Answer:
It take 37.5 hours to fill the tank
Step-by-step explanation:
Given:
Time Taken to fill the tank = 15 hours
Time Taken to empty the tank = 25 hours
To Find:
Time taken to fill the tank when both the inlet and outlet is opened at the same time = ?
Solution:
Let the time to fill the tank be x
In 15 hours the tap fills the tank
Rate at which the tank is filled = ![\frac{1}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B15%7D)
In 25 hours the tap empties the tank
Rate at which the tank is drained = ![\frac{1}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B25%7D)
The net gain per minute on the total filling rate is
=>
Rate at which the tank is filled - Rate at which the tank is drained
=>![\frac{1}{x} = \frac{1}{15} - \frac{1}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D%20-%20%5Cfrac%7B1%7D%7B25%7D)
=>![\frac{1}{x} = \frac{25-15}{15 \times 25}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B25-15%7D%7B15%20%5Ctimes%2025%7D%20)
=>![\frac{1}{x} = \frac{10}{375}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B10%7D%7B375%7D%20)
=> 10x = 375
=>![x = \frac{375}{10}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B375%7D%7B10%7D)
=>x = 37.5
Answer:
180.975 square feet
Step-by-step explanation:
est: 181 square feet
Answer: ![y=x-6](https://tex.z-dn.net/?f=y%3Dx-6)
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where "m" is the slope and "b" is the y-intercept.
By definition, the slopes of perpendicular lines are negative reciprocals.
Given the line:
We know that a line perpendicular to this line must have this slope:
![m=\frac{1}{1}=1](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B1%7D%3D1)
Since that line goes through the point (8,2), we can substitute the slope 1 and these coordinates into
and solve for "b":
![2=(1)(8)+b\\\\2-8=b\\\\b=-6](https://tex.z-dn.net/?f=2%3D%281%29%288%29%2Bb%5C%5C%5C%5C2-8%3Db%5C%5C%5C%5Cb%3D-6)
Therefore, the equation of this line is:
![y=x-6](https://tex.z-dn.net/?f=y%3Dx-6)
Answer:
10:12:8
Step-by-step explanation:
so, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. so it would look like this 10:12:8
Answer:
The equation you should solve to find b is:
Option D. sin 35° / 9 = sin 40° / b
Step-by-step explanation:
m<A=35°
m<B=40°
a=9
b=?
We can use the Law of sines:
sin A / a = sin B / b
Replacing the given values:
sin 35° / 9 = sin 40° / b
This is option D.