<h2>
Rate at which area is increasing is 1.08 m²/s.</h2>
Step-by-step explanation:
Area of triangle is with side a and b and angle C between them is given by
A = 0.5 ab SinC
Here we need to find how area changes with a and b fixed and C is changing,
![\frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%20%280.5%20absinC%5Cright%20%29%5C%5C%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%3D0.5ab%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%20%28sinC%5Cright%20%29%5C%5C%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%3D0.5abcosC%5Cfrac%7BdC%7D%7Bdt%7D)
We have
a = 8 m
b = 9 m
![C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cpi%7D%7B3%7Drad%5C%5C%5C%5C%5Cfrac%7BdC%7D%7Bdt%7D%3D0.06rad%2Fs)
Substituting
![\frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D0.5%5Ctimes%208%5Ctimes%209%5Ctimes%20cos%5Cleft%20%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright%20%29%5Ctimes%200.06%5C%5C%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%3D1.08m%5E2%2Fs)
Rate at which area is increasing is 1.08 m²/s.
Nick has tennis practice every sixth day = 6
Mark has tennis practice every 4th day = 4
They both had tennis practice on = 31st July
We have to find when will be the next time that they both have practice on the same day?
For this, we will find the LCM of 4 and 6
So, LCM of 4 and 6 is 12.
So, it will be 12 days after 31st July, that they will practice on the same day.
So it is 12th August.
Answer:
15,000 liters
Step-by-step explanation:
First, find the volume in meters. 5*3*1=15 meters
1 meter = 1000 liters
(x15)
15 meters = 15000 liters
Hope this helped :D