What is the slope of the line?
2 answers:
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Given:
The bases of a trapezoid lie on the lines
To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is
Where, m is slope and b is y-intercept.
On comparing with slope intercept form, we get
On comparing with slope intercept form, we get
The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.
The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.
So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get
Therefore, the equation of line that contains the midsegment of the trapezoid is .
Answer:
The volume for the solid of revolution is and its value is 401.43623.
Step-by-step explanation:
Since the function is rotating over the y-axis and it is a function in terms of x we can use Shell integration which general formula is given by
a) Setting up the integral.
We are given one end point for x which is x = 2, but we are not given the other, so we can set y = 0 on the given equation to get:
Notice that the exponential function is not going to be equal to 0, so we get the other endpoint for the interval as
which give us
Thus we integate from x = 0 to 2, so we will get:
And we can simplify that to
b) Using a calculator to evaluate the integral.
We can use a calculator to write the integral including the interval to get:
And its value rounded to 5 decimal places is