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Given the curve y=x^2 +1 and the line y=k, find, using graphical methods only, the value of k for which there is exactly one solution.

Graphically, the solution of a pair of simultaneous equations is the point of intersection between both curves. If we want only one solution to the system of equations, then there should only be one point...

Answered by Marcos T. • Maths tutor

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Factorise the following expression x^2+11x+24=0

Find two values that multiply together to make 24, and add together to make 11
List the factors of 24:24,112,26,48,3
Here we can see the only numbers that add together to make 11 are 8 and 3, s...

Answered by Lauren M. • Maths tutor

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Draw the following inequality on a graph: x^2+4x+1<-2

First we must ensure the equation is in a form that is easy for us to plot!This means we equate the quadratic to 0 by shifting the -2 to the other side. We do this by adding +2 to both sides.Now, we draw ...

Answered by Saad A. • Maths tutor

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two connected triangles in an overall shape ABCD, find length AD

Use cosine rule to find the length of BD then use this with the sine rule to find length AD, will be more obvious with the diagram on the whiteboard.

Answered by Jack K. • Maths tutor

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A cuboid has edge 7 centimetres, 5 centimetres and a total surface area of 142 centimetres squared. A larger, similar cuboid has a shortest edge of 12 centimetres. Find the third edge of the smaller cuboid and the volume of the larger cuboid.

Let's call the length of the third edge "Y" so we have edges of 7cm, 5cm and Ycm.There are 6 faces but opposite faces are the same, so there are 3 pairs of faces which are 5cm by 7cm, 5cm by Ycm...

Answered by Ollie R. • Maths tutor

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