Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:
Simplify:
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Answer:
Step-by-step explanation:
Given the Total revenue R(x) = 2x
Cost C(x) = 0.01x²+0.3x+30 where;
x = 30 and dx/dt = 9units per day.
Rate of change of revenue dR/dt = dR/dx • dx/dt
dR/dt = 2dx/dt
dR/dt = 2(9) = $18
Rate of change of revenue with respect to time is 18dollars/day.
Rate of change of cost dC/dt = dC/dx • dx/dt
dC/dt = (0.02x+0.3)dx/dt
dC/dt at x = 30 and dx/dt = 9 will give;
dC/dt = {0.02(30)+0.3}×9
dC/dt = (0.6+0.3) × 9
dC/dt = 0.9×9
dC/dt = $8.1
Rate of change of cost with respect to time is 8.1dollars/day
Profit = Revenue - Cost
Profit = 18-8.1
Daily Profit = $9.9
Answer:
x = 12
Step-by-step explanation:
IMPORTANT: Both answers should add up to 180 if they dont you did it wrong!
(10x - 20) + (6x + 8 ) = 180 plug in 12 for both of them
(10 * 12 - 20) + 6 * 12 + 8) = 120
(120 - 20) + (72+ 8 ) = 180
(100) + (80) = 180
so x = 12
hope this helps please make brainliest
Answer: 27 rows contain 25 vines.
Step-by-step explanation:
Let x represent the number of rows that contain 20 vines.
Let y represent the number of rows that contain 25 vines.
Sarah plants 760 vines in rows containing either 20 vines or 25 vines. This means that
20x + 25y = 760- - - - - - - - - - -1
There are 3 times as many rows containing 25 vines as there are rows containing 20 vines. This means that
y = 3x
Substituting y = 3x into equation 1, it becomes
20x + 25 × 3x = 760
20x + 75x = 760
95x = 760
x = 760/95
x = 9
y = 3x = 3 × 9
y = 27
