We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
Answer:
Hydrostatic Force = 14952.35N
Step-by-step explanation:
From the question, we are given;
Diameter of hemispherical plate = 6 ft
Height of submergence = 2ft
Weight density of water = 62.5 lb/ft³
Now, if we assume that the hemispherical plate is residing on x and y axis, then bottom of the plate is on x-axis while the left side of the plate touches the y-axis
Now, the plate is defined by the upper half of the circle as;
(x - 3)² + (y-0)² = 3²
(x - 3)² + y² = 9
Thus, y² = 9 - (x - 3)²
y = √(9 - (x - 3)²)
To solve this, hydro static force on one side of plate is given as;
F = ∫ ρgd•xw(x)δx =
2∫ρgx√(9 - (x - 3)²)δx at boundary of 3 and 0
F = 62.5•9.8•2∫x√(9 - (x - 3)²)δx at boundary of 3 and 0
F = 1225[(27π/4) - 9]
F = 1225 x 12.206 = 14952.35N
Answer:
h= 33mm
volume of square pyramid =1/3 Sh
5 x 5=25 /3 =8.3
275/8.3 =33
12. 1/7
13. 1/2
14. 1/2
15. 1/8
16. 1/4
Answer:
It depends what x equals.
Step-by-step explanation:
There's plenty of resources on places like Khan Academy to help.