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Maths
A Level

A stone is thrown from a bridge 10m above water at 30ms^-1 30 degrees above the horizontal. How long does the stone take to strike the water? What is its horizontal displacement at this time?

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by appl...

SU
Answered by Sarah U. • Maths tutor
5541 Views

What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x).
Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)).

Then by the power...

LP
Answered by Luke P. • Maths tutor
4741 Views

A circle C with centre at the point (2, –1) passes through the point A at (4, –5). Find an equation for the circle C.

You would start with this equation (x – a)2 + (y – b)2 = r2, with the center being at the point (a, b) and the radius being "r". Therefore you would have (x-2)

IN
Answered by Ishan N. • Maths tutor
5180 Views

Find the indefinite integral of cos^2 x

First, we need to write cos2x in a form that is easily integrable. We can use the double angle formula cos(2x) = 2cos2x - 1 to see that cos2x = 1/2cos(2x)+1/2. Now, we can...

ER
Answered by Ethan R. • Maths tutor
8133 Views

The point A lies on the curve with equation y=x^0.5. The tangent to this curve at A is parallel to the line 3y-2x=1 . Find an equation of this tangent at A. [5 marks]

Differentiate equation

dy/dx=0.5*x-0.5

Gradient is the same as the second equation

2/3=0..5*x-0.5 

Solving this ...

AM
Answered by Arnold M. • Maths tutor
6138 Views

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