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(GCSE) A rectangle has the following characteristics: its length is (2x + 5), its width is (3x - 2). The perimeter of the rectangle is 46 cm. What is the value of x?

First of all draw the rectangle, name its sides and annotate its characteristics. Define the data you have and what you are looking for. Write down the general formula for the perimeter of a rectangle: p = a...
GD
Answered by Giulia D. • Maths tutor
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How do you determine the nature of a graphs stationary point? e.g y = 1+2x-x^2

We have our function of y = 1+2x-x 2 The gradient of a stationary (or turning) point is 0, in essence a peak or a trough. In order to determine the gradient, we need to differentiate our function with respec...
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Answered by Joseph A. • Maths tutor
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How do I integrate 2^x?

Let's first consider the differential of 2 x . We know that this becomes ln(2)*2 x . We can compare this to the integrand and see that this is very close indeed! The only problem is that ln(2) . So now consi...
JH
Answered by Jordan H. • Maths tutor
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A particle of mass 0.8 kg moving at 4 m/s rebounds of a wall with coefficient of restitution 0.3. How much Kinetic energy is lost?

Coefficient of Restitution (CoR): Speed of Approach x CoR = Speed of Seperation 4 x 0.3 = 1.2 ms -1 Kinetic Energy (KE) Lost: KE lost = Initial KE - Final KE Initial KE = 1/2mv 2 = 1/2 x 0.8 x 4 2 = 6.4 J Fi...
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Answered by George M. • Maths tutor
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Solve the pair of simultaneous equations; (1) y + 4x + 1 = 0, (2) y^2 + 5x^2 + 2x = 0 .

Rearrage equation (1) to make y the subject of the formula. This gives y = -4x -1 . Substitute this value of y into equation (2). This gives (-4x -1)^2 +5x^2 +2x = 0 . Expanding out the brackets gives 16x^2 ...
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Answered by Melanie G. • Maths tutor
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