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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...

Answered by Sarah U. Maths tutor
5091 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...

Answered by Luke P. Maths tutor
4332 Views

Solve the following equation: 4x + 7 = 2x - 5

Some students struggle to solve equations with unknowns on both sides. I think the easiest way to solve these types of equations is to use the balance method. This is where you treat the equation like a w...

Answered by Nicholas D. Maths tutor
10479 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)

Answered by Ishan N. Maths tutor
4852 Views

simplify (2q+4)/(p(p+1)) -q/p

times the whole equation by the denominator of the left fraction giving p(2q+4)(p+1) - (qp(p+1))/p

notice that p can be cancelled in the right fraction, and then times out to give

2qp^2 + 4p...

Answered by Madeleine B. Maths tutor
2694 Views

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