Answer:
![\large\boxed{\ln\sqrt[3]{e^4}=\dfrac{4}{3}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cln%5Csqrt%5B3%5D%7Be%5E4%7D%3D%5Cdfrac%7B4%7D%7B3%7D%7D)
Step-by-step explanation:
![\text{Use}\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\ln a^n=n\ln a\\\\\ln e=1\\-----------\\\\\ln\sqrt[3]{e^4}=\ln e^\frac{4}{3}=\dfrac{4}{3}\ln e=\dfrac{4}{3}\cdot1=\dfrac{4}{3}](https://tex.z-dn.net/?f=%5Ctext%7BUse%7D%5C%5C%5C%5C%5Csqrt%5Bn%5D%7Ba%5Em%7D%3Da%5E%5Cfrac%7Bm%7D%7Bn%7D%5C%5C%5C%5C%5Cln%20a%5En%3Dn%5Cln%20a%5C%5C%5C%5C%5Cln%20e%3D1%5C%5C-----------%5C%5C%5C%5C%5Cln%5Csqrt%5B3%5D%7Be%5E4%7D%3D%5Cln%20e%5E%5Cfrac%7B4%7D%7B3%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cln%20e%3D%5Cdfrac%7B4%7D%7B3%7D%5Ccdot1%3D%5Cdfrac%7B4%7D%7B3%7D)
Answer:
7. (-1, 10)
8. (7,-6)
9. C
10. One solution, Infinitely Many Solutions, No Solution
11. Adult tickets: 52 Student tickets: 68
5 wholes = 5
2 fifths = 2/5
5 - 2/5 = 4 3/5 (4 and 3 fifths)
Answer = 4 3/5
Check work:
4 3/5 + 2/5 = 5 (wholes)
The force needed to keep the cart at rest is 149.022 pounds
<h3>Force and Motion</h3>
Given Data
- Weight of cart = 200 pounds
The force needed to keep the cart at rest is the vertical component of the resultant force, hence we have
Fy = Mg sin θ
Substituting our given data we have
Fy = 200 sin 40
Fy = 200 *0.74511
Fy = 149.022 pounds
Learn more about force here:
brainly.com/question/12970081
