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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 derivative. ...
AR
Answered by Archie R. • Maths tutor
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How do I integrate tan^2 x?

Firstly, use the trigonometric formula tan 2 x = sec 2 x - 1 , which you can easily derive from sin 2 x + cos 2 x =1, by dividing both sides by cos 2 x and re-arranging. Now, you should remember that differe...
JC
Answered by Jakub C. • Maths tutor
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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
8266 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 10315.1) = 10830.55p Convert...
AG
Answered by Andrew G. • Maths tutor
3757 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
4566 Views