Answer:
Step-by-step explanation:
Amount of brine = 100 gal
amount of salt = 80 lb
rate of water running = 4 gal / min
Let A be the amount of salt in lb in the tank at any time t.
(a) dA/dt = rate of salt in - rate of salt out
Rate of salt in = 0
rate of salt out = A x 4 / 100 = A / 25 lb/min
So, dA/dt = 0 - A/25 = - A/25 lb/min
![\frac{dA}{A}=-\frac{1}{25}dt](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7BA%7D%3D-%5Cfrac%7B1%7D%7B25%7Ddt)
![\int \frac{dA}{A}=-\frac{1}{25}\int dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdA%7D%7BA%7D%3D-%5Cfrac%7B1%7D%7B25%7D%5Cint%20dt)
![A(t) = C e^{-0.04t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20C%20e%5E%7B-0.04t%7D)
When t = 0, A = 80 lb
So,
![A(t) = 80 e^{-0.04t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2080%20e%5E%7B-0.04t%7D)
(b) Now, A = 40 lb
So,
![40 = 80 e^{-0.04t}](https://tex.z-dn.net/?f=40%20%3D%2080%20e%5E%7B-0.04t%7D)
![0.5 = e^{-0.04t}](https://tex.z-dn.net/?f=0.5%20%3D%20e%5E%7B-0.04t%7D)
take log on both the sides
![ln 0.5 = - 0.04 t](https://tex.z-dn.net/?f=ln%200.5%20%3D%20-%200.04%20t)
t = 17.3 minutes
Answer:
Bar will not fit in the box.
Step-by-step explanation:
Given:
Length = 9 in
Width = 8 in
Height = 3 in
Length of bar = 13 in
Find:
Bar fit in box or not
Computation:
If length of bar is equal to length of diagonal than it will fit in box.
Diagonal of a cuboid = √l² + b² + h²
Diagonal of a cuboid = √9² + 8² + 3²
Diagonal of a cuboid = √81 + 64 + 9
Diagonal of a cuboid = √154
Diagonal of a cuboid = 12.40 in
Diagonal of a cuboid < Length of bar
So,
Bar will not fit in the box.
Slope-intercept form: y = -2x - 1. Convert this to point-slope form:
Find a point on the graph. It's (0, -1), since y = -2(0) - 1 = -1.
Then the point-slope form is
y-(-1) = -2(x - 0)
Answer:
It is because a rectangle has 4 congruent sides.
A rectangle has 4 congruent sides since it has four 90 degrees sides, its corners. This someone say a shape with 3 congruent sides is a rectangle.
This is why it is wrong.