A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base. The base needs to be stronger than the sides, so it costs more. The base costs $9 per f t 2 , while the sides only cost $6 per f t 2 . We wish to find the dimensions of the box that minimize the cost of material used.

Answers

Answer 1

Answer:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]

Step-by-step explanation:

Given

[tex]Volume = 128ft^3[/tex]

[tex]L = 2W[/tex]

[tex]Base\ Cost = \$9/ft^2[/tex]

[tex]Sides\ Cost = \$6/ft^2[/tex]

Required

The dimension that minimizes the cost

The volume is:

[tex]Volume = LWH[/tex]

This gives:

[tex]128 = LWH[/tex]

Substitute [tex]L = 2W[/tex]

[tex]128 = 2W * WH[/tex]

[tex]128 = 2W^2H[/tex]

Make H the subject

[tex]H = \frac{128}{2W^2}[/tex]

[tex]H = \frac{64}{W^2}[/tex]

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

[tex]A = LW + 2(WH + LH)[/tex]

The cost is:

[tex]Cost = 9 * LW + 6 * 2(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12(WH + LH)[/tex]

[tex]Cost = 9 * LW + 12H(W + L)[/tex]

Substitute: [tex]H = \frac{64}{W^2}[/tex] and [tex]L = 2W[/tex]

[tex]Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)[/tex]

[tex]Cost =18W^2 + \frac{768}{W^2}*3W[/tex]

[tex]Cost =18W^2 + \frac{2304}{W}[/tex]

To minimize the cost, we differentiate

[tex]C' =2*18W + -1 * 2304W^{-2}[/tex]

Then set to 0

[tex]2*18W + -1 * 2304W^{-2} =0[/tex]

[tex]36W - 2304W^{-2} =0[/tex]

Rewrite as:

[tex]36W = 2304W^{-2}[/tex]

Divide both sides by W

[tex]36 = 2304W^{-3}[/tex]

Rewrite as:

[tex]36 = \frac{2304}{W^3}[/tex]

Solve for [tex]W^3[/tex]

[tex]W^3 = \frac{2304}{36}[/tex]

[tex]W^3 = 64[/tex]

Take cube roots

[tex]W = 4[/tex]

Recall that:

[tex]L = 2W[/tex]

[tex]L = 2 * 4[/tex]

[tex]L = 8[/tex]

[tex]H = \frac{64}{W^2}[/tex]

[tex]H = \frac{64}{4^2}[/tex]

[tex]H = \frac{64}{16}[/tex]

[tex]H = 4[/tex]

Hence, the dimension that minimizes the cost is:

[tex]Width = 4ft[/tex]

[tex]Height = 4ft[/tex]

[tex]Length = 8ft[/tex]


Related Questions

WHATS THE ANSWER? MULTIPLE CHOICE 50 PTS

Answers

Answer:

D

Step-by-step explanation:

Seventeen less than p infers that the number is p minus 17. This number is then divided by 8, which requires us to put parenthesis in order to properly divide the number after doing p - 17

Please give brainliest thank you

[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]

The quotient when 17 less than p is divided by 8.

Well, let's first take 17 less than p. That'll be :-

[tex] \sf \: p - 17[/tex]

Note :- 'p' comes first as the question has the words - less than p.

Now, we have the remaining -> 'is divided by 8'.

The equation will become :-

[tex] \sf \:( p - 17) \div 8[/tex]

Note :- We have put the bracket because they have asked the quotient. To form a quotient you need 2 numbers - a divisor & a dividend. Hence, 2 numbers -> (p - 17) & 8.

So, Option D [tex]\boxed{\underline{\bf \: (p-17)÷8}}[/tex] is the correct answer.

________

Hope it helps.

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NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ WILL REPORT FAKE ANSWERS

Answers

Answer:

The graph has a domain of {x|0 < x < infinite} and approaches 0 as x decreases

The graph has a domain of {y| -infinite < y < infinite} and decreases as x approaches 0.

Step-by-step explanation:

I was confused at first because I was like "There is 2 answers" and I reread the question again and found my mistake.

And sorry for the wait because "I am in class"

Please help!! Timed assignment

Arrange the figures in increasing order of their volumes. Use Pi =22/7

Answers

Answer:

see the list below

Step-by-step explanation:

did all the formulas for each and I believe the order is from (smallest to biggest)

1. The half sphere or hemisphere (3rd in the picture)

2.The pyramid

3.slanted cone

4.cone

5.slanted cylinder

6.and finally the cylinder

Mira uses the mapping rule to find the coordinate of a point that had been rotated 90° clockwise about the origin. Examine Mira’s solution to determine which step has an error.


M(–5, –6) is rotated 90° clockwise.

Step 1. Use the rule (x, y)g(y, –x).

