Which of the following relations is a function?
1 answer:
You might be interested in
Answer:
The ratio of their volumes is:
Step-by-step explanation:
If the cones are similar, then the ratio of their heights should equal the ratio of their radiuses. If we call R the radius of the larger cone (the one of height 9 cm) and r the radius of the smaller cone (the one of height 4 cm), then the following proportion should be verified:
where we have solved for "R" in terms of "r".
Now we input this information in the formula for the volume (V) of the largest cone, and for the volume (v) of the smaller cone, recalling that the volume of a cone is the product of the area of the cone's circular base ().
So now the ratio of their volumes (V/v) can be obtained:
Given:
The function is:
To find:
a. Slope and Y-intercept.
b. Is the function increasing, decreasing, or constant, justify your answer.
c. Graph the function, label x, and y-intercepts.
Solution:
a. We have,
...(i)
The slope intercept form of a line is:
...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
Therefore, the slope of the line is -2 and the y-intercept is 1.
b. If the slope of a linear function is negative, then the function is decreasing.
If the slope of a linear function is positive, then the function is increasing.
If the slope of a linear function is 0, then the function is constant.
The slope of the linear function is negative.
Therefore, the function is decreasing.
c. We have,
At , we get
So, the y-intercept is at (0,1).
At , we get
So, the x-intercept is at .
Plot the points and connect them by a straight line as shown below:
