Answer:
t = 460.52 min
Step-by-step explanation:
Here is the complete question
Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Solution
Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.
inflow = 0 (since the incoming water contains no dye)
outflow = concentration × rate of water inflow
Concentration = Quantity/volume = Q/200
outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.
So, Q' = inflow - outflow = 0 - Q/100
Q' = -Q/100 This is our differential equation. We solve it as follows
Q'/Q = -1/100
∫Q'/Q = ∫-1/100
㏑Q = -t/100 + c
when t = 0, Q = 200 L × 1 g/L = 200 g
We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2
㏑0.01 = -t/100
t = -100㏑0.01
t = 460.52 min
Answer:
The answer is a= 128.95 and b = 14.75
Step-by-step explanation:
Solution
Given
let the equation of the hyperbola be denoted as x2/a2 - y2/b2 = 1 here, we will consider the foci on the x-axis. All units are considered to be in mm.
From question stated, with x and y coordinates represents height and radius respectively,
Then,
When x = 83 + a, y is = 45/2 = 22.5 and
At x = 180 + a, y is = 57/2 = 28.5
It is important to know that, the height is estimated from the focus so we a a is included to the heights.
Thus,
(83+a)2/a2 - 22.52/b2 = 1 and (180+a)2/a2 - 28.52/b2 = 1
By using a calculator we have, a = 128.95 and b = 14.75
Therefore a= 128.95 and b = 14.75
Answer:
Step-by-step explanation:
Given
Shape: Right Circular cone
Height, h = 12.5 cm
Base circumference, C = 5.8cm
Required:
Calculate Volume
The volume of a cone is calculated as thus;
Volume, 
Where V, r and h represent the volume, the radius and the height of the cone respectively
But first we need to calculate the radius of the cone.
Using formula of circumference.
We have C to be 5.8cm
By substituting this value;
Divide through by 
Now, we can calculate the volume of the cone
By substituting and h = 12.5 cm;
becomes
Take 
as 3.14
---- Approximated
Hence, the volume of the cone is;
I think the answer is 1,600 totals students taking metaphysics
168/3 = 56
<em>Therefore, Chad is driving the car in 56 mph.</em>
672/56 = 12
<em>Therefore, Chad drives 672 miles in 12 hours.</em>
308/11 = 28
<em>Therefore, Chad drives 28 miles per gallon of gas.</em>
672/28 = 24
<em>Therefore, Chad uses 24 gallons of gas to drive 672 miles.</em>
