Answer:
Between 1000 and 5000 snowboards will make the function AP(x) >0.
Step-by-step explanation:
Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.
In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.
P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:
![r_1,r_2 = \frac{-6 ^+_- \sqrt{6^2-4*(-1)*(-5)} }{2*(-1)} = \frac{-6^+_-\sqrt{16}}{-2} = \{1, 5\}](https://tex.z-dn.net/?f=r_1%2Cr_2%20%3D%20%5Cfrac%7B-6%20%5E%2B_-%20%5Csqrt%7B6%5E2-4%2A%28-1%29%2A%28-5%29%7D%20%7D%7B2%2A%28-1%29%7D%20%3D%20%5Cfrac%7B-6%5E%2B_-%5Csqrt%7B16%7D%7D%7B-2%7D%20%3D%20%5C%7B1%2C%205%5C%7D)
Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:
- P(0) = -5 < 0 ( P is negative in (-∞ , 1) )
- P(2) = -4+6*2-5 = 3 > 0 (P is positive in (1,5) )
- P(6) = -36+36-5 = -5 < 0 (P is negative in (5, +∞) )
The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)
4 3/16=(4·16+3)/16=67/16=4,1875 (pink ribbon)
5 1/16=(5·16+1)/16=81/16=5,0625 (green ribbon)
4,1875+5,0625=9,25 (total)
9,25·1,60=$14,8
<em>Answer: $14,8</em>
This would be 1/6 of 180 or 1/6 x 180 which makes the cities 30 miles apart.
Complete Question:
Kim accidentally leaves the water hose running half a day. the graph represents the loss of water during that time. use the graph to complete the following statement:
The rate at which water flows from the hose is *blank* gallons per hour.
See attachment for graph
Answer:
8 gallons per hour
Step-by-step explanation:
Required
Determine the rate of water loss
<u>To get the rate, we simply calculate the slope (m) of the graph using the following formula</u>
![m = \frac{y_1 - y_2}{x_1 - x_2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_1%20-%20y_2%7D%7Bx_1%20-%20x_2%7D)
Where the x's and y's represent corresponding values of x and y on the graph
So, we have:
![(x_1,y_1) = (5,40)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%285%2C40%29)
![(x_2,y_2) = (10,80)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2810%2C80%29)
becomes
![m = \frac{40 - 80}{5 - 10}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B40%20-%2080%7D%7B5%20-%2010%7D)
![m = \frac{- 40}{- 5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-%2040%7D%7B-%205%7D)
![m = \frac{40}{5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B40%7D%7B5%7D)
![m = 8](https://tex.z-dn.net/?f=m%20%3D%208)
<em>Hence, the rate at which water flows from the hose is 8 gallons per hour</em>
I think the answer is -48°F