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Find the gradient of the curve (x^3)-4(y^2)=12xy at the point P(-8,8)

First of all differentiate the equation of the curve implicitly, giving: 3x 2 -8y(dy/dx)=12y+12x(dy/dx) => (dy/dx)(12x+8y)=3x 2 -12y => dy/dx=(3x 2 -12y)/(12x+8y) As dy/dx is the gradient of the curve,...
FG
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whats the integral of x.e^x wrt x

e^x(u-1)
PC
Answered by Peter C. • Maths tutor
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An open-topped fish tank is to be made for an aquarium. It will have a square base, rectangular sides, and a volume of 60 m3. The base materials cost £15 per m2 and the sides £8 per m2. What should the height be to minimise costs?

Establish the areas of each of the five faces of the aquarium in terms of x and y, and then sum to obtain a function of the cost in x and y. Then identify that the volume also gives a function in x and y. Re...
JP
Answered by Jonny P. • Maths tutor
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Trigonometry: what is it, and how do I do it?

Trigonometry is used in maths to find angles and the lengths of edges in triangles. There are three main operations: sin, cos and tan, and these are used to convert the information you have about a triangle,...
AR
Answered by Amy R. • Maths tutor
4903 Views

what is the Pythagoras theorem?

The pythagoras theorem is the rule used to work out the length of side of a right angle triangle with one length mising and two known lengths of side. The rule states that a 2 = b 2 +c 2 . "a" repr...
JK
Answered by Joseph K. • Maths tutor
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