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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 ...

PP
Answered by Patrick P. Maths tutor
4899 Views

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 th...

TD
Answered by Tutor87017 D. Maths tutor
4618 Views

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 ...

KP
Answered by Karolina P. Maths tutor
8225 Views

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 ...

MB
Answered by Megan B. Chemistry tutor
8503 Views

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 = 6pir. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the v...

HB
Answered by Henry B. Maths tutor
5472 Views

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