Answer:
m = -6
Step-by-step explanation:
For the given function h(x), we have:
a) at x = -2 and x = 2.
b) y = 0 and y = 3.
<h3>
How to identify the maximums of function h(x)?</h3>
First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.
By looking at the horizontal axis, we can see that the maximums are at:
x = -2 and at x = 2.
Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.
- The first maximum value is at y = 0 (the one for x = -2)
- The second maximum is at y = 3 (the one for x = 2).
If you want to learn more about maximums:
brainly.com/question/1938915
#SPJ1
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
- is surjective implies there exists a function such that .
- If there exists a function such that , then is surjective
Let us start by the first implication.
Our hypothesis is that the function is surjective. From this we know that for every there exist, at least, one such that .
Now, define the sets . Notice that the set is the pre-image of the element . Also, from the fact that is a function we deduce that , and because the sets are no empty.
From each set choose only one element , and notice that .
So, we can define the function as . It is no difficult to conclude that . With this we have that , and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function such that .
Take an element , then . Now, write and notice that . Also, with this we have that .
So, for every element we have found that an element (recall that ) such that , which is equivalent to the fact that is surjective. Therefore, the prove is complete.
Answer:
Step-by-step explanation:
If you had a solid cylinder, in order to find the amount of material that makes up that solid cylinder, you would find the volume using the radius of 4 (half of the diameter 8). BUT we want to know the volume of the solid with the radius of 4 minus the solid that has a radius of 2.5 (half of the diameter 5).
That's volume outer - volume inner. To find the outer volume:
so
and
and do the same for the inner volume:
and
Subtract the inner from the outer:
If you need your answer in decimal form, then the volume is
9189.16 cm³