Emmett's total yards rounded to the nearest thousand is 18,000 yards.
Answer:![12.74 ft^2/s](https://tex.z-dn.net/?f=12.74%20ft%5E2%2Fs)
Step-by-step explanation:
Given
Two sides of triangle of sides 5 ft and 7 ft
and angle between them is increasing at a rate of 0.9 radians per second
let
is the angle between them thus
Area of triangle when two sides and angle between them is given
![A=\frac{ab\sin C}{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bab%5Csin%20C%7D%7B2%7D)
![A=\frac{5\times 7\times \sin \theta }{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B5%5Ctimes%207%5Ctimes%20%5Csin%20%5Ctheta%20%7D%7B2%7D)
Differentiate w.r.t time
![\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\cos theta }{2}\times \frac{\mathrm{d} \theta }{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B35%5Ccos%20theta%20%7D%7B2%7D%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Ctheta%20%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
at ![\theta =\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B5%7D)
![\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\times cos(\frac{\pi }{5})}{2}\times 0.9](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B35%5Ctimes%20cos%28%5Cfrac%7B%5Cpi%20%7D%7B5%7D%29%7D%7B2%7D%5Ctimes%200.9)
![\frac{\mathrm{d} A}{\mathrm{d} t}=12.74 ft^2/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20A%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D12.74%20ft%5E2%2Fs)
To solve this problem we can make a proportion.
6 5
-- = ---
10 x
to solve this proportion we can cross multiply and divide.
5 times 10 is 50. divided by 6 is 8.3
it will take her 8.3 minutes to run 5 laps
Answer:
360 feet
Step-by-step explanation:
multiple 6 by 12 to get the area of the individual plot of land given to a single worker.
Then multiply by 5 for all 5 workers getting the same plot of land.