Answer:
0.07017
Step-by-step explanation:
Answer:
0.5152
Step-by-step explanation:
Answer:
Step-by-step explanation:
The average length of the weird trapezoidal shape on the left is
(2 m + 10 m)/2, or 6 m. The width is 4 m, so the area is 24 m^2.
The area of the semicircle is (1/2)(pi)(2 m)^2, or 2pi m^2.
Thus, the overall area of the green shape is 24 m^2 + 2pi m^2.
Answer:
2(x - 7)(x + 2)
Step-by-step explanation:
Given
2x² - 10x - 28 ← factor out 2 from each term
= 2(x² - 5x - 14) ← factor the quadratic
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2 , since
- 7 × 2 = - 14 and - 7 + 2 = - 5 , thus
x² - 5x - 14 = (x - 7)(x + 2) and
2x² - 10x - 28 = 2(x - 7)(x + 2)
Answer:
160 units and $6400
Step-by-step explanation:
We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2
the price per unit is 100, therefore revenue for each unit would be 100 * x
However:
profit = revenue - cost
p (x) = 100 * x - 20 * x - 0.25 * x ^ 2
for the maximum value profit we must derive and equal 0:
p '(x) = 100 - 20 - 0.5 * x
0 = 80 - 0.5 * x
0.5 * x = 80
x = 80 / 0.5
x = 160
Therefore, the maximum profit occurs when there are 160 units, replacing we have:
p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2
p (x) = 6400
that is to say that the $ 6400 is the maximum profit.
