Search our library of Maths questions

Top answers

Maths

All levels

Using mathematical induction, prove De Moivre's Theorem.

De Moivre's theorem states that (cosø + isinø)ⁿ= cos(nø) + isin(nø). Assuming n = 1
(cosø + isinø)¹= cos(1ø) + isin(1ø)
which is true so ...

Answered by Scott E. • Maths tutor

77178 Views

Solve for y: 5(y – 2) + 2(y – 3) = 19

Most important thing is to do the same thing to both sides of the equation. 5(y – 2) + 2(y – 3) = 19 Step 1. Multiply out the brackets: 5y - 10 + 2y - 6 = 19 Step 2. Collect like terms & Simpli...

Answered by Rahul J. • Maths tutor

10030 Views

Solve the following simultaneous equations: 3x + 2y = 16 2x + 3y = 14

Answer: x = 4, y = 2

Method: Eq 1) 3x + 2y = 16 Eq 2) 2x + 3y =14

Eq 1 x 2) 6x + 4y = 32 Eq 2 x 3) 6x + 9y = 42

New Eq 2 - New Eq 1) 5y = 10, so y = 2

...

Answered by Elizabeth O. • Maths tutor

7130 Views

Jorgen has 20 sweets in his pocket. The sweets are either blue or yellow. He picks a sweet and eats it and takes another sweet and eats it again. The probability of him picking two blue sweets is 6/30. How many yellow sweets does he have in his pocket.

1st step: Firstly we know 3 things: 1. There are 20 sweets in total 2. The sweets are either blue or yellow 3. The probability of picking two blue sweets in 6/30 We let the total number o...

Answered by Yusuf S. • Maths tutor

5875 Views

Find the coordinates where the curve f(X)= X^2+X-6 touches the x axis using factorisation.

The first part of this question requires be student to realise that touching the x axis equates to f(x) equalling 0, so we must equate the expression to 0.

Next we need to factorise the expression....

Answered by William T. • Maths tutor

2668 Views