Answer:
7.5 miles / hour
Step-by-step explanation:
See the step-by-step solution in the picture attached below.
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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
The solution to the compound inequality given as 6b < 36 or 2b + 12 > 6 is b < 6 or b > -3
<h3>How to solve the
compound inequality?</h3>
The compound inequality is given as:
6b < 36 or 2b + 12 > 6
Evaluate the like terms in the individual inequalities
6b < 36 or 2b > -6
Divide the individual inequalities by the coefficients of b
b < 6 or b > -3
Hence, the solution to the compound inequality given as 6b < 36 or 2b + 12 > 6 is b < 6 or b > -3
Read more about compound inequality at
brainly.com/question/1485854
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Yes, the simplified fraction would 423/500
