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Find the integral of 3x^2 + 4x + 9 with respect to x.

We must first remember that to integrate, we must increase the power by 1 and divide by this new power. Therefore, to integrate 3x^2 + 4x + 9, we take the first term, 3x^2 . Using the above method, we find t...
DJ
Answered by Dylan J. • Maths tutor
10138 Views

Factorise and solve x^2 + 3x - 4 = 0

To factorise this equation, we must find two numbers that add together to make 3 and multiply to make -4 . These numbers must be -3 and -1 . We would then rewrite the equation as (x-3)(x-1)=0. To solve this ...
DJ
Answered by Dylan J. • Maths tutor
12018 Views

What is the integral of (cos(x))^2?

cos(2x) = 2cos 2 (x)-1 by the double angle formula. Rearrange to give cos 2 (x) = (cos(2x)+1)/2 Integrating this gives sin(2x)/4 + 1/4x + c
MC
Answered by Max C. • Maths tutor
7162 Views

Find the equation of the line passing through the point ( 2, −3) which is parallel to the line with equation y + 4x = 7

First we rearrange the equation y + 4 x = 7 to y = −4 x + 7 So we can see that the gradient of this equation is −4. Since the line we are looking for is parallel, it must have the same gradient, −4. So now w...
JK
Answered by James K. • Maths tutor
5895 Views

A group of 120 Year 4s and Year 5s are going on a school trip. 60% of the children going on the trip are Year 4s, and of the Years 4s, 1/4 are boys. How many Year 4 girls are going on the trip?

There are quite a few stages to this problem, so let's work through each piece of information one by one. We know that the total number of children is 120, and 60% are Year 4s. Finding 60% straight away can ...
JK
Answered by James K. • Maths tutor
3717 Views