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Free_Kalibri [48]
3 years ago
9

What is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Mathematics
1 answer:
Neko [114]3 years ago
5 0

Answer:

  2

Step-by-step explanation:

For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.

The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...

  f'(1) = 2(1) = 2

The average rate of change of f(x) on [-2, 4] is 2.

__

<em>Alternate solution</em>

The average rate of change is the slope of the line between the end points of the interval:

  m = (y2 -y1)/(x2 -x1)

  m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2

The average rate of change on [-2, 4] is 2.

_____

The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.

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3 years ago
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Answer:

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Step-by-step explanation:

In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards , at least one of the two is a face card.

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Now let’s calculate the number of face cards we have.

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Now, we want to calculate the probability of at least one of the cards drawn are face cards.

Mathematically, what we are needing to calculate is

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Now let’s calculate.

The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

Now in probabilities, whenever we are having the statement or, we add the probabilities together

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Step-by-step explanation:

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