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If I throw a ball vertically upwards with a velocity of 15 m/s and we assume the gravitational acceleration is 10 m/s^2. Draw the distance-time, and velocity-time graphs, how long is the ball in the air before it returns to the point I threw it from?

We will need a SUVAT equations, so first fill in what information we have:S = 0 (the point where the ball returns to the start)U = +15 m/sV = -15 m/s (from graph)A = -10 m/s (important that this is the op...

Answered by Barnaby F. • Maths tutor

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Find the equation of the tangent line to the parabola y=x^2+3x+2 at point P(1, 6).

In order to find the equation of the tangent line, first we have to find its slope. To do this, we take the first derivative of the function. In this particular case, we just need to apply the power rule ...

Answered by Boris A. • Maths tutor

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The equation x^2 + 3px + p = 0, where p is a non-zero constant, has equal roots. Find the value of p.

Firstly, we need to recognise that the question stated that the quadratic equation has equal roots. This tells us that the discriminant of the equation (b^2 - 4ac) will be an important pa...

Answered by Emmanuel B. • Maths tutor

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complete the square of x^2 + 2x - 6

There is always a systematic approach to answering questions that require you to complete the square. Before you start answering the question make sure the coefficient of x^2 is 1. For th...

Answered by Viroshan G. • Maths tutor

3538 Views

dy/dx = y3xcos2x, given that when x = π/6, y = e, solve this differential equation, giving y in terms of x

dy/dx = y3xcos2xS 1/y dy = S 3xcos2x dx, let u=x, u'=1, v'=cos2x, v=1/2sin2xIf I = 3xcos2x dx, then I = uv - S u'vln y = 3x(1/2sin2x) - S 3(1/2sin2x) dx = 3/2xsin2x - 3/2(-1/2cos2x) + c =3/2xsin2x + 3/4co...

Answered by Matt O. • Maths tutor

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