Complete the point-slope equation of the line through (-8,-1)(−8,−1)
1 answer:
Answer:
The equation of the line is y = -1
Step-by-step explanation:
In order to find the equation,y = mx + c, you have to find the gradient first using the formula :
Let (x1,y1) = (-8,-1) & (x2,y2) = (-8,-1),
m = (-1)-(-1)/-8-(-8)
= 0
Now, we have found the gradient, next using the formula, y = mx + c to find the equation :
y = mx + c
Let m=0,
At (-8,-1)
-1 = 0(-8) + c
c = -1
y = -1
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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