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The point on the circle x^2+y^2+6x+8y = 75 which is closest to the origin, is at what distance from the origin? (Taken from an MAT paper)

This is a good example of a question where intuition about geometry is important. Completing the square is a standard A level practice to find the equation of a circle. Doing this we get (x+3) 2 -9 +(y+4) 2 ...
JM
Answered by Jack M. • Maths tutor
7695 Views

Can you prove to me why cos^2(X) + sin^2(X) = 1?

The answer to this lies in the geometry of a circle. At GCSE you were taught that a circle has a radius (which I will call R ) which is the distance from the centre to a point on the circle. We put the centr...
JM
Answered by Jack M. • Maths tutor
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Find the turning point of the line y = x^2 + 2x -1

d(x 2 +2x-1)/dx = 2x+2when dy/dx = 0, x = -1when x = -1, y = -2 therefore the turning point is (-1,-2)
EO
Answered by Ebun O. • Maths tutor
5178 Views

Evaluate the integral (write on whiteboard, too complicated to write here)

Make sure integral is in terms of sines and cosines onlyFactor out sine of numerator and make fraction in terms of cosineSubstitution y=cos(x)Fractions decompositionAnother 2 substitutionsSolve
GL
Answered by Gemma L. • Maths tutor
3814 Views

Simplify: 4log2 (3) + 2log2(5)

4log2 (3) + 2log2(5)= log2 (3)^4 + log2 (5)^2= log2 (3^4x5^2)=log2(81x25)=log2(2025) The solution will be explained with the formula for- loga(x) +loga(y)=loga(xy)
MM
Answered by Mihaela M. • Maths tutor
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