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Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.

We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)). Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x). We can now split the integral into...
PP
Answered by Patrick P. • Maths tutor
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How can I solve equations like 2x + 3 = 8x + 21?

Questions like this ask you to solve an equation; this means to find a value of x that when put into the equation allows each side of the equation to be equal. There are three important rules to follow when ...
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Answered by Tutor87017 D. • Maths tutor
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We have the following fractions: 6/16, 9/24, 12/32 and 15/35. Which fraction is not equivalent to 3/8?

Numerator and denominator of a fraction 6/16 can be divided by 2 to get 3/8. Numerator and denominator of a fraction 9/24 can be divided by 3 to get 3/8. Numerator and denominator of a fraction 12/32 can be ...
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Answered by Karolina P. • Maths tutor
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An alcohol, X has an Mr of 74 and percentage composition of 64.9% Carbon, 13.5% Hydrogen and 21.6% Oxygen. It does not turn potassium dichromate (VI) green. Determine the structural formula of X, and state its name.

64.9/12 = 5.40833 21.6/16 = 1.35 5.40833/1.35 = 4 so 4 Carbons 13.5/1.35 = 10 so 10 Hydrogens 1.35/1.35 = 1 so 1 Oxygen 4x12+10+16 = 74 so emperical formula = Molecular formula it is a tertiary alcohol becau...
MB
Answered by Megan B. • Chemistry tutor
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A hollow sphere of radius r is being filled with water. The surface area of a hemisphere is 3pi*r^2. Question: When the water is at height r, and filling at a rate of 4cm^3s^-1, what is dS/dT?

By the chain rule ds/dt = ds/dr * dr/dv * dv/t. At a height of r, the water fills a hemisphere. So ds/dr = 6pi r. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the volume ...
HB
Answered by Henry B. • Maths tutor
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