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Edexcel C1 2015 Q10. A curve with equation y = f (x) passes through the point (4, 9). Given that f′(x)=3x^(1/2)-9/(4x^(1/2))+2. Find f(x), giving each term in its simplest form.

I would go through a similar example of integration with the student using the whiteboard and would explain the use of integration, and would then get them to do the above question, giving them hints when...

Answered by Issy A. • Maths tutor

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Define the term "Gravitational Potential" and write down a formula which defines it.

The Gravitational Potential is the work done in moving a unit mass (1kg) from an infinite distance to a point in a radial gravitational field. The Gravitational Potential is defined as being zero an infin...

Answered by Jay B. • Physics tutor

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A gardener uses this formula to work out how much he charges to make a lawn. C = (7(14+A))/3. C is the charge in £, A is the area in m^2. He makes a rectangular lawn measuring 12.5 m by 17.6 m. How much does he charge? [3 marks]

Rectangular Lawn of 12.5 x 17.6m. (Draw Rectangle) Area=LengthHeight A=12.517.6 A=220m^2

Substitute into formula: C=(7(14+A))/3 C=(7(14+220))/3 C=(7(234))/3 C=(1638)/3 C=546

The gar...

Answered by Joshua F. • Maths tutor

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Factorise f(x) = 6x^3 -7x^2 -x +2 = 0

Try to find first root: f(1) = 6 - 7 -1 + 2 = 0, therefore x-1 is a root. Find quadratic by inspection: (x-1)( )= 6x^3 -7x^2 -x +2 (x-1)(6x^2 - x - 2) Factorise quadratic: (x-1)(2x+1)(3x-2) = 0

Answered by Tutor40745 D. • Maths tutor

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Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.

Rearrange differential equation to get 1/x(x+1) dx = 1/y dy. Separate x side into partial fractions where 1/x(x+1) = 1/x - 1/(x+1). Integrate each side. Resulting equation involves natural logs. Substitut...

Answered by Alexander T. • Maths tutor

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