What is the value of a?
1 answer:
Answer:
15 units
Step-by-step explanation:
By using the Pythagoras Theorem,
C^2 = A^2 + B^2
Substitute in the given values,
25^2 = a^2 + 20^2
625 = a^2 + 400
625 - 400 = a^2 + 400 - 400
a^2 = 225
= 15
Hope this too helped! ^^
I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.
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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
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.