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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...
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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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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 ...
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Answered by Henry B. • Maths tutor
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Suppose we have a circle whose radius is 5cm. If a sector of this circle has an area of 15 cm^2, what is the size its angle (in degrees)?

Firstly, you would need to figure out what formula you can use to solve this problem. You know the radius and area of the sector, and you need to find the angle. So, the correct equation to use would be the ...
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Answered by Roxani S. • Maths tutor
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