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Show that 2tan(th) / (1+tan^2(th)) = sin(2th), where th = theta

We have 2tan(th) / (1 + tan^2(th)) = sin(2th) We know that tan(A) = sin(A) / cos(A), and 1 + tan^2(A) = sec^2(A) Therefore => (2sin(th) / cos(th)) / sec^2(th) => 2sin(th)*cos^2(th) / cos(th) => 2sin...
IC
Answered by Ian C. • Maths tutor
4214 Views

Use logarithms to solve the equation 3^(2x+1) = 4^100

We have 3^(2x+1) = 4^100 => log(3^(2x+1)) = log(4^100) => (2x+1)log(3) = 100log(4)
IC
Answered by Ian C. • Maths tutor
7200 Views

There are 3 red beads and 1 blue bead in a jar. A bead is taken at random from the jar. what is the probability that the bead is blue?

1/4
DM
Answered by Daniel M. • Maths tutor
9928 Views

Use the binomial series to find the expansion of 1/(2+5x)^3 in ascending powers of x up to x^3 (|x|<2/5)

We want to rearrange the expression to the form (1+y)^n so we can use the general result: (1+y)^n=1+ny+[n(n-1)/2]y^2+[n(n-1)(n-2)/3!]y^3+... 1/(2+5x)^3 = (2+5x)^-3 = [2(1+5x/2)]^-3 = (2^-3)(1+5x/2)^-3 using ...
SJ
Answered by Saskia J. • Maths tutor
14797 Views

White paint costs £2.80 per litre. Blue paint costs £3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture.

Amount of paint needed: White paint = (18 ÷ 5) × 3 = 10.8 litres Blue paint = (18 ÷ 5) × 2 = 7.2 litres Cost of white paint = 10.8 x £2.80 = £30.24 Cost of blue paint = 7.2 x £3.50 = £25.20 Total cost = £30....
JM
Answered by Jared M. • Maths tutor
4400 Views