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Why is the gradient of a curve at a point the same as the gradient of the tangent if you can't use gradient formula on a curve?

This may be initially confusing to get your head around but gradient is really just an expression of "rate of change" on a curve the rate of change is always changing at every point, this about it ...
BD
Answered by Brendan D. • Maths tutor
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Solve the following simulateous equations: 3x+y=11 and 2x+y=8

Minus 2x+y=8 from 3x+y=11 so that the y's cancel out (y-y=0). Then we get the equation 3x-2x=11-8.So we get x=3.We can substitute this value back into one the orginal equations: y=11-3(3)=2 - so y=2.We can c...
CG
Answered by Cameron G. • Maths tutor
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Find the coordinates of the point of intersection of the lines y = 3x - 2 and x + 3y = 1.

(A-level Maths) Simultaneous equations: 1) y = 3x -2 2) x + 3y = 1 Substitute y = 3x - 2 into equation 2: x + 3y = 1x + 3(3x-2) = 1 1 mark x + 9x - 6 = 1 Expand brackets 10x - 6 = 1 Solve equation 10x = 1 + ...
KB
Answered by Kiran B. • Maths tutor
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The circle C has centre (2,1) and radius 10. The point A(10,7) lies on the circle. Find the equation of the tangent to C at A and give it in the form 0 =ay + bx + c.

Whenever possible it is always a good idea to draw a graph to give a better understanding of what is going on in the question. As we have already been given a point on the tangent, namely A(10,7), it is a go...
GG
Answered by George G. • Maths tutor
5530 Views

Find partial fractions of : (x+7) / ((x-3)(x+1)^2)

First, separate the algebraic fraction:(x+7) / ((x-3)(x+1) 2 = A/(x+3) + B/(x+1) + C/(x+1) 2 Multiply both sides by (x-3)(x+1) 2 : (x+7) = A(x+1) 2 + B(x+1)(x+3) + C(x+3) Set x=-1 in order to eliminate A and...
JV
Answered by Janni V. • Maths tutor
3626 Views