To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: 

where

 is the volume 

 is the radius 

 is the height 
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words: 

. We also know that the radius is r cm and height is h cm, so 

 and 

. Lets replace the values in our formula:





Next, we are going to use the formula for the area of a cylinder: 

where

 is the area 

 is the radius 

 is the height
We know from our previous calculation that 

, so lets replace that value in our area formula:



By the commutative property of addition, we can conclude that:
 
 
        
        
        
Answer:
   y = (5/4)2^x
Step-by-step explanation:
The function value increases by a factor of 40/10 = 4 when x increases by 2. The function can be written as ...
   y = (reference value)·(growth factor)^((x -reference)/(change in x for growth factor))
   y = 10·4^((x-3)/2) . . . . . . using point (3, 10) as a reference
This can be simplified to ...
   y = 10·2^(x -3) = 10/8·2^x
   y = (5/4)2^x
 
        
             
        
        
        
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.
. 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
. In this equality we can perform a right multiplication by  and obtain
 and obtain  . Then, in the obtained equality we perform a left multiplication by P and get
. Then, in the obtained equality we perform a left multiplication by P and get  . If we write
. If we write  and
 and  we have
 we have  . Thus, B↔A.
. 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
 and from B↔C we have  . Now, if we substitute the last equality into the first one we get
. 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
. So, if we denote R=QP we obtained that
 . Hence, A↔C.
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.
 
        
             
        
        
        
Answer:
(5,7.5) (12,18) (18,27)
Step-by-step explanation:
It costs $1.50 per cupcake.
y = 1.5x, where x is the amount of cupcakes and y is the amount of money in dollars.
7.5 = 1.5 times 5
18 = 1.5 times 12
27 = 1.5 times 18
 
        
             
        
        
        
3.10 
I think, Im very sorry if this is wrong!