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Maths
A Level

For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?

100=ab

P=2a+2b

P=2a+200/a

dP/da=2-200/a^2

dP/da=0 implies 2=200/a^2

a^2=100

a=-10,10

a is a length so t...

DN
Answered by Daniel N. Maths tutor
10700 Views

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

DJ
Answered by Dylan J. Maths tutor
8505 Views

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

cos(2x) = 2cos2(x)-1 by the double angle formula.

Rearrange to give cos2(x) = (cos(2x)+1)/2

Integrating this gives sin(2x)/4 + 1/4x + c 

...

MC
Answered by Max C. Maths tutor
5300 Views

What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?

A stationary point simply means a point in a curve where the gradient is equal to 0.For example, in the June 2015 C3 Paper it is asked:Find the exact values of the coordinates of the stationary points of ...

ML
Answered by Martin L. Maths tutor
5081 Views

A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.

At first glance, this looks quite tricky, as usually when we are asked to find dy/dx, we have one equation, but here we have 2.So in this case, we need to use the statement that dy/dx = (dy/dt) * (dt/dx)T...

WM
Answered by Wesley M. Maths tutor
10043 Views

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