Search our library of Maths questions

Top answers

Maths

All levels

a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - ...

Answered by Mario R. • Maths tutor

19663 Views

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

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term...

Answered by Alex C. • Maths tutor

7913 Views

Simplify fully: (24 - √ 300)/(4√ 3 - 5). Give your answer in the form a√ b where a and b are integers and find the values of a and b.

rationalise the denominator (remove the surds) by multiplying by a fraction = 1, known as the rationalising factor = (24 - √ 300)/(4√ 3 - 5) * (4√ 3 + 5)/(4√ 3 + 5) = (24 - √ 300)(4√ 3 + 5)/(48 - 25) = (2...

Answered by Aloysius L. • Maths tutor

6307 Views

Solve the simultaneous equations. 2x + y = 18 . x - y = 6

x = 6 + y
2(6+y) + y = 18
12+2y+y = 18
3y = 18-12
3y=6
y = 6/3 = 2. So y = 2 if y = 2 then x is = ?
x - y = 6 so, x-2 = 6
so x is 6+ 2 = 8
x = 8 and y = 2<...

Answered by Olufunke O. • Maths tutor

3026 Views

How do you integrate ln(x)?

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a specia...

Answered by Omkar D. • Maths tutor

3633 Views