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postnew [5]
3 years ago
5

Find the area lying above the x-axis and below the parabolic curve y = 4x -x2 A. 8 B. 16 C. 10 2/3 D. 8 1/3

Mathematics
1 answer:
dimaraw [331]3 years ago
7 0
To find the area between the x-axis and the parabolic curve, take the integral of the area in which the curve is above the x-axis.
function of the graph is
y = 4x - x²
We can tell by the function (specifically -x²) that the parabola will point downward.
To find the domain in which y>0, let's find the roots (0's) of the function:
0 = 4x - x²
0 = x (4 - x) 
x = 0 or x = 4
Between x=0 and x=4, the curve is above the x-axis. To find the area of the graph, let's take the integral on this range:

First, take the antiderivative of 4x - x²:
2x² - (1/3) x³
Then, plug x=4 into the anti-derivative, and subtract the anti-derivative at x=0:
2(4)² - (1/3)(4³) - (0 - 0)
32 - 64/3
96/3 - 64/3 = 32/3 

Closest Answer is C) 10
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The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to construct the followin
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The inter quartile range is 55

Step-by-step explanation:

<u>Interquartile range</u>:-

<u>Definition</u>:-

The inter quartile range is the difference between the upper (Q3) and lower(Q1) quartiles, and describes the middle  50% of values when ordered from lowest to highest.

Interquartile range = higher quartile - lower quartile

given data 50.25.80.10

write the ascending order 10 25 50 80

Step:-1

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is

({\frac{n+1}{2} })^{th}observations

Step2:-

The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is even, then the median is ({\frac{n}{2} })^{th}

({\frac{n+1}{2} })^{th}

In given data the number of observations is '4'(even)

If the number of observations is even, then the median is ({\frac{n}{2} })^{th}

({\frac{n+1}{2} })^{th}

median is ({\frac{4}{2} })^{th} is 2 observations and ({\frac{4+1}{2} })^{th} is 2.5 observations.

so we have to select average of these two observations.

therefore the median is '3' observation

median of the given data = 50

<u>Step:3</u>

Interquartile range = higher quartile - lower quartile

                                  = 80-25

                                  =55

3 0
3 years ago
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