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First of all differentiate the equation of the curve implicitly, giving:

3x²-8y(dy/dx)=12y+12x(dy/dx)

=> (dy/dx)(12x+8y)=3x²-12y

=> dy/dx=(3x²-1...

e^x(u-1)

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....

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 c...

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 o...