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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 correct for n = 1 Assume n = k is true so (cosø + isinø) k = cos(k...
SE
Answered by Scott E. • Maths tutor
83040 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 & Simplify: 5y + 2...
RJ
Answered by Rahul J. • Maths tutor
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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 Sub y into Eq 1) 3x + 4 = 16, 3x = 12, so x = 4
EO
Answered by Elizabeth O. • Maths tutor
8845 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 of blue sweets in his...
YS
Answered by Yusuf S. • Maths tutor
7087 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. This mean...
WT
Answered by William T. • Maths tutor
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