Let x = one of the side lengths of the base.
Then area of the base = x². So volume of the base = x²h.
That gives us x²h = 20. Solving for x, we get x = √(20/h²).
Glass is needed to cover the sides of the aquarium. There are 4 sides and 1 base. Area of a side = hx = h√(20/h²). Area of the base = x² = 20/h. Total area of glass = h√(20/h²) + 20/h. So the cost for glass = 8 * [h√(20/h²) + 20/h] = 8 h√(20/h²) + 160/h.
Metal frame is needed along the edges of the sides. There are 4 edges on the top, 4 edges in the bottom and 4 vertical edges. So the total length of metal frame = 4x + 4x + 4h = 8 √(20/h²) + 4h. Then the cost for metal frame = 7 * [8 √(20/h²) + 4h] = 56 √(20/h²) + 28h.
So the total cost = 8 h√(20/h²) + 160/h + 56 √(20/h²) + 28h
The slope for number one would be negative 3 i think
negative 5 x less than or equals minus 10
-5x<=-10
divide by -5 (this will flip the inequality)
x>=2
Solution: x>=2
. An integrating factor would
to get
![\dfrac{\mathrm d}{\mathrm dy}[x\log y]=\dfrac{\log y}y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dy%7D%5Bx%5Clog%20y%5D%3D%5Cdfrac%7B%5Clog%20y%7Dy)
