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Solve the simultaneous equations to find x and y: 2x - 2y = 20, x + 4y = 5

Equation1: 2x - 2y = 20, equation 2: x + 4y = 5First method (subtraction):Multiply equation1 by 2: 4x - 4y = 40Add the two equations together canceling out the y unknowns: 4x + x = 40 + 5Solve for ...

Answered by John S. • Maths tutor

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A curve has equation y = f(x) and passes through the point (4, 22). Given that f ′(x) = 3x^2 – 3x^(1/2) – 7, use integration to find f(x), giving each term in its simplest form.

Firstly we can use the difference rule to split f'(x) into three components which we can consider separately. Then using the knowledge that the integral of x^n is 1/(n+1)*x^(n+1) we get the expression for...

Answered by Abbey S. • Maths tutor

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y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which dy/dx < 0

a) We need to differentiate this equation using the quotient rule (Given that it is a fraction with an x term on both the top and bottom of the fraction). We assign the numerator and denominator as follow...

Answered by James F. • Maths tutor

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How do I calculate a percentage increase? For example; there are 15 fish in a fish tank, after a year they have bred and now there are 20 fish in the tank. By what % has the number of fish increased?

Original value = 15 New Value = 20 Difference = New value - original value 20 - 15 = 5
(Difference / original) x 100(5/15) x 100 = 33.3%

Answered by Seyi A. • Maths tutor

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Circle with centre C, and points A,B,D and E on the circumference of the circle. BD is the diameter of the circle. Angle CDA is 18 deg and angle AED is 31 deg. Find angle EDA.

Circle theorem: angle in a semi-circle is a right angle.Therefore angle BAE = 90 + 31 = 121 degrees ABDE is a cyclic quadrilateral and:Circle theorem: Opposite angles in a cyclic quadrilateral sum to 180 ...

Answered by Jasmin H. • Maths tutor

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