Answer: 
Step-by-step explanation:
Given
The volume of the pool is 
Depth of water is 
Suppose A is the base of the pool

This area can be written as

Answer:
z=6 and z=-6
Step-by-step explanation:

Divide both sides by 7

Find the square root
z=±√36
z=±6
Therefore, z=6 and z=-6.
I hope this helps!
Answer:
9.8
Step-by-step explanation:
<em>updated</em>
9^2=x^2+4^2
9*9=x*x+4*4
81=x*x-16
+16. +16
97=x*x
√97=√x*x
√97=x
So the answer is √97, but the question wants it rounded so it's actually 9.8
Answer:
Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.
<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that
. Thus, A↔A.
<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that
. In this equality we can perform a right multiplication by
and obtain
. Then, in the obtained equality we perform a left multiplication by P and get
. If we write
and
we have
. Thus, B↔A.
<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have
and from B↔C we have
. Now, if we substitute the last equality into the first one we get
.
Recall that if P and Q are invertible, then QP is invertible and
. So, if we denote R=QP we obtained that
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.