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A circle with centre C has equation x^2 + y^2 + 2x + 6y - 40 = 0 . Express this equation in the form (x - a)^2 + (x - b)^2 = r^2. Find the co-ordinates of C and the radius of the circle.

We can express the equation of any circle in the form (x - a)^2 + (y- b)^2 = r^2 . The centre of the circle is then the point (a, b) and its radius is r . If we multiply out the brackets in the equation abov...
BK
Answered by Baran K. • Maths tutor
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The line AB has equation 3x + 5y = 7. What is the gradient of AB?

The gradient of a line in the form y = ax + b, where a and b are some numbers, is the number a . So we need to get the equation 3x + 5y = 7 into the above form, with y on one side on its own! We first move t...
BK
Answered by Baran K. • Maths tutor
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What is the gradient of y = xcos(x) at x=0?

First we want to calculate the derivative of y. To do this we use the product rule:If we rewrite y as y = uv, then dy/dx = v du/dx + u dv/dx.Here, we have u = x and v = cos(x).That means du/dx = 1 and dv/dx ...
FF
Answered by Fraser F. • Maths tutor
4818 Views

Find the integral of sin^2(X)

As soon as you see a question asking you to integrate the square of sin, cos or tan, your first approach should be to use trigonometric identities and double angle formulas . For sin 2 (X), we will use the c...
KF
Answered by Kyna F. • Maths tutor
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Showing all your working, evaluate ∫ (21x^6 - e^2x- (1/x) +6)dx

When integrating a long chain of functions, we can integrate each term seperately and combine them. Let us now integrate:∫21x 6 dx = 21∫x 6 dx. Using the Power Rule [∫x a dx = (x a+1 /a+1)], we can say that ...
RA
Answered by Raghav A. • Maths tutor
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