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Solve 2^(3x-1) = 3

2^{3x - 1} = 3log₂(2^3x-1) = log₂(3)3x - 1 = log₂(3)3x = 1 + log₂(3)x = ¹/₃ + ¹/₃log₂(...

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Express cos2x in the form a*cos^2(x) + b and hence show that the integral of cos^2(x) between 0 and pi/2 is equal to pi/a.

Apply the double angle formula to cos2x to yield the requested result.
cos2x = 2cos^2(x) - 1
Spot that the question asks us to prove the value of cos^2(x) when integrated, and that we can move t...

Answered by Louis P. • Maths tutor

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Solve the differential equation dx/dt = -2(x-6)^(1/2) for t in terms of x given that x = 70 when t = 0.

First, manoeuvre variables so that we can integrate the equation.
1/(x-6)^(1/2) dx = -2 dt
Integrate the equation and add the constant.
2(x-6)^(1/2) = -2t +c
Solve for t.
t = -(x-...

Answered by Louis P. • Maths tutor

5381 Views

Complete the square of the following expression: 2x^2 -8x+21

2(x-2)^2 +13

Answered by Iliya F. • Maths tutor

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A point lies on a circles diameter such that the distance from the point to the edge of circle is 4 times the distance from the point to the centre. What is the circles area in cm^2 if the distance from the point to edge is 5cm?

first we know that the length given has a 4:1 ratio with the remaining length of the radius so 5/4 + 5 = 25/4 = radius, the formula for the area of a circle is A=pi*(r^2) so the area is 625/16*pi.

Answered by Luka R. • Maths tutor

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