The perimeter of the park is 3x^2 + 37x - 4
<h3>How to determine the perimeter?</h3>
The side lengths of the triangular park are:
10x + 3x^2 - 8, 12x and 15x + 4
Add these sides to determine the perimeter
P = 10x + 3x^2 - 8 + 12x + 15x + 4
Collect the like terms
P = 3x^2 + 10x + 12x + 15x - 8 + 4
Evaluate the sum
P = 3x^2 + 37x - 4
Hence, the perimeter of the park is 3x^2 + 37x - 4
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Answer:
1,825 days
Step-by-step explanation:
730 / 2 = 365 (one year, or the number of days a single revolution around the sun takes)
Now just multiply by 5
[365 · 5 = 1,825], thus 1,825 days are the duration of 5 revolutions.
The problem could also be initially expressed as:
x = (720/2) · (5) with x representing the missing value
Answer:
Spreadsheet values
- B3 = $15 (shown)
- C4 = $420 (shown)
- D6 = $272.5
- E4 = $6
- F2 = $16
- F6 = $5
Other values
- profit maximizing Q: 35
- profit maximizing P: $13
- maximum profit: $227.5
Step-by-step explanation:
Labeling the columns of the spreadsheet A--F, and the rows 1--7, we want to find the values as follows.
a) The relationship between quantity, price, and revenue is ...
total revenue = quantity × price
price = (total revenue)/quantity
Then ...
- B3 = 375/25 = 15 (as shown)
- C4 = 30×14 = 420 (as shown)
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b) The relationship between total cost and marginal cost is ...
mc2 = (tc2 -tc1)/(q2 -q1)
tc2 = (mc2)(q2 -q1) +tc1
Then ...
- D6 = 9(40 -35) +227.5 = 272.5
- E4 = (192.5 -162.5)/(30 -25) = 6
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c) Marginal revenue is figured the same way as marginal cost.
mr2 = (r2 -r1)/(q2 -q1)
Then ...
- F2 = (320 -0)/(20 -0) = 16
- F6 = (480 -455)/(40 -35) = 5
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d) The quantity maximizing profit will be the quantity such that marginal revenue is equal to marginal cost. That is, marginal profit is zero. That quantity is 35, where both marginal cost and marginal revenue are 7.
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e) The price at a quantity of 35 is 13. This value is read from the given table.
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f) The maximum profit is the difference between revenue and cost at the profit-maximizing quantity:
maximum profit = 455 -227.5 = 227.5
Answer:2693
Step-by-step explanation:
Answer:
Each cube with side lengths of 1/4 has a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.
Step-by-step explanation:
