Search our library of Maths questions

Top answers

Maths

All levels

Imagine a sector of a circle called AOB. With center O and radius rcm. The angle AOB is R in radians. The area of the sector is 11cm². Given the perimeter of the sector is 4 time the length of the arc AB. Find r.

11 = 1/2 r²RAB = x = rRr + r + x = 4x2r = 3rRR = 2/3r²R = 22r² = 33r = √33

4187 Views

Find x and y using the equations 3x + y= 10, x + y = 4

First of all there are 3 different methods of working out simultaneous equations: Elimination, Substitution and Graphical. Today I will show the substitution method.
If x + y = 4 then rearranging the...

Answered by Tobi O. • Maths tutor

3821 Views

x^3 + 3x^2 + 2x + 12

3x² + 6x + 2

Answered by Jiawang Q. • Maths tutor

3153 Views

How to perform integration by substitution. (e.g. Find the integral of (2x)/((4+(3(x^2)))^2)) (10 marks)

We begin by looking at the integral by itself. The first thing we must do is evaluate what type of integration we should perform. It's always important to make sure that it's not a standard integral such ...

Answered by Kenneth B. • Maths tutor

3515 Views

A function is defined as f(x) = x / sqrt(2x-2). Use the quotient rule to show that f'(x) = (x-2)/(2x-2)^(3/2)

u = x v = (2x-2)^(0.5)u' = 1 v' = (2x-2)^(-0.5)f'(x) = (vu' - uv') / v^2Therefore, f'(x) = (((2x-2)^(0.5) * 1) - (x * (2x-2)^(-0.5))) / ((2x-2)^(0.5))^2f'(x) = (2x - 2 - x) / (2x-2)^(3/2) = (x-2) / (2x-2)...

Answered by Isaac F. • Maths tutor

8680 Views