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Find the coordinates of the centre C and the length of the diameter of a circle with the equation (x-2)^2 + (y+5)^2 = 25

Equation of a circle -> (x-a)² + (y-b)^2 = r² where the centre = (a,b) and the radius = r

Thus using the equation above we can conclude that the centre is (2,-5)

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Answered by Michael C. • Maths tutor

5280 Views

The curve y = 4x^2 + a/ x + 5 has a stationary point. Find the value of the positive constant a given that y-ordinate of the stationary point is 32.

This question might look hard but can be easily answered by breaking it down into steps and remembering a few key things. The first step is to recognise that the question is mentioning a stationary point ...

Answered by Helen B. • Maths tutor

11136 Views

Solve to find sin x , 4cos^2 + 7sin x -7 =0

4cos² x + 7 sinx - 7 =0 we know that sin²+ cos² = 1 so 4(1-sin²x) + 7sinx -7 = 0 if we times out the brackets -4sin²x + 7 sinx -3 =0 4sin²

Answered by Jo P. • Maths tutor

3501 Views

When performing differentiation in core 3, in what circumstances do I apply the chain, product and quotient rule?

You must apply the chain rule whenever you see a function contained within another function. For example, if you were to differentiate (sin x)² you would apply the chain rule as the sin functi...

Answered by James S. • Maths tutor

3078 Views

Integrate xcos(x)

This problem will be solved using the integration by parts method, taking the integrated function as udv which answer is uv-(integration of vdu) : u=x and dv=cos(x) so, du=dx and v=sin(x). We have, xsin(x...

Answered by Lucia A. • Maths tutor

3398 Views