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
lyudmila [28]
3 years ago
13

a rectangular box with two sqaure opposite ends is to hold 8000 cubic inches. find the dimensions of the cheapest box if tge rec

angular sides cost 15 times more as much per square inche as the top, bottom, and square ends
Mathematics
1 answer:
AveGali [126]3 years ago
3 0

Answer:

the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in

Step-by-step explanation:

since the box has a volume V

V= x*y*z = b=8000 in³

since y=z (square face)

V= x*y² = b=8000 in³

and the cost function is

cost = cost of the square faces *  area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides

C = a* 2*y² +  a* 2*x*y + 15*a* 2*x*y =  2*a* y² +  32*a*x*y

to find the optimum we can use Lagrange multipliers , then we have 3  simultaneous equations:

x*y*z = b

Cx - λ*Vx = 0 → 32*a*y -  λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ

Cy - λ*Vy = 0  → (4*a*y + 32*a*x) - λ*2*x*y = 0

4*a*32/λ  + 32*a*x - λ*2*x*32*a/λ = 0

128*a² /λ +  32*a*x - 64*a*x = 0

32*a*x = 128*a² /λ

x  = 4*a/λ

x*y² = b

4*a/λ * (32*a/λ)² = b

(a/λ)³ *4096 =  8000 m³

(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in

then

x  = 4*a/λ = 4*5/4 in = 5 in

y=32*a/λ = 32*5/4 in = 40 in

then the box has dimensions 5 in x 40 in x 40 in

You might be interested in
Evaluate the function rule for the given value f(x)=15x for x=3
lesya692 [45]

Answer:

f(3) = 45

Step-by-step explanation:

Substitute x = 3 into f(x) and evaluate

f(3) = 15 × 3 = 45

7 0
3 years ago
Read 2 more answers
3a + 6 = a<br><br><br> 7th Grade Linear Question
castortr0y [4]
A= -3 hope this helped:)



3 0
3 years ago
Read 2 more answers
PLS HELP MEEEEEEE
ExtremeBDS [4]

Answer:

The one that wieghs 10 grams

Step-by-step explanation:

4 0
2 years ago
The stem-and-leaf plot shows the scores of a class of sixth graders on a math test.
SOVA2 [1]

A stem and leaf plot shows sets of two digit numbers, by separating the ten’s place and the one’s place. On the left is the different ten’s values, while on the right next to each of the values on the left is the one’s values that associate with each of the ten’s values. This means that the numbers in this set of data are 32, 47, 51, 55, 55, 55, 58, 64, and so on. From there, you can use that knowledge to figure out how many scores were above 60.


The terms that are above 60 are 64, 65, 73, 74, 77, 87, 88, 91, 93, 93, 97, 99, and 99, for a total of 13 of the 20 scores being above 60.

8 0
3 years ago
PLZ HELP MEH WITH MATH XD
irina [24]
To add any fraction You need to make sure that the denominator of the fractions are same. ( denominator in your sum is 19 )

10/19 + 3/19 ( we have the same denominator )
we can also write this problem like
( 10 + 3 ) / 19  { add the numerators together }
13 / 19

So correct option is B.

hope this helped..  :)
6 0
3 years ago
Read 2 more answers
Other questions:
  • The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park
    9·1 answer
  • Please explain how u got the answer!!!!!
    7·2 answers
  • Mike's soccer team went out for pizza after the game. Each pizza cost $12.99, and the team bought 5 pizzas.
    8·1 answer
  • A rectangular swimming pool has a length of 50 m, a width of 25 m, and a depth of 1.75 meters. What is the volume
    15·2 answers
  • A square piece of tile has a width of 13 cm. What is the area of the piece of tile?
    13·2 answers
  • Sasha works at a greenhouse during the summer . She has to wrap mum plants with colored foil . There are 130 rows with 40 mums i
    11·1 answer
  • A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together
    7·1 answer
  • Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation bel
    15·2 answers
  • What is 9×10^4 equal to
    15·1 answer
  • Makayla wants to spend no more than $50 to celebrate her birthday with her four friends. Each box of her favorite pizza costs $7
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!