A rectangular building with a square front is to be constructed of materials that costs 11 dollars per ft2 for the flat roof, 14 dollars per ft2 for the sides and the back, and 15 dollars per ft2 for the glass front. We will ignore the bottom of the building. If the volume of the building is 5,600 ft3, what dimensions will minimize the cost of materials? (Round your answers to the nearest hundreth such that the dimensions increase from the smallest to the largest.)

Answers

Answer 1

Answer:

y = 23.14 ft

x = 15.56 ft

so the dimensions of the building will be = 15.56 ft x 15.56 ft x 23.14 ft

Step-by-step explanation:

the area of the roof = xy

cost of the roof = 11xy

the area of the sides and back = 2xy + x²

cost of the sides and back = 14(2xy + x²) = 28xy + 14x²

area of the glass front = x²

cost of the glass front = 15x²

minimize:

total cost = 11xy + 28xy + 14x² + 15x² = 39xy + 29x²

total volume = x²y = 5600 ⇒ constraint

39y + 58x = 2λxy

39x = λx2

x²y = 5600

λx = 39 which we replace into the first equation

39y + 58x = 78y

58x = 39y

(58x)²y = 58² · 5600

now we replace 58x by 39y

(39y)²y = 58² · 5600

39² · y³ = 58² · 5600

y³ = (58² · 5600) / 39² = 12,385.53583

y = ∛12,385.53583  = 23.14 ft

x² = 5600/ 23.14 = 242.04

x = 15.56 ft


Related Questions

which equation has the same solution as x - 12 = 40

A. x/2 = 14
B. x + 12 = 40
C. 12 - x = 40
D. x/4 = 13

Answers

Answer:

Answer: D. x/4 = 13

Step-by-step explanation:

Equations

Solve the following equation:

x - 12 = 40

Adding 12:

x = 52

Let's test each option to find which one of them has the same solution.

A. x/2 = 14

Multiplying by 2:

x = 28

B. x + 12 = 40

Subtracting 12:

x = 28

C. 12 - x = 40

Subtracting 12:

-x = 28

Multiplying by -1:

x = -28

D. x/4 = 13

Multiplying by 4:

x = 52

This last option is true.

Answer: D. x/4 = 13

Find the exact solution to the equation. Just type in the final solution, do NOT include x=
250(1/5)^x/2=2

Answers

Answe is 2/25
Merry Christmas

The scale from a map to the actual distance is 2.5 cm to 620 mi. The distance on the map between Chicago and Boston is about 3.5 cm. What is the approximate distance, in miles, between Chicago and Boston? Show your work.

Answers

Answer 868 miles

Step by step

Given: The scale from a map to actual distance is 2.5 cm to 620 miles. If the distance on the map between Chicago and Boston is about 3.5 cm. Hence, the approximate distance between Chicago and Boston = 868 miles.

If the distance on the map between Chicago and Boston is about 3.5 cm.

Then, the actual distance between them =  3.5\times 248 \text{ miles}=868 \text{ miles}

Hence, the approximate distance between Chicago and Boston = 868 miles.

i.e.  1 cm on map = 620/2.5 miles =  248 miles

Answer:868 miles

Step-by-step explanation: 1cm=620/2.5 = 248

distance is about 3.5

3.5x 248=868

The height of mountain P is 1086 feet the height of Mt. Q is four times the height of Mt. P the area model shown below represents one way to find the height of Mt. Q what is the missing value for a, b and c

Answers

Answer:

ITS A I TOOK THE TEST

Step-by-step explanation:

Answer:

A=4000, B=80, C=24

Step-by-step explanation:

We have the fact that Mountain Q is 4 times the height of Mountain P. That's the "4" we have in the left side of our model. It's like having a multiplication table, next to the "4" we have "A" and upper this we have "1000", the only thing we have to do is Multiplify 4*1000=4000. The next letter we have is B and below it we have "320", we divided it by 4, 320/4=80. The last letter we have is C, and is below a "6", we only have to Multiplify it by 4, 6*4=24.

At the end we only sum our

A + 320 + c = 4344 (4 times the height of Mountain P).

1000 + B + 6 = 1086(the height of the Mountain P).

slope intercept form parallel to y = -x + 3 and through (0,6)

Answers

Answer:

Step-by-step explanation:

parallel means the slope is the same

y = -x + b

since it has to pass thru (0,6) we’ll plug those in to the equation to find b

6 = -(0) + b

6 = b

the final equations is y = -x + 6

What is the decimal equivalent of 9 1/2%

Answers

9.5% woop and I need to add more characters to this answer

The decimal equivalent of 9 1/2% is 0.095.

