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Kaylis [27]
2 years ago
12

A box with a square base and open top must have a volume of 97556 c m 3 cm3 . We wish to find the dimensions of the box that min

imize the amount of material used. First, find a formula for the surface area of the box in terms of only x x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x x .] Simplify your formula as much as possible.
Mathematics
1 answer:
Kipish [7]2 years ago
6 0

Answer:

S(x)  =  x²  +  390224/x

Step-by-step explanation:

Volume of the open box  =   V  = 97556 cm³

Material needed:

Let´s call x the side of the square base then  the  area of the base is

A(b) = x²

For the sides of the box, we have 4 sides each one with area of x*h

where h is the height of the box

The volume of the box    V(b) = 97556 = x²*h   then    h  =  97556/x²

S(x,h) = x²  +  4*x*h*

The surface area of the box as function of x is:

S(x)  =  x²  + 4*x*97556/x²

S(x)  =  x²  +  390224/x

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Solve linear equations -4(b+3)-12=2b-16+5b
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Answer:

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Step-by-step explanation:

-4(b+3)-12=2b-16+5b

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3 0
3 years ago
Select the three ratios that represent the number of red cars to blue cars.
Lorico [155]

Three ratios that represent the number of red cars to blue cars are

2 : 3

6 : 9

8 : 12

\texttt{ }

<h3>Further explanation</h3>

<u>Given:</u>

Number of Red Cars = 4

Number of Blue Cars = 6

<u>Asked:</u>

Ratio = ?

<u>Solution:</u>

<em>Let:</em>

<em>Number of Red Cars = R</em>

<em>Number of Blue Cars = B</em>

The ratio that represent the number of red cars to blue cars is :

R : B = 4 : 6

We can find other ratio by dividing or multiplying the above comparison with the same number :

R : B = (4/2) : (6/2) = 2 : 3

R : B = (4 \times 2) : (6 \times 2) = 8 : 12

R : B = (4 \times \frac{3}{2}) : (6 \times \frac{3}{2}) = 6 : 9

\texttt{ }

<h3>Conclusion:</h3>

Three ratios that represent the number of red cars to blue cars are:

  • 2 : 3
  • 6 : 9
  • 8 : 12

\texttt{ }

<h3>Learn more</h3>
  • The LCM and HCF : brainly.com/question/420337
  • A car’s service book  : brainly.com/question/422755
  • Verify that HCF × LCM = product of two numbers : brainly.com/question/10942748

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Ratio

Keywords: Lower , Common , Multiple , Highest , Ratio , Proper , Jar , Pickles , Patties , Buns  

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