9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The equation of a vertical line is of the form ...
x = constant
In order to make that line go through a point that has an x-coordinate of 5, the value of the constant must be 5.
x = 5
Chrissy's vacation would have been 5 days total. To find this, you can set up a proportion. I did 40 over 100, (40%), equals 2 over x. You cross multiply 2 and 100. You take that number, 200 in this case, and divide it by 40 to get the variable by itself. This would leave you with what the variable equals, 5.
Answer:
11.547 ft wide by 5.774 ft high
769.800 ft³ capacity
Step-by-step explanation:
Volume is maximized for a given area by having the area of a pair of opposite sides equal the area of the bottom. That means the overall area of the container is 3 times the area of the bottom. Then the square bottom will have a width of ...
w = √(400/3) ≈ 11.547 . . . feet
The height is half that, so is ...
h = w/2 = 11.547/2 ≈ 5.774 . . . feet
The capacity is then ...
w²h = (11.547 ft)²(5.774 ft) = 769.800 ft³
The container is 11.547 ft wide by 5.774 ft high. It has a capacity of 769.800 cubic feet.
_____
You want to maximize w^2h subject to w^2 + 4wh = 400. Solving the constraint equation for h, we get h = (400 -w^2)/(4w) and the volume we want to maximize can be written as ...
V = w(400-w^2)/4
This will be an extreme when dV/dw = 0, so we want to solve ...
dV/dw = 0 = 100 -(3/4)w^2
w^2 = 400/3
w = √(400/3) . . . . . as above
It is <em>1/100 . It is simple </em>
