Answer:
a vertical shift of f, c units down
Step-by-step explanation:
Given:
- A function h(x) is defined as:
h(x) = f(x) − c
Find:
- The effect of "c" on the f(x) function.
Solution:
- The effect of adding or subtracting any constant to or from a given function f(x) shifts the f(x) value for all values of x by an amount "c"
- This effect can be modeled on a graph by a "vertical shift" i.e there is an increase/decrease in every "y" value by amount "c" units.
- In the case given we see that "c" units have been subtracted from original f(x).
- Meaning, all f(x) values have decreased for every value of x. This can be categorized as vertical shift of f(x) with "c" units down.
Answer:
Time,t that it will elapse before the concerntration of the dye in the tank reaches1% of its original value is 460.52 seconds
Step-by-step explanation:
Let Q(t) = amount of dye for all time,t.
Let Q'= rate in - rate out.
But Q/200 = concerntration of dye
Therefore rate out= Q/200 ×2.
Q'/Q = - 1/100
Dividing by Q gives
Ln/Q/ + c = -1/100t + c1
Integrating both sides with respect to t
Ln/Q/ = -1/100t + c2.
c1 and c1 are just another constants
Q= c3e^-t/100
Exponentiating both sides will cause the absolute values to get absorbed into the constants giving rise to a new constant c3
200= c3-0/100
c3= 200
2= 200e^-t/100
Ln1/100= - t/100
Ln0.01 = - t/ 100
Cross multiply
t= Ln0.01 × 100
t = 4.6052 ×100
t = 460.52seconds