Step 2. Switch x and y coordinates:
(–6, –5)

Step 3. Multiply the new x-coordinate by –1:
((–1)–6, –5)

Step 4. Simplify:
(6, –5)


Mira made an error in Step

Answers

Answer:

3

Step-by-step explanation:

Answer: You multiply the old x coordinate by negative 1, so the error is at step 3.

It should give (-6, (-1)-5).

Step-by-step explanation:

15) Find the product. Show all your work.
Reduce all your answers into simplest
form
3 - x
5
л |N

Answers

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

3 [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex]

or another way

[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]

[tex]\frac{3}{2}[/tex] x [tex]\frac{1}{1}[/tex] = [tex]\frac{3}{2}[/tex]

1.) Apply the distributive property and simplify the expression : 4(2x + y)
Your answer

Answers

Answer:

8x + 28

Step-by-step explanation:

Can anyone help me out

Answers

Answer:

14.49 people per square mile

Step-by-step explanation:

Divide to find the answer:

836,109/57,714 = 14.49

1) A farmer has sheep and cattle in the ratio 8:3.
a) How many sheep has the farmer if he has 180 cattle?

b) Find the ratio of the number of sheep to the total number of animals.

c) Find the ratio of the total number of animals to the number of cattle.

2)My fortune of $ 810 000 is to be divided in the ratio 4:3:2. How much does each person receive?
Good

Answers

Answer:

Q 1)

a) No of sheep = 480

b) 8 : 11

c) 11 : 3

Q 2)

Each person will receive: $360,000, $270,000 and $180,000

Step-by-step explanation:

Ratio of sheep to cattle = 8 : 3

Let the number of sheep be 8x

And number of cattle be 3x

a)

No of cattle = 180 (Given)

Therefore,

3x = 180

x = 180/3

x = 60

Therefore, 8x = 8*60 = 480

No of sheep = 480

b)

Total animals = 180 + 480 = 660

Ratio of sheep to the total number of animals

= 480 : 660

= 8 : 11

c)

Ratio of total animals to the number of cattle

= 660 : 180

= 11 : 3

Q 2) Let each person will receive 4x, 3x and 2x dollars.

Therefore,

4x + 3x + 2x = 810,000

9x = 810000

x = 810000/9

x = 90,000

Therefore,

4x = 4*90,000 = $360,000

3x = 3*90,000 = $270,000

2x = 2*90,000 = $180,000

So, each person will receive $360,000, $270,000 and $180,000.

HELP ASAP WILL GIVE MOST BRANILIST

Answers

The line fills three boxes before hitting a corner so I believe it is 1/3
3/1 because it’s up 3 and over 1

the spinner below is spun twice. What is the probability of the arrow landing on a 3 and then an odd number?

Please help​

Answers

Answer:

4/3

Step-by-step explanation:

write the equation for a parabola with a focus at (-3,-5) and a directrix at x=-7

x=​

Answers

Answer:

hope this helps

Step-by-step explanation:

equation for a parabola is:

What is parabola?

The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.

Given: focus= (3,-5), directrix at x =-7.

To find equation of parabola we will use distance formula,

√(x+7)²=√(x+3)² + (y+5)²

(x+7)²=(x+3)² + (y+5)²

x²+14x+49= x²+9+6x + (y+5)²

8x + 40 = (y+5)²

x= (y+5)²/8 -5

Hence, the equation of parabola is x= (y+5)²/8 -5

Learn more about equation of parabola here:

https://brainly.com/question/4025891

#SPJ2

Can someone please help me I will mark u brilliant for both

Answers

For the first question, y = 1/2
For the second question, x = 4

Answer:

1. 1/2

2. 4

Step-by-step explanation:

2. 14x = 56

56 / 14

x = 4

My faces are not all
congruent.
I contain 12 edges.
I contain 6 faces.

Answers

Answer:

its a rectangle

Step-by-step explanation:

The X and Y coordinates (in feet) for station Shore are 2058.97 and 6980.06, respectively, and those for station Rock are 1408.03 and 6980.06, respectively. What are the azimuth, bearing, and length of the line connecting station Shore to station Rock

Answers

Answer:

Hence, the azimuth, bearing, and length of the line connecting station Shore to station Rock are [tex]270^{\circ},90^{\circ}[/tex] and [tex]650.94[/tex] feet.

