1. John can create 5 paintings per week.
2. Sasha can walk 30 minutes per mile.
3. Todd takes 24 minutes per room he cleans.
4. Victoria takes half of one day per necklace she makes.
5. Byron can make 12 cakes per day.
6. Charlie paid $130 for each table.
Answer:
1000000
Step-by-step explanation:
10x10x10x10x10x10=1000000
Answer: -7 = e
Step-by-step explanation: To solve this equation for <em>e</em>, we need to get <em>e</em> by itself on the right side of the equation. Since <em>e</em> is multiplied by 16, in order to get <em>e</em> by itself, we need to divide by 16 on the right side of the equation. If we divide by 16 on the right side of the equation, we must also divide by 16 on the left side of the equation.
On the right side of the equation the 16's cancel and we have <em>e</em>. On the right side of the equation -112 divided by 16 is -7. Remember that a negative divided by a positive is a negative.
So we have -7 = e which is the solution to our equation.
To check our solution, we can plug -7 in for <em>e</em> in the original equation. So we have -112 = 16 (-7) or -112 = -112 which is a true statement so our answer checks.
Answer:
It makes sense to me but I don't know if anyone else agrees
Step-by-step explanation:
Let c > 0. Then split the integral at t = c to write
By the FTC, the derivative is
![\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdf%7D%7Bdx%7D%20%3D%20%5Cleft%28%5Cfrac1x%20%2B%20%5Csin%5Cleft%28%5Cfrac1x%5Cright%29%5Cright%29%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%5Cfrac1x%5Cright%5D%20-%20%28%5Cln%28x%29%20%2B%20%5Csin%28%5Cln%28x%29%29%29%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%5Cln%28x%29%5Cright%5D%20%5C%5C%5C%5C%20%3D%20-%5Cfrac1%7Bx%5E2%7D%20%5Cleft%28%5Cfrac1x%20%2B%20%5Csin%5Cleft%28%5Cfrac1x%5Cright%29%5Cright%29%20-%20%5Cfrac1x%20%28%5Cln%28x%29%20%2B%20%5Csin%28%5Cln%28x%29%29%29%20%5C%5C%5C%5C%20%3D%20-%5Cfrac1%7Bx%5E3%7D%20-%20%5Cfrac%7B%5Csin%5Cleft%28%5Cfrac1x%5Cright%29%7D%7Bx%5E2%7D%20-%20%5Cfrac%7B%5Cln%28x%29%7Dx%20-%20%5Cfrac%7B%5Csin%28%5Cln%28x%29%29%7Dx%20%5C%5C%5C%5C%20%3D%20-%5Cfrac%7B1%20%2B%20x%5Csin%5Cleft%28%5Cfrac1x%5Cright%29%20%2B%20x%5E2%5Cln%28x%29%20%2B%20x%5E2%20%5Csin%28%5Cln%28x%29%29%7D%7Bx%5E3%7D)
