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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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A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates where the line crosses the x and y axes

m=3 y1=1 x1=2 y-y1=m(x-x1) y-1=3(x-2) y-1=3x-6 y=3x-5 at the x-axis, y=0. Sub in to find the x co-ordinate: 0=3x-5 x=5/3. Hence the co-ordinates at which the line crosses the x axis are (5/3,0) at the y-axis...
AC
Answered by Anna C. • Maths tutor
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What is the partial fraction expansion of (x+2)/((x+1)^2)?

First we write the fraction in terms of partial fractions with two unknown numerators, A and B, as follows: (x+2)/(x+1) 2 = A/(x+1) + B/(x+1) 2 Note that since the denominator of the original fraction is of ...
KR
Answered by Kim R. • Maths tutor
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find the integral of 1+3 root x

now for any integral the method to deal with it is look for the easiest method, things can get trickier later down the line but always start by looking for the easy solution. this example allows us to see it...
HD
Answered by Harry D. • Maths tutor
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The element of a cone has length L. For what height H (with respect to L) will the volume of the cone be the largest?

This is a good exercise to introduce student to the idea of derivatives and their possible practical use. Firstly, I should draw the cone and notice that its volume is equal to 1/3 pi H*R 2 (where R - radius...
MK
Answered by Max K. • Maths tutor
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