For this case we have that by definition, the volume of a rectangular prism is given by:

Where:
It is the area of the base
h: It's the height
According to the data we have:


Then:

Thus, the volume is:

Answer:

Your answer to the first one is incorrect.
We can cut the plan into two figures, a rectangle with side lengths of 4 cm and 5 cm and a rectangle with side lengths of 1 and 2 cm.
Perimeter of a Rectangle:
P = 2(l + w)
P = 2(4 + 5)
P = 2(9)
P = 18
Perimeter of a Rectangle:
P = 2(l + w)
P = 2(2 + 1)
P = 2(3)
P = 6
Add up the perimeters:
18 + 6 = 24
So the total perimeter is 24.
For the 2nd one, your answer is also incorrect.
We multiply 5 to the perimeter of the plans:
5 * 24 = 120
Not sure what the third one is asking.
For the fourth one we just multiply 'k' to the perimeter:
24 * k = 24k
Answer:
(a) 
(b) Domain:
<em>(See attachment for graph)</em>
(c) 
Step-by-step explanation:
Given



Solving (a): A function; l in terms of w
All we need to do is make l the subject in 
Divide through by 2

Subtract w from both sides


Reorder

Solving (b): The graph
In (a), we have:

Since l and w are the dimensions of the fence, they can't be less than 1
So, the domain of the function can be 
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To check this
When 



When 


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<em>See attachment for graph</em>
<em></em>
Solving (c): Write l as a function 
In (a), we have:

Writing l as a function, we have:

Substitute
for l in 
becomes
