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Simplify fully: (7x^2 - 21x)/(x^2 + 2x - 15)

This one is quite complicated to answer typed up like this and i would definitley use a white board Show that 7x^2 - 21x can be come x(7x-21) which can in turn become 7x(x-3) Show that x^2 + 2x - 15 can b...

DG
Answered by Dominic G. Maths tutor
4855 Views

A tank is filled with water up to the height H0. At the bottom of the tank, there is a tap which is opened at t=0. How does the height of liquid change with time?(Hint: dH/dt is proportional to -H)

This is a typical C4 differential equation question. The same algorithm could be used for a lot of other problems.

First of all, from the hint we have that dH/dt = -kH (1).

We need to separa...

MB
Answered by Maxim B. Maths tutor
6693 Views

Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square

First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7).  

y = x2 - 10x , we want to change the form of this equation from  x2

JP
Answered by James P. Maths tutor
9362 Views

How do you integrate ln(x) with respect to x?

Rewrite ln(x) as 1ln(x) then integrate by parts.  The formula for integration by parts is  uv' = uv -  vu', here use u = ln(x) and v' = 1.  By differentiating u we get u' = 1/x, an...

AG
Answered by Anthony G. Maths tutor
2847 Views

What is 2/3 + 1/4?

When adding or subtracting fractions, we must always start by putting the fractions over the same denominator, that is the number on the bottom half of the fraction. To do this, we need to find ...

CC
Answered by Catherine C. Maths tutor
191228 Views

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