Please help me solve this
1 answer:
9514 1404 393
Answer:
a) q = 15 at minimum average cost; q = 10 at minimum marginal cost
b) marginal cost = average cost = 225 at q = 15
Explanation:
The average cost is the total cost divided by the number of units.
A = C/q = 300 -10q +1/3q^2
The marginal cost is the derivative of the total cost.
M = 300 -20q +q^2
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a) The minimum average cost is where its derivative is zero.
A' = 0 = -10 +2/3q ⇒ q = 15
The minimum marginal cost is where its derivative is zero.
M' = -20 +2q ⇒ q = 10
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b) The average cost for 15 units produced is ...
A(15) = 300 -10(15) +1/3(15^2) = 225
The marginal cost at that same production level is ...
M(15) = 300 -20(15) +15^2 = 225
The average cost and marginal cost are equal at the minimum average cost.
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Answer:
x = 4
Step-by-step explanation:
If you do not want to read the explanation go the the next part in bold
Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.
This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.
Below here is where the work is shown
a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²
5² = 25
3² = 9
we would then have 25 = 9 + b²
Next we subtract 9 from each side
25 - 9 = 16
9 - 9 cancels out
Now we have 16 = b²
finally we want to get rid of the ²
To do so we take the square root of each side
we're left with b = 4 which means that x = 4