert 105% to decimal; 1.05 (1.05 X 10315...

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Answered by Andrew G. Maths tutor
3121 Views

Solve the simultaneous equations: [4x-y=3] and [6x +2y=1]

(1) 4x-y=3(2) 6x+2y=1Eliminate y; (1) X 2 => (3) 8x-2y=6 Add (2) to (3) 8x - 2y = 6 +(6x + 2y) = 114x = 7x=1/2 If x=1/2 then,2-y=3 y= -1

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Answered by Andrew G. Maths tutor
3695 Views

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