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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...

Answered by Maxim B. • Maths tutor

6628 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

Answered by James P. • Maths tutor

9286 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...

Answered by Anthony G. • Maths tutor

2802 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 ...
Answered by Catherine C. • Maths tutor
188914 Views

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?
The key concepts to apply in this question will be the product and chain rules, namely: if f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x).

Equivalen...
Answered by Bromlyn C. • Maths tutor
4611 Views

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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)

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

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

What is 2/3 + 1/4?

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?

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