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Find the normal to the curve y = x^2 at x = 5.

Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve. Dy/dx = 2x Therefore m = 2 Calculate the negative reciprocal (m2) which will give the gradi...
AS
Answered by Aphisha S. • Maths tutor
4334 Views

Use the identity for sin(A+B) to find the exact value of sin 75.

From reading the question, we need to use the addition formula for sin(A+B)= sinAcosB+cosAsinB. So we need to think what are two common values for sine and cosine that we know and have exact answers for that...
RD
Answered by Ruth D. • Maths tutor
4928 Views

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 = r 2 where the centre = (a,b) and the radius = r Thus using the equation above we can conclude that the centre is (2,-5) In order to find the diamerer fo the cir...
MC
Answered by Michael C. • Maths tutor
6062 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 whi...
HB
Answered by Helen B. • Maths tutor
12248 Views

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

4cos 2 x + 7 sinx - 7 =0 we know that sin 2 + cos 2 = 1 so 4(1-sin 2 x) + 7sinx -7 = 0 if we times out the brackets -4sin 2 x + 7 sinx -3 =0 4sin 2 x -7sinx +3 =0 (4sinx-1)(sinx +2)=0 so therefore sinx =1/4 ...
JP
Answered by Jo P. • Maths tutor
4042 Views