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Further Mathematics
GCSE

The circle c has equation x^2+ y ^2=1 . The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.

The equation for a line is y(x)=ax+b.Because it intersects the y axis at x=0 at y=1y(x)=b=1a is equal to the gradient of the function so the line is given as y(x)=3x+1In order to get the two intersection...

Answered by Csaba B. Further Mathematics tutor
2492 Views

A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.

A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x2-6x. We can substitute x = 2 into this equation to give 0 (alternatively solve ...

Answered by Tom C. Further Mathematics tutor
7434 Views

If y=x^3+9x, find gradient of the tangent at (2,1).

To find the gradient of the tangent, we can differentiate to give dy/dx=3x^2+9. We can now put in x=2 to find the gradient at (2,1): 3(2)^2+9=21. Therefore the gradient is 21 at (2,1).

Answered by Angus M. Further Mathematics tutor
1990 Views

How to solve the inequality 1 - 2(x - 3) > 4x

Firstly you should expand the brackets in this situation in order to collect the like terms, so get all the x's on one side and all the constants on the other side of the inequality. Expanding the bracket...

Answered by Fred E. Further Mathematics tutor
3047 Views

Expand (2x+3)^4

We will you use Pascal's triangle in order to find coefficients:         1        1  1       1 2 1     1 3  3 1    1  4  6  4  1 so, our coefficients will be 1,4,6,4,1 now, let's expand: (2x+3)4

Answered by Cezar P. Further Mathematics tutor
2708 Views

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