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
Answer:
Step-by-step explanation:
The first four
Answer:
19 members
Step-by-step explanation:
54 / 2 = 227
27 / 3 = 9
9-1 = 8
27 - 8 = 19
19
Answer:
4 hours
Step-by-step explanation:
The distances and average speeds for the first two days driven are show below.
Step 1
We calculate the total distance covered in the first two days
First day: 6 hours at an average speed of 60 miles per hour
Hence:
1 hour = 60 miles
6 hours = x
x = 60 × 6
x = 360 miles
Second day: 4 hours at an average speed of 65 miles per hour
Hence:
1 hour = 65 miles
4 hours = x
x = 65 × 4
x = 260 miles
The distance covered for the first two days =
(360 + 260)miles
= 620 miles
Step 2
The total distance for the entire trip = 820 miles
Hence, the distance left to cover on the third day = (820 - 620)miles
= 200 miles
In the question, we are told:
If the average speed on the third day is 50 miles per hour,
The number of hours it will take for them to reach their family friends home is calculated using the formula
Time = Distance/Speed
Time = 200 miles/50 miles per hour
Time = 4 hours