We have,

To explain the process of finding the decimal equivalent of 9 1/2%, we need to understand what a percentage represents and how to convert it to a decimal.

A percentage is a way of expressing a part of a whole in terms of hundredths. In this case, 9 1/2% represents 9.5 parts out of 100.

To convert a percentage to a decimal, we divide the percentage value by 100. This is because a percentage is essentially a fraction with a denominator of 100.

Now,

To find the decimal equivalent of 9 1/2%, we divide the percentage value by 100.

9 1/2% can be expressed as a fraction: 9 1/2% = 9.5/100.

Dividing 9.5 by 100 gives us the decimal equivalent:

= 9.5 ÷ 100

= 0.095

Therefore,

The decimal equivalent of 9 1/2% is 0.095.

Learn more about expressions here:

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Parallelograms pre test on edg 2020
!ANSWERS !

1.c
2.c
3.a
4.b
5.c
6.c
7.d
8.d
9.d
10.c

You’re welcome ;)

Answers

thanksssssa smmmmmmmmm

Name: Joe
Wednesday
Sandra is traveling 20 mph on her bicycle. After 4 hours, how far will she have traveled?

Answers

Answer:

is 300 an answer? If not let me know then I'll correct it.

Step-by-step explanation:

The price of a shoes was reduced from $60 to $45. by what percentage was the priceof the shoes reduced? 60-45÷ 60 a 15% b 25% c 75% d 40%

Answers

Answer: C

75% of 60 is 45 lol

The correct answer would be C, 75%. You're Welcome! I work really hard and I would like it if you gave me brainiest! Have a great day.

An amount of $38,000 is borrowed for 10 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.

Answers

Answer:

$76,516.77

Step-by-step explanation:

Use the compound interest formula. A = P(1 + r/n)^t. Subsitute the values in and solve.

Answer:

$76517

Step-by-step explanation:

Given

Amount = $38000Interest rate = 7.25% Time = 10 yearsCompound  = 1 per year

Total:

38000*(1 + 0.0725)^10 = 76516.76 ≈ $76517 rounded to the nearest dollar

Solve: 2y - 3.1 when y = 3.41

Answers

Answer:

3.72

Step-by-step explanation

2x3.42=6.82

6.82-3.1=3.72

Answer:

First, substitute y by the value

2(3.41)-3.1

Multiply the bracket by 2

It will be 0.58651026393, so you’ll round it up to make it shorter to make it easy for calculation

0.59-3.1=-2.51

-2.51 is the answer to your question

Step-by-step explanation:

I hope this helped, please give me brainliest

Order these fractions from least to greatest.
2 2 2
8' 3' 6

Answers

2/8 is the least, 2/3 is the greatest, 2/6 is the middle

The SS attached. Just need the slope :)

Answers

Answer:

1/2

Step-by-step explanation:

Rise = 1

Run = 2

~theLocoCoco

22 divided by 6 equals

Answers

22/6 is about 3.666666
What the person above me said ^

What is the sale price to the nearest cent? $239 television; 10% discount

Answers

Answer:

The sale price will be:  $215.10

Step-by-step explanation:

We know that:

Sale price = Regular price × (100% - Discount %)

                 = Regular price × (100% - 10%)

                 = 239 × 90%

                 = 239 × 0.9

                 = 215. 10 $

Therefore, the sale price will be:  $215. 10        

I don’t really understand

Answers

Answer:

42 tickets

Step-by-step explanation:

If you divide all the choices by 8 they all equal an even number except 42

it is not possible for them to use forty-two tickets because forty-two is not a multiple of eight. since there are eight people, and each ride cost one ticket per person, they should use eight tickets for each ride. forty, twenty-four, and sixteen are all multiples of eight, and are therefore possible answers.

en una clase de 90 alumnos , 15 son nacidos en estados unidos . que porcentaje son nacidos en estados unidos?

Answers

Answer:

la respuesta será 77%

Step-by-step explanation:

será 77% porque si lo divides sale así 90/15% será 77%

Help pleaseeee xxxxxx

Answers

Answer:

27.5

Step-by-step explanation:

Evaluate:|-12| - |4|- |-8|?​

Answers

Answer:

when you evaluate a number if it is positive do nothing if it is negative switch it to a positiive sooo 12   4    and   8 :)

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

find the absloute value and then subtract

What is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2 cm and height of 9 1/2 cm?

