Answer:
5 : 30
Step-by-step explanation:
Note that  × 10 = 5
 × 10 = 5
Thus 3 × 10 = 30
Hence
 : 3 = 5 : 30
 : 3 = 5 : 30
 
        
             
        
        
        
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
<h3>How can the dimensions and volume of the box be calculated?</h3>
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;

Which gives;

6•x² - 106•x + 315 = 0

Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in. 
- Length of the box ≈ 35 - 2×4.55 in.  = 24.89 in. 
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
Learn more about differentiation and integration here:
brainly.com/question/13058734
#SPJ1
 
        
             
        
        
        
Answer:
I believe x=6 1/2 which is 6.5 in decimal form :)
 
        
             
        
        
        
G has 2 local minimums, you can tell because there are 2 dips in the line before it goes of to infinity.
Both questions have the same answer so the answer to both would be
Local Min: (-2,-3), (3,0)
        
             
        
        
        
Answer:
Option d
Step-by-step explanation:
Other options are not eligible because
a) Integers are not irrational
b)Whole numbers start from 0 and consists positive integers only.But integers consist negative integers also.
c)Natural number consists of positive integers only.
If the question had been asked as some integers are also, then options b) and c) could have been written . But in this case , it is asked every integer is also.
Thank you!