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The line AB has equation 3x + 5y = 7. Find the gradient of line AB.

First, let's make y the subject of the equation.

Let's achieve this by having only y on the left hand side of the equation. To do this we need to minus 3x from both sides of the equation. This leav...

Answered by Tom O. • Maths tutor

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The volume of liquid in a container is given by v=(3h^2+4)^(3/2)-8, find dV/dh when h = 0.6

Chain rule: dV/dh=9h(3h^2+4)^(1/2)
sub in h=0.6 , dV/dh = 12.17

Answered by Johnny H. • Maths tutor

8959 Views

Given that y=(4x^2)lnx, find f"(x) when x=e^2

Product rule: first order derivative = 8xlnx+4x Second order derivative = 8lnx+12 Sub in e^2 , 16lne + 12 = 24

Answered by Johnny H. • Maths tutor

5149 Views

What is the difference between differentiation and integration, and why do we need Calculus at all?

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a sp...

Answered by Samuel H. • Maths tutor

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The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula)

First plug in valu...

Answered by Rachel Y. • Maths tutor

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