<h2>It takes 3 hours to empty the tank when the pumping rate is 180 gallons per hour.</h2>
Step-by-step explanation:
The time t (in hours) that it takes a pump to empty a tank of water varies inversely with the pumping rate r (in gallons per hour).
![t=\frac{k}{r}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bk%7D%7Br%7D)
where k is a constant.
It takes 9 hours to empty a tank of water when the pumping rate is 60 gallons per hour.
![9=\frac{k}{60}\\\\k=540gallons](https://tex.z-dn.net/?f=9%3D%5Cfrac%7Bk%7D%7B60%7D%5C%5C%5C%5Ck%3D540gallons)
We need to find how long does it take to empty the tank when the pumping rate is 180 gallons per hour ( r = 180)
We have
![t=\frac{k}{r}\\\\t=\frac{540}{180}\\\\t=3hours](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bk%7D%7Br%7D%5C%5C%5C%5Ct%3D%5Cfrac%7B540%7D%7B180%7D%5C%5C%5C%5Ct%3D3hours)
It takes 3 hours to empty the tank when the pumping rate is 180 gallons per hour.
Answer:
its 2 8/11
Step-by-step explanation:
i hope this helps have a good day
Answer:
Juan wins the race
Step-by-step explanation:
<u>The graph is shown in attached image.</u>
<u />
The black line is Juan's graph.
The green line is Antonio's graph.
The graph shows the distance (y-axis) with time (x-axis).
The end of the curve(s) means the end of the race. Both curve's ending point in y-axis is 4 miles so the end of the race is 4 miles.
But in x-axis, we see the time:
Juan finishes at 13 minutes
Antonio finishes at 15 minutes
<u>Definitely Juan wins the race</u>
Answer:
The volume would be 18.85
Step-by-step explanation:
hope this helps and have a good day : )
Answer:
8) h = 30
r = 16
l= 34
Surface Area= 2514.28
Volume= 8045.71
9) r = 12
h = 2
l = 5/2
Surface Area= 908.08
Volume= 298.42
Step-by-step explanation:
8)
h = 30
r = 16
l=?
Since its is right angled triangle, using pythogras theorem we can find the length of cone
l^2 = h^2 + r^2
l^2 = (30)^2 + (16)^2
l^2 = 900 + 256
l^2 = 1156
Taking square root on both sides
√l^2 = √1156
l = 34
Surface Area =
[/tex]
π = 22/7, r = 16, h=30
Surface Area = ![=\frac{22}{7}* 16(16+\sqrt{(30)^2+(16)^2})\\=\frac{22}{7}* 16(16+34)\\=\frac{22}{7}* 800\\=2514.28](https://tex.z-dn.net/?f=%3D%5Cfrac%7B22%7D%7B7%7D%2A%2016%2816%2B%5Csqrt%7B%2830%29%5E2%2B%2816%29%5E2%7D%29%5C%5C%3D%5Cfrac%7B22%7D%7B7%7D%2A%2016%2816%2B34%29%5C%5C%3D%5Cfrac%7B22%7D%7B7%7D%2A%20800%5C%5C%3D2514.28)
Volume = ![\pi r^2\frac{h}{3}](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%5Cfrac%7Bh%7D%7B3%7D)
π = 22/7, r = 16, h= 30
Volume = ![\frac{22}{7} * (16)^2 *\frac{30}{3}\\=\frac{22}{7} * 256 *10\\= 8045.71](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B7%7D%20%2A%20%2816%29%5E2%20%2A%5Cfrac%7B30%7D%7B3%7D%5C%5C%3D%5Cfrac%7B22%7D%7B7%7D%20%2A%20256%20%2A10%5C%5C%3D%208045.71)
9)
r = ?
h = 2
l = 5/2
Since its is right angled triangle, using pythogras theorem we can find the radius of cone
l^2 = h^2 + r^2
(5/2)^2 = (30)^2 + (r)^2
25/4 = 900 + r^2
r^2 = 900 * 4/25
Taking square root on both sides
√r^2 = √144
r = 12
Surface Area =
[/tex]
π = 3.14, r = 12, h=2
Surface Area = ![=3.14* 12(12+\sqrt{(12)^2+(2)^2})\\=3.14* 12(12+12.1)\\=3.14* 289.2\\=908.08](https://tex.z-dn.net/?f=%3D3.14%2A%2012%2812%2B%5Csqrt%7B%2812%29%5E2%2B%282%29%5E2%7D%29%5C%5C%3D3.14%2A%2012%2812%2B12.1%29%5C%5C%3D3.14%2A%20289.2%5C%5C%3D908.08)
Volume = ![\pi r^2\frac{h}{3}](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%5Cfrac%7Bh%7D%7B3%7D)
π = 22/7, r = 12, h= 2
Volume = ![3.14 * (12)^2 *\frac{2}{3}\\=3.14 * 144 *0.66\\= 298.42](https://tex.z-dn.net/?f=3.14%20%2A%20%2812%29%5E2%20%2A%5Cfrac%7B2%7D%7B3%7D%5C%5C%3D3.14%20%2A%20144%20%2A0.66%5C%5C%3D%20298.42)