Answer:
See Below
Step-by-step explanation:
The function is a piecewise function defined as:
a)
We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).
We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.
This means the maximum number of fish at this pond is 1600, no matter how long it goes on.
b)
A function is continuous at a point if we have the limit and the functional value at that point same.
Functional value at t = 8 is (we use 2nd part of equation):
We do have a value and limit also goes to this as t approaches 8.
So, function is continuous at t = 8
c)
We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:
The time is 4 years when the number of fishes in the pond is 250
Answer:
Santana's thinking is not correct, because the correct translation is 2 units to the left, not right.
Step-by-step explanation:
I just got that question and I got it right.
Answer:
The solution to f(x) = t(x) is x = 2010
Option 3 is true.
Step-by-step explanation:
The first-year , second-year , and third-year enrollment values for a technical school are shown in the table below.
Year (x) First Year f(x) Second Year s(x) Third Year t(x)
2009 785 756 756
2010 740 785 740
2011 690 710 781
2012 732 732 710
2013 781 755 800
Now we will check each option.
Option 1: The solution to f(x) = s(x) is x = 2,009
In year 2009, f(x)=s(x)
But 785≠756
Thus, False
Option 2: The solution to f(x) = s(x) is x = 785
x represents year, but 785 it no year
Thus, False
Option 3: The solution to f(x) = t(x) is x = 2010
In year 2010, f(x)=t(x)=740
But 740=740
Thus, True
Option 4: The solution to f(x) = t(x) is x =740
x represents year, but 740 it no year
Thus, False
The first thing we must do for this case is to find the equation of the line.
We have then:
We choose an ordered pair:
Substituting values:
From here we conclude:
Intersection with y:
We evaluate x = 0 in the function:
Slope of the line:
Point (-2, -5):
We evaluate the value of x = -2 and the value of y = -5
The equation is satisfied.
Point (8, 0):
It is part of the table, therefore belongs to the line.
Answer:
The slope is 1/2
The y-intercept is -4.
The points (-2, -5) and (8, 0) are also on the line.
Answer:
9
Step-by-step explanation:
Multiply the total number of tiles by the fraction of tiles that are blue
24 *3/8
24/8 *3
3*3
9
