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Given a curve has the equation f'(x) = 18x^2-24x-6 and passes through the point (3,40), use integration to find f(x) giving each answer in its simplest form.

Firstly we need to integrate f(x). The general rule is: the integral of x^n = (1/(n+1))x^(n+1)+CSo apply that rule to each term of f'(x) as so:Integral of 18x^2 = (18/(2+1))x^(2+1) = 6x^3 Integral of -24x = ...
HB
Answered by Henry B. • Maths tutor
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Solve the simultaneous equations x – 2y = 1 and x^2 + y^2 = 29.

Start by modifying the first equation and making a third x=2y+1x 2 = (2y+1) 2 x 2 =4y 2 +4y+1therefore, if we sub this 3rd equation into the 2nd equation we get :4y 2 +4y+1+y 2 =29 5y 2 +4y-28=0 5y 2 -10y+4y...
AP
Answered by Adamya P. • Maths tutor
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There is a Ferris wheel where the passengers are placed 10m away from the centre. At what speed must they be moving in order for them to feel completely weightless at the top of the wheel.

In order for the passenger to feel weightless, they must have a vertical acceleration equal to the acceleration due to gravity, i.e. they must be accelerating downward at a rate of 9.81m/s 2 . acceleration =...
Answered by • Maths tutor
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Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi

This is a question that relates to the topic of differentiation. Typically students encounter this topic near the end of the first term of the first year of their A Level.The equation of the curve, y = sin(2...
AS
Answered by Agnieszka S. • Maths tutor
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A Polynomial is defined as X^3-6X^2+11X-6. a)i Use the factor theorem to show that X-3 is a factor. ii Express as a linear and quadratic b)Find the first and second derivative c) Prove there is a maximum at y=0.385 to 3DP

a)i Factor Theorem states that if a polynomial has a factor of X-a, when a is substituted in, the polynomial = 0. Therefore substitute 3 into the polynomial, which then equals 0 ii Long Devision- Unsure how ...
OM
Answered by Oliver M. • Maths tutor
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