Answers

Answer:

2,018

Step-by-step explanation:

College roommates John and David were driving home to the same town for the holidays. John drove 55mph, and David, who left an hour later, drove 60mph. How long will it take for David to catch up to John?

Answers

Answer:

sorry

Step-by-step explanation:

It will take for David 11 hours to catch up with John

Speed is the ratio of distance traveled to the total time taken. Speed is given by:

Speed = distance / time

Let d represent the distance at which both John and David meet up at time t hour.

Since drove at 55 mph and is an hour faster, hence:

55 = d / (t + 1)

d = 55t + 55    (1)

John is driving at 60 mph, hence:

60 = d / t

d = 60t    (2)

equating equation 1 and 2:

55t + 55 = 60t

5t = 55

t = 11 hours

Hence, it will take for David 11 hours to catch up with John

Find out more at: https://brainly.com/question/2261058

Is (-5)+12 equal to 7 or is (-5)+(-12) equal to 7?

Answers

Answer:

-5+12=7

Step-by-step explanation:

the second option is adding two negatives, which sums up to -17 rather than -7

xoxo,your highness...

Danielle created a painting using only similar hexagons.

Which statement about the hexagons must be true?

The hexagons are all the same size and shape.

The hexagons have corresponding sides that are proportional.

The hexagons have corresponding angles that are not congruent.

The hexagons are different shapes but the same size.

Answers

Answer: B- The hexagons have corresponding sides that are proportional.

The statement is true about hexagons, if Danielle created a painting using only similar hexagons, The hexagons have corresponding sides that are proportional, so option B is correct.

What is a hexagon?

A hexagon is a two-dimensional geometric shape with six sides that may or may not have the same length. The hexagon shape can be seen in everyday objects like floor tiles, pencil cross-sections, clocks, honeycombs, etc.

Given:

Danielle created a painting using only similar hexagons,

A closed, two-dimensional shape with six equal sides and six equal angles is referred to as a regular hexagon. The regular hexagon has 120-degree angles on each side. And 120 x 6 = 720 degrees is the total of all inner angles.

Both have 6 vertices, 6 internal angles, and 6 sides, All six inner angles add up to 720 degrees, All six outer angles added together result in 360 degrees. These two hexagons are comparable because they have matching sides in the same ratio and matching angles that are both equal.

Thus, hexagon hexagons have corresponding sides that are proportional.

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If you scale a figure by less than or less than 100% does the new copy increase or decrease in size? PLS HURRY IT'S LATE PLS I DON'T WANNA STAY FOR 1HR​

Answers

Answer:

Less

Step-by-step explanation:

100% is full size

An experiment consists of dealing 6 cards from a standard 52-card deck. What is the probability of being dealt 6 hearts?

Answers

Answer: 0.0000842890

Step-by-step explanation:

Given that :

Number of cards in a deck = 52

Number of hearts in a deck = 13

Probability of being dealt 6 hearts :

Probability = (required outcome / Total possible outcomes)

Required outcome = choosing 6 hearts from a possible 13

13C6:

Recall : nCr = (n! / (n-r)!r!)

13C6 = 13! / (13-6)!6!

13C6 = 13! / 7!6!

13C6 = (13*12*11*10*9*8)/(6*5*4*3*2*1)

13C6 = 1235520 / 730

13C6 = 1716

Total possible outcomes :

52C6 = 52! / (52-6)!6!

52C6 = 52! / 46!6!

52C6 = (52*51*50*49*48*47)/(6*5*4*3*2*1)

52C6 = 14658134400 / 720

52C6 = 20358520

Hence,

P(6 hearts) = 1716 / 20358520

P(6 hearts) = 0.0000842890

resolver
4×3
____
7+5

Answers

Answer:

THEY ARE EQUAL =

Step-by-step explanation:

Which expression is equivalent to 6a + 15? PLZ HELP WILL AWARD BRAINLIEST


6(a + 5)
3(2a + 5)
3(3a + 12)
6(a + 12)

Answers

Answer:

3(2a+5)

Step-by-step explanation:

What you do is you use the Distributive Property. So you multiply 3 into 2 and 5 to get 6a+15.

what is 4(5+3) pls what is it

Answers

Answer:

is 32

hope that helps!

Find the missing angle.
130°. X

Answers

Answer:

50°

Step-by-step explanation:

Determine the slope and the y-intercept of the table.

Answers

Step-by-step explanation:

x 3 6 9

y -1 -2 -3

Change in x = + 3

Change in y = -1

slope is -1/3

y-intercept = I think there is none (it goes through the origin) but I don't have graph paper on hand so not quite sure on that. Anyway, hope this helped!

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