If the y-intercept and the x-intercept of a linear function are equal, is the slope 1 ?
1 answer:
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Answer:
A
Step-by-step explanation:
The base of a solid in the region enclosed by the graphs of <em>y</em> = eˣ, <em>y</em> = 0, <em>x </em>= 0, and <em>x</em> = 1. Each cross-section perpendicular to the <em>x</em>-axis is an equilateral triangle. We want to find the volume of the solid.
Please refer to the graph below. We are concerned with the red region.
In order to find the volume, we essentially sum up the area of the figure at each <em>x</em> value. So, we integrate from <em>x </em> = 0 to <em>x </em>= 1.
The area for an equilateral triangle is given by:
Where <em>s</em> is the side length of the triangle.
Since the triangle lies perpendicular on the region, the side length of the triangle at <em>x</em> is simply <em>y</em>, which is eˣ.
Therefore, our volume is:
Substitute:
Evaluate the integral. Simplify:
Integrate using u-substitution:
Evaluate:
Therefore, the volume of the solid is:
Our answer is A.
Answer:
Kindly check attached picture for box plot
Step-by-step explanation:
Given the data :
43 46 49 51 52 52 58 55 65 66 67 66 66 67 67 69 71 73 75 79 77 83 85 86 87
Using the software to create a box plot, the box plot five number summary is a given below ;
Sample size: 25
Median: 67
Minimum: 43
Maximum: 87
First quartile: 53.5
Third quartile: 76
Interquartile Range: 22.5
With no outliers.
