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Prove that (4x–5)^2 – 5x(3x – 8) is positive for all values of x.

To begin we need to simplify the expression. First we multiply out (4x–5)^2 to get 16x 2 +40x+25 and then we multiply out 5x(3x – 8) to get 15x 2 -40x. This makes the whole expression 16x 2 +40x+25-(15x 2 -4...
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Answered by Hannah W. • Maths tutor
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Find the values of x where the curve y = 8 -4x-2x^2 crosses the x-axis.

A curve crosses the x-axis when y=0, if we put that into the equation above we get the quadratic equation 0=8-4x-2x 2 . The solutions to this equation are the values of x where y=0, which is the same as sayi...
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Answered by Hannah W. • Maths tutor
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Calculate the angle x in the following diagram. The area of the square is 16cm squared and the total area is 36.6cm squared.

This question was very difficult to explain through words; if it were to be used in a question paper, it would be presented as a diagram. I intend to use the whiteboard during the inteview to explain both th...
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Answered by Daniel P. • Maths tutor
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Solve the simultaneous equations: 3x + 2y =4 4x + 5y =17

You are trying to find out the value of 'x' and the value of 'y'. This means that you need to be able to take away one equation from the other. 3x + 2y = 4 - we are going to times this equation by 4 = 12x + ...
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Answered by Ellie W. • Maths tutor
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A stone, of mass m, falls vertically downwards under gravity through still water. At time t, the stone has speed v and it experiences a resistance force of magnitude lmv, where l is a constant.

A stone, of mass m, falls vertically downwards under gravity through still water. At time t, the stone has speed v and it experiences a resistance force of magnitude lmv, where l is a constant. QUESTION: a. ...
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Answered by Ronan H. • Maths tutor
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