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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 take positive a, a=10 so b=10 gives perimeter 40m Notice a=10 b=10 is a square Squares are rectangles of ...
DN
Answered by Daniel N. • Maths tutor
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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
10087 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
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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 the...
ML
Answered by Martin L. • Maths tutor
6409 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)Then...
WM
Answered by Wesley M. • Maths tutor
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