Answer:
C
Step-by-step explanation:
164.7/8.6 = 19.15
about 20 miles per gallon
Answer:
The answer is 3.
Explanation:
Factors of 18:
1, 2, 3, 6, 9, 18.
Factors of 21:
1, 3, 7.
The highest number that both sets contain is 3, so the GCF will be 3.
Answer:
a) No. t < 0 is not part of the useful domain of the function
b) 2.0 seconds
Step-by-step explanation:
a) A graph of the function is shown below. It shows t-intercepts at t=-0.25 and t=2.0. We presume that t is measured forward from some event such as the ball being thrown or hit. The model's predicted ball location has no meaning prior to that event, when values of t are negative.
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b) It is convenient to use a graphing calculator to find the t-intercepts. Or, the equation can be solved for h=0 any of several ways algebraically. One is by factoring.
h = 0 = -16t² +28t +8 . . . . . . . . . . . . the ball hits the ground when h = 0
0 = -4(4t² -7t -2) = -4(4t +1)(t -2)
This has t-intercepts where the factors are zero, at t=-1/4 and t=2.
The ball will hit the ground after 2 seconds.
To find the GCF of the two terms, continuous division must be done.
What can be used to divide both terms such that there is not a remainder?
Start small, let's take 2. It could be a GCF.
Move up higher, say 3. Yes, it can be a GCF.
To see if there might be a greater common factor, divide the constants by 3.
48/3 = 16
81/3 = 27
Upon inspection and contemplation, there is no more common factor between 16 and 27. So, 3 is the GCF.
Moving on, when it comes to variables. The variable with the least exponents is easily the GCF. For the variable m, the GCF is m2 and for n, the GCF is n.
Combining the three, we have the overall GCF = 3m2n
We find the base of the rectangles by taking the difference between the interval endpoints, and dividing by 2.
Base of rectangle = (6 - 2) / 2
= 2
The area of the first rectangle:
(4 - 2)f(4) = 2[4 + cos(4π)]
The area the second triangle:
(6 - 4)f(6) = 2[6 + cos(6π)]
Now just compute the two areas and combined them. That will give you the estimated under the curve.
To evaluate the midpoint of each rectangle, we take the midpoint of the base lengths of each rectangle. This midpoint is the x value. Then evaluate the function at that x value.
The midpoint of the first rectangle is x=3. Evaluate f(3).
The midpoint of the second rectangle is x=5. Evaluate f(5).