Given :

The shore station point [tex](X_1,Y_1)[/tex] in feet,

        [tex](X_1,Y_1)=(2058.97, 6980.06)[/tex]

The Rock station point [tex](X_2,Y_2)[/tex] in feet

       [tex](X_2,Y_2)=(1408.03,6980.06)[/tex]

From the figure

     [tex]x=2058.97-1408.03=650.94[/tex] feet

    [tex]y=6980.06-6980.06=0\\[/tex] feet

Length of the line [tex]L=\sqrt{x^2+y^2}[/tex]

                           [tex]\Rightarrow L=\sqrt{(650.94)^2+0}=650.94[/tex]

                            [tex]\Rightarrow L=650.94[/tex] feet

[tex]\because[/tex] [tex]\tan \theta=\frac{y}{x}=\frac{0}{x}=0[/tex]

[tex]\Rightarrow \theta=\tan^{-1}(0)=0[/tex]

Azimuth of line[tex]=270^{\circ}+\theta[/tex]

                       [tex]=270^{\circ}+0[/tex]

                      [tex]=270^{\circ}[/tex]

[tex]\therefore[/tex] Bearing [tex]=360^{\circ}-\text{Azimuth}[/tex]

                [tex]=360^{\circ}-270^{\circ}[/tex]

                [tex]=90^{\circ}[/tex]

(x-4)2 + 3x at the value x = 7

Answers

Answer:

30

Step-by-step explanation:

x = 7

( x - 4 )^2 + 3x

= ( 7 - 4 )^2 + 3 ( 7 )

= 3^2 + 21

= 9 + 21

= 30

Answer:

The answer is 27

Step-by-step explanation:

(X-4)2 + 3x

x is equal to 7

first substitute the values.

(7-4)2 + 3 x 7

solve-

(3)2 + 21

=27

A system has two identical components, and requires both the components for system success. If one component fails, the other cannot fail while the failed component is being repaired. The component failure rates and repair rates are 0.1 failures/year and 365 repairs/year respectively. If a similar component is carried as a spare with an average installation time of 1 hour, evaluate the probability of failure, frequency of failure and the average down time of the system.

Answers

Answer:

Step-by-step explanation:

We are given that:

The failure rate = 0.1 failure/year

i.e.  = [tex]\dfrac{0.1}{365\times 24}= 0.00001 \ failure /hour[/tex]

The repair rate = 365 repair/year, if we convert this to repair/hour; we get:

[tex]= \dfrac{365}{365\times 24} \\ \\ = 0.04 \ repair/ hour[/tex]

Time (t) = 1 hour

P(failure) = 1 - R  ; if (t=1)

where:

[tex]Reliability (R ) = e^{-\lambda t}(1+ \lambda t) \\ \\ = e^{-0.00001*1}(1+0.00001 *1) \\ \\ \simeq 0.9999[/tex]

P (failure) = 1 - R  

= 1 - 0.9999

= 0.0001

≅ 0

The frequency meantime of failure = [tex]\dfrac{1}{\lambda}[/tex]

[tex]\dfrac{1}{0.00001}[/tex]

= 100000

The average downtime of repair for the system = [tex]\dfrac{1}{\mu}[/tex]

[tex]=\dfrac{1}{0.04}[/tex]

= 25


This graph shows the altitude of an airplane over time. Which story matches the graph?
A.)The aircraft rose quickly into the air at takeoff, and then it continued at a constant altitude.
B.)The aircraft rose steadily over the entire flight.
C.)The aircraft rose quickly to its maximum height, and then it immediately began going back down toward the grou
D.)The aircraft rose quickly into the air at takeoff, and then it rose slowly for the rest of the flight.
SHOW HINT

Answers

Answer:

A.) The aircraft rose quickly into the air at takeoff, and then continued at a constant altitude.:)

Answer:

Omg, thank u so much I am on this question rn on Edulatic and I have 100 Q's and I'm only on Q 45, This Question rly helped me a lot bc it came with the answer. God Bless you!!

Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried an 8.5 percent interest rate?

Answers

Answer:

the answer 57.8

85 x 8 x 8.5% = 57.8

Step-by-step explanation:

brainliest pls

#11. The space occupied by a wooden block is 4cm × 2cm × 2cm=_____cm 3 Which is equivalent to_______mililiters​

Answers

4x2x2=16cm^3, which is 160mm

a loaf of bread has 12 slice. micky ate 1/4 of the loaf. write the fraction of the loaf micky ate in twelfths

Answers

Answer:

3/12

Step-by-step explanation:

1/4*3/3=3/12

PLEASE HELP MATH QUESTION 99 POINTS HELP ASAP PLEASE
LOOK AT LINKED IMAGE FOR QUESTION.

Answers

Answer:

Graph A. not a function

Graph B. is a function

Mapping A. is a function

Mapping B. not a function

Table A. not a function

Table B. is a function

Answer:

a graph. not a function

b graph.function

a table. not a function

b table. function

maaping a. function

mapping b. not a function

Step-by-step explanatio n:

mark me brainelst plz

The local weather forecast has been accurate for 24 of the past 30 days. Based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate

Answers

Step-by-step explanation:

the empirical probability is 24/30, or 4/5. this is also the desired probability.

What is the measure of angle L

Answers

