The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. Wha
t is the rate of change?
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
2 answers:
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Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".
Explanation:
The given equation is,
It can be written as,
Find the zeros of the equation. Equation the function equal to 0.
So, the three zeros are 0, 1 and 2.
The graph of the equation is shown below.
From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.
The area enclosed by curve and x-axis is,
From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.
Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".
