Answer:
The change in revenue from the sale of one more doghouse if 110 doghouses have already been sold is dR/dx=66.67 $/doghouse.
Step-by-step explanation:
We have a revenue function that is:
We have to approximate the change in revenue from the sale of one more doghouse, if 110 doghouses have already been sold.
That is the marginal revenue at x=110.
The marginal revenue is expressed as the first derivative of the revenue.
Then, we calculate the derivative of R:
![\dfrac{dR}{dx}=\dfrac{d}{dx}[14,000\cdot \text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\dfrac{d}{dx}[\text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot \dfrac{d}{dx}(0.01x+1)\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot 0.01\\\\\\\dfrac{dR}{dx}=\dfrac{14,000}{x+100}](https://tex.z-dn.net/?f=%5Cdfrac%7BdR%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5B14%2C000%5Ccdot%20%5Ctext%7Bln%7D%280.01x%2B1%29%5D%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Cdfrac%7Bd%7D%7Bdx%7D%5B%5Ctext%7Bln%7D%280.01x%2B1%29%5D%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Ccdot%5Cdfrac%7B1%7D%7B0.01x%2B1%7D%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%280.01x%2B1%29%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D14%2C000%5Ccdot%5Cdfrac%7B1%7D%7B0.01x%2B1%7D%5Ccdot%200.01%5C%5C%5C%5C%5C%5C%5Cdfrac%7BdR%7D%7Bdx%7D%3D%5Cdfrac%7B14%2C000%7D%7Bx%2B100%7D)
We then evaluate this marginal revenue at point x=110:
Answer:
Both sides must remain equal.
Step-by-step explanation:
An equation features an equal sign in the middle, therefore showing that both sides are always equal to each other. That is why the answer is equal.
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➷ Multiply the total value by 1/4:
1/4 x 8 = 2
He practiced it for 2 hours.
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Answer: The answer is 972.
Step-by-step explanation: The formula for the volume if a cylinder is πr2h and the radius is 9 and to the second power is 81. So then the radius multiplied by the height (which is 12) is 972 which is the answer.
Answer:
Step-by-step explanation: It would take him 15 minutes more to mow the whole yard
1/2 hour is 30 mins divided by 2 which is 15 mines times 3 is 45 mins total mins
