BAH! Domains & ranges

[starbuckscoffee]

HELP! (from the essential maths methods book Ex 1H)

1. The dimension of an enclosure are shown (the diagram at the bottom). The perimeter of the enclosure is 160m.
a. Find a rule for the area, A m^2, of the enclosure in terms of x (i got -x^2 + 76x -528 but that's wrong)

b. State a suitable domain of the function A(x)

2. A cuboid tank is open at the top and the internal dimension of its base are x m and 2x m. The height is h m. The volume of the tank is V cubic metres and the volume is fixed. Let S m^2 denotes the internal surface area of the tank.
a. i. Find S in terms of x and h,  ii. V and x

Thanks, (ps i've spent the last 3 hrs trying 2 figure it out with no luck)   

[/0]

EDIT: In the book the side length on the bottom is 20m. I am using that for my answer.

1.

a)

Area can be given by:

Also, the perimeter gives
                       

Solving for y gives:

And substituting this into gives:



b) From the diagram, we must have . We also must have , by so the domain of the Area function is

2.

a)
i)

ii) The volume of the tank is

Since we only need it to be in terms of V and x, we don't need h, so we solve for h.

[phagist_]

Quesion 1
Well you know the perimeter is 160 and from the diagram you can find that in terms of x and y.

I got as 160=2x+2y.

Then find the Area of the said shape in terms of x and y:



Now re-arrange first equation in terms of y;


Sub that into the Area formula you came up with to get;
which after expanding comes to;



Question 1b
You know
Looking at the diagram and thus the implied tomain is

I'll do the other one when I got time, but gotta run now.

[Mao]

b) From the diagram, we must have . We also must have , by so the domain of the Area function is

It should be therefore

[/0]

b) From the diagram, we must have . We also must have , by so the domain of the Area function is

It should be therefore

I decided to answer the question he referred to in the book.

[droodles]

im doing that enclosure question right now, god i really hate it