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The equation of a line is y=e(^2x)-9 and the line has points at (0,a) and (b,0). Find the values of a and b.

y=e 2x -9. When x=0 y=a.a=e 2(0) -9a=1-9=-8. When x=b y=0.0=e 2(b) -99=e 2b ln(9)=ln(e 2b )ln(9)=2b(1/2)ln(9)=bln(9 (1/2) )=bb=ln3
CJ
Answered by Callum J. • Maths tutor
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A circle, C, has an equation: x^2 + y^2 - 4x + 10y = 7 . Find the centre of the circle and its radius?

The equation given needs to be transformed into a more familiar equation of a circle which we know the properties of and are therefore able to find its centre. Do you know what type of equation im speaking o...
AA
Answered by Alex A. • Maths tutor
9049 Views

Find the integral of the following equation: y = cos^2(x)

First convert y into a suitably form.cos(2x) = 1 - 2cos 2 (x)cos 2 x = (1-cos(2x))/2 integral of y = integral of (1-cos(2x))/2 = (1/2)*(x-(1/2)sin(2x)) + C = x/2 - sin(2x)/4 + C
MH
Answered by Marc H. • Maths tutor
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The equation of a curve is xy^2= x^2 +1. Find dx/dy in terms of x and y, and hence find the coordinates of the stationary points on the curve.

dy/dx = (2x-y 2 )/(2xy)Stationary points: (1, root(2)) , (1, -root (2))
RS
Answered by Rishi S. • Maths tutor
9524 Views

How do I expand a bracket to a negative power if it doesn't start with a 1.

Okay so consider (2 + x)^-1, we can only do the expansion we know if the bracket starts with a 1, to fix this we can factor a 2 out of the bracket so that it becomes (2(1 + x/2))^-1. Then by our rules of pow...
SM
Answered by Shaun M. • Maths tutor
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