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Solve these simultaneous equations. 2x + y = 18 x - y = 6

With simultaneous equations there is more than one unknown. First we’ll get one unknown on its own so we rearrange the bottom equation to get x on its own. By adding y to each side of the equation this le...

Answered by Lizzie S. • Maths tutor

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Find the value of x: x^2-3x-3=1

To begin this question you need to bring all of the terms to one side, so the equation equals 0. It is easiest to do this by subtracting 1 from each side.x^2-3x-3-1=1-1x^2-3x-4=0Now we need to factorise t...

Answered by Emma H. • Maths tutor

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The height x metres, of a column of water in a fountain display satisfies the differential equation dx/dt = 8sin(2t)/(3sqrt(x)), where t is the time in seconds after the display begins. (a) Solve the differential equation, given that x(0)=0

Our DE (Differential Equation) dx/dt = 8sin(2t)/(3sqrt(x)) is separable because dx/dt can be expressed as a product of two functions of the form dx/dt = f(t)g(x) = (8sin(2t)) * (1/(3sqrt(x))).To solve the...

Answered by James M. • Maths tutor

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What is the equation of the straight line perpendicular to the midpoint of the straight line that passes through (0,5) and (-4,7)?

Firstly, it's important to note that the question concerns straight lines, so it will be possible to express the answer in the form y=mx+c where m is the gradient and c is the y...

Answered by Adam L. • Maths tutor

3422 Views

James wins the lottery and gets £200,000. He decides to spend 10% of his winnings and invest the rest. From the money he has invested, he receives interest of 3% per year. How much money does James have after 5 years (to the nearest pound)?

James starts with £200,000.
He then spends 10% of his winnings:
200,000*(1-0.1)=180,000
The 1 represents 100%, which the amount of money James starts with. He then spends 10%, which is repr...

Answered by Edward H. • Maths tutor

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