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: 9 days
Step-by-step explanation: you have to do the reverse
3d+2=29 Subtract 2 from both sides
3d=27 Divide 27 from both
d=9 The plant was planted 9 days ago
The van will need 25 gallons of gas for it to travel 550 miles. This is calculated by dividing 10 gallons to 220 miles to get the miles per gallons, which in this case is 22 miles per gallon. Then we have to divide 550 miles by 22 miles per gallon to get the total gas consumption, which is 25 gallons.
1,150ft + 35ft = 1,185ft
The reason you wouldnt subtract would be that you cant have negative 35 ft. You add the two heights together to produce your answer.
