Answer:
Story in Explanation
Step-by-step explanation:
There are three different types of sandwiches available for you and your friend to eat. They all look yummy, and you and your friend decide to get half of every sandwich. When you cut sandwiches in half, how many do you now end up with?
Answer:
x=-1
Step-by-step explanation:
![\frac{x ^{100} + 1 }{x + 1}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%5E%7B100%7D%20%2B%201%20%7D%7Bx%20%2B%201%7D%20)
![x + 1 = 0](https://tex.z-dn.net/?f=x%20%2B%201%20%3D%200)
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20%20-%201)
Answer:
a. Average cost equation
![\bar c=0.02Q+0.65+250Q^{-1}](https://tex.z-dn.net/?f=%5Cbar%20c%3D0.02Q%2B0.65%2B250Q%5E%7B-1%7D)
b. Q = 112 units
c. Average cost (Q = 112 units) = GHS 5.12
d. Usually, the actual production capacity.
Step-by-step explanation:
We will use $ as the currency symbol for GHS.
a) We have:
- Variable costs: 0.65Q
- Fixed costs: 250
- Special costs: 0.02Q^2
Then we can write the total cost equation as:
![C(Q)=0.65Q+250+0.02Q^2](https://tex.z-dn.net/?f=C%28Q%29%3D0.65Q%2B250%2B0.02Q%5E2)
The average cost function can be calculated dividing the total cost equation by Q. Then, we have:
![\bar c=\dfrac{C(Q)}{Q}=\dfrac{0.02Q^2+0.65Q+250}{Q}=0.02Q+0.65+250Q^{-1}](https://tex.z-dn.net/?f=%5Cbar%20c%3D%5Cdfrac%7BC%28Q%29%7D%7BQ%7D%3D%5Cdfrac%7B0.02Q%5E2%2B0.65Q%2B250%7D%7BQ%7D%3D0.02Q%2B0.65%2B250Q%5E%7B-1%7D)
b) The output level that minimize the average cost can be calculated deriving the average cost equation and making it equal to zero:
![\dfrac{d\bar c}{dQ}=0.02+(-1)250Q^{-2}=0.02-250Q^{-2}=0\\\\\\\dfrac{250}{Q^2}=0.02\\\\\\Q^2=250/0.02=12,500\\\\Q=\sqrt{12,500}\approx 112](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5Cbar%20c%7D%7BdQ%7D%3D0.02%2B%28-1%29250Q%5E%7B-2%7D%3D0.02-250Q%5E%7B-2%7D%3D0%5C%5C%5C%5C%5C%5C%5Cdfrac%7B250%7D%7BQ%5E2%7D%3D0.02%5C%5C%5C%5C%5C%5CQ%5E2%3D250%2F0.02%3D12%2C500%5C%5C%5C%5CQ%3D%5Csqrt%7B12%2C500%7D%5Capprox%20112)
The output level that minimizes cost is Q=112 units.
c. The average cost of production for the output level of 112 is:
![\bar c=0.02Q+0.65+250Q^{-1}\\\\\bar c(112)=0.02*112+0.65+250/112\\\\\bar c(112)=2.24+0.65+2.23\\\\\bar c(112)=5.12](https://tex.z-dn.net/?f=%5Cbar%20c%3D0.02Q%2B0.65%2B250Q%5E%7B-1%7D%5C%5C%5C%5C%5Cbar%20c%28112%29%3D0.02%2A112%2B0.65%2B250%2F112%5C%5C%5C%5C%5Cbar%20c%28112%29%3D2.24%2B0.65%2B2.23%5C%5C%5C%5C%5Cbar%20c%28112%29%3D5.12)
d. The limitation is not specified, by this models have a range of Q values where it is valid. These range is usually dependent on the scale of the production. The factory will have a maximum level of production, and over this level, the cost equation is different as other investments are needed.
Answer:
Option D is correct.
The equation with roots 3 plus or minus square root 2 is x² - 6x + 7
Step-by-step explanation:
The roots of the unknown equation are
3 ± √2, that is, (3 + √2) and (3 - √2)
The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation
x = (3 + √2) or x = (3 - √2)
The equation is this
[x - (3 + √2)] × [x - (3 - √2)]
(x - 3 - √2) × (x - 3 + √2)
x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)
= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2
Collecting like terms
= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2
= x² - 6x + 7
Hope this Helps!!!
Answer:
-3x + 5
Step-by-step explanation:
"Rise over Run"
(0, 5) => (1,2): Goes down (negative slope) 3 units and right 1 unit.
The Y intercept is 5 so the constant is 5.