1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena-14-01-66 [18.8K]
3 years ago
6

i need a box with a square base and an open top that cna hold 500 in^3. what is the least amount of material i can use to build

this box
Mathematics
1 answer:
exis [7]3 years ago
8 0

Answer:

M(x)  =  452,56 in

Step-by-step explanation:

The volume of the open box is  500 in³

V = Area of the base times height

V(b) =  x² * h               where x is the side of the square and h the heigh

Then     500 =  x²*h

Total material to use is: material of the base + material of 4 sides

material of the base is  x²

material of one side is x*h  we have 4 sides then  4*x*h

Total material M(b)

M(b)  =  x²  +  4*x*h

And    as    h  =  500/ x²

M(x)  =  x²  +  4* x* 500/x²

M(x)  =  x²  +  2000/x

Tacking derivatives on both sides of the equation

M´(x)  =  2*x   - 200/x²

M´(x)  =  0         2*x  -  200/x²  = 0

x³ -  100  =  0

x³   =  100

x   =  4,64 in

And By substitution     h  =  500/x²

h  =  500/(4,64)²           h  =  23,22  in

How do we know that x = 4,64 make V(x) minimum

we get the second derivative

M´´(x)  =  2  +  200*2x/ x⁴    =  2  +  400/x³

M´´(x) is always positive

M´´(x) > 0     then M(x) has a minimum for  x= 4,64 in

The least amount of material is:

M(x)  =  x²    +    2000/x

M(x)  =  (4,64)²  *  2000/4,64

M(x)  = 21,53  +  431,03

M(x)  =  452,56 in

You might be interested in
To move a function, you need to _____ it.
Flura [38]

Answer:

the answer for apex is shift

Step-by-step explanation:

8 0
3 years ago
An ant can run an inch per second. How long will it take the same ant to run a foot?​
RideAnS [48]
12 seconds bc 12 in in a foor
8 0
3 years ago
Read 2 more answers
Find the measures of HAB and CAB.
Paha777 [63]

Answer: Angle HAB= 66 and Angle CAB= 44

Step-by-step explanation:

Since angle EAF=90 and FAD=20 then DAH must equal 70 degrees because it is 180 degree angle. Since DAH and EAC are vertical angles they are equal so EAC = DAH= 70 degrees. For the other side of 180 degrees then 70+5x=180

5x=110

x=22

CAB= 2(22)= 44 degrees

HAB= 3(22)=66 degrees

4 0
2 years ago
3.602 × 10 − 4 thx luvs
lorasvet [3.4K]

♡ The Question ♡

- 3.602 × 10 − 4

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Answer ♡

- 32.02

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

- 3.602 x 10 - 4

Multiply the numbers: 3.602 x 10 = 36.02

= 36.02 - 4

Subtract the numbers: 36.02 - 4 = 32.02!

= 32.02

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ Tips ♡

- No tips provided!

6 0
2 years ago
Read 2 more answers
Which of the following is equal to (2x3)5?
Sergio [31]

Answer:

A.56

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Line m has no y-intercept, and its x-intercept is (3, 0). Line n has no x-intercept, and its y-intercept is (0, -4).
    14·2 answers
  • HELPPPPP !!!!! Answers ????
    9·2 answers
  • The diagonals of quadrilateral ABCD intersect at E(−2,4). ABCD has vertices at A(1,7) B(−3,5). What must be the coordinates of C
    14·1 answer
  • What is the quotient of 14 - (-5)<br><br> Please show ALL work
    13·1 answer
  • Solve this system of equations.<br><br><br><br> {3x+4y=36y=−12x+8
    13·1 answer
  • What is an outlier? Use complete sentences and the words "line of best fit in your explanation.​
    13·1 answer
  • Help Please Slope!!!!
    6·2 answers
  • A dartboard has a circumference of 26pi in. Calculate the total are on which the dart may land?
    10·1 answer
  • 6/8 divide by 8/12<br> A. 9/2<br><br><br> B. 8/9<br><br><br> C. 9/8<br><br><br> D. 9/32
    5·1 answer
  • Find the number of positive factors of 540​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!