Answer:
Step-by-step explanation:
After 3 hours, Spike charges 6 dollars per hour. For 3 hours, the charge is only $5×3 = $15 (which is $3 less than $6×3). So the rate after 3 hours can be modeled by ...
s(h) = 6h -3
For 8 hours, s(8) = 6·8 -3 = 45 . . . . dollars
__
After 4 hours, Main Deck charges 8 dollars per hour. For 4 hours, the charge is only $18 (which is $14 less than $8×4). So the rate after 4 hours can be modeled by ...
m(h) = 8h -14
For 8 hours, m(8) = 8·8 -14 = 50 . . . . dollars
__
For 8 hours, the $45 charge at Spike's is $5 less than the $50 charge at Main Deck.
Average =
2 + 7 + 19 + 24 + 25
——————————
5
=
77
—
5
= 15.4
Answer:
D. 8-cm square
Step-by-step explanation:
The smaller square shown on the figure has an area of 15×15 = 225. The sum of the two smaller square areas must equal the larger square area, so the smallest square must have an area of ...
289 -225 = 64
Its side dimensions will be √64 = 8 cm.
The diagram is correctly completed by the 8 cm square.
By calculating the slope, the average rate of change is -2
-1-11
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1--5
Answer: The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Step-by-step explanation: This is a optimization with restrictions problem.
The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).
This restriction can be expressed as:
being x: the side of the square of the cross section and L: length of the package.
The volume, that we want to maximize, is:
If we express L in function of x using the restriction equation, we get:
We replace L in the volume formula and we get
To maximize the volume we derive and equal to 0
We can replace x to calculate L:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.