For problems such as this, it can be handy to remember that
.. 1/(1/a +1/b) = ab/(a +b)
The time required to do a job is the inverse of the rate at which the job is done. Rates are added when people work together (in math problems, not in real life).
(2:44)*(3:14)/(2:44 +3:14) = 1:28:52.3
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2:44 = 41/15 hours = 82/30 hours
3:14 = 97/30 hours
Using the formula above, we have a "working together" time of
.. (82/30)*(97/30)/(82/30 +97/30) = 82*97/(30*179) = 3977/2685 . . . hours
.. = 1 hour 28 156/179 minutes
.. = 1 hour 28 minutes 52 52/179 seconds
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Learn to use the fraction functions on your calculator. They can be very helpful.
It's A 15.6
I know it's late but i hope i helped :D
Look at the picture.
![\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Csin%5Ctheta%7D%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7By%7D%7Br%7D%7D%3D%5Cdfrac%7Br%7D%7By%7D)
We have the right triangle x, y and r. From the Pythagorean theorem we have:
![r^2=x^2+y^2\to r=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=r%5E2%3Dx%5E2%2By%5E2%5Cto%20r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
We have the point
![\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%3B%5C%20%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29)
Substitute:
![r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29%5E2%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B4%7D%7B9%7D%2B%5Cdfrac%7B5%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B9%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D1)
![\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csqrt5%7D%7B3%7D%7D%3D%5Cdfrac%7B3%7D%7B%5Csqrt5%7D%3D%5Cdfrac%7B3%5Ccdot%5Csqrt5%7D%7B%5Csqrt5%5Ccdot%5Csqrt5%7D%3D%5Cboxed%7B%5Cdfrac%7B3%5Csqrt5%7D%7B5%7D%7D)
Answer: ![\bold{x^8}](https://tex.z-dn.net/?f=%5Cbold%7Bx%5E8%7D)
<u>Step-by-step explanation:</u>
![x^3\cdot x^5\quad =x^{3+5}\quad =\large\boxed{x^8}](https://tex.z-dn.net/?f=x%5E3%5Ccdot%20x%5E5%5Cquad%20%3Dx%5E%7B3%2B5%7D%5Cquad%20%3D%5Clarge%5Cboxed%7Bx%5E8%7D)
Answer:
The length of the ladder is 9.2m
Step-by-step explanation: