Answer:
10
Step-by-step explanation:
 
        
             
        
        
        
Answer:
2/3 already simplified
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
V=64
Step-by-step explanation:
What you do is go based off the volume formula of a cube which is V=a^3.
You have a side length of 4.
V=4^3.
V=64. 
 
        
             
        
        
        
Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
                                                       = x²y cubic feet
1000 = x²y
y =  -------(1)
 -------(1)
Material used in the prism = Surface area of the rectangular prism
                                             = 2(lb + bh + hl)
Here, h =  height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
                                   S = 2(x² + 2xy) - x²
                                   S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² + 
   = x² + 
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x - 
2x -  = 0
 = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y = 
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.
 
        
             
        
        
        
Answer:
<em>The value of y when x has a value of 9 is 18</em>
Step-by-step explanation:
<u>Functions</u>
The variables x and y are said to have a quadratic relationship. That information is not enough to set up a general equation for both variables.
Furthermore, we know that tripling the value of x causes the value of y to be multiplied by 9. That leads us to establish a proportional equation between them, as follows:

Where k is an unknown constant.
Let's use the given point (3,2) to find the value of k:


Solving for k:

The equation is now:

Now find y when x=9:


The value of y when x has a value of 9 is 18