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Square ABCD has length (x+3)cm and area 10cm^2. Show x^2 + 6x = 1

First sketch square ABCD. Split length into 3cm and then xcm for side AB and the same for side AD. Split the area of this square into 4 segments (a, b, c and d) such that a is a 3cm by 3cm square, b and c ar...
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Answered by Meghna M. • Maths tutor
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The curve with the equation: y=x^2 - 32sqrt(x) + 20 has a stationary point P. Find the coordinates of P.

A stationary point implies that the gradient at this point will be equal to 0, it is a turning point in the graph. So we need to find the value of X at which dy/dx = 0. [where dy/dx is the gradient.]So we fi...
MB
Answered by Maninder B. • Maths tutor
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Solve the equation 2(cos x)^ 2=2-sin x for 0 <=x<=180

Recall the identity ((cos x)^2+(sin x)^ 2=1). Rearrange the identity to give cos x in terms of sin x. Substitute this into the equation. Rearrange so all terms are on one side of the equation and factories t...
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Answered by Pablo G. • Maths tutor
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Henry invest £8000 in youtube at a compound interest rate of 2% per year. He wants to earn more than £500 interest. Work out the least time, in whole years, that this would take?

Each year his money will increase by 2%, meaning he will get 102% of his money from the previous year. This can be written as 1.02. After n years, he will make 8000 x 1.02 n . Calculate this for 1, 2, 3, 4.....
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Answered by Gillian L. • Maths tutor
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If I had an equation with both 'x' and 'y' present, how would I find the gradient?

Using the equation (x+y) 2 =xy 2 as an example base to see how it would work in practice. The most important fact is that dy/dx =y' . Simply put, the derivative of y is dy/dx. This allows you to go through a...
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Answered by Oli K. • Maths tutor
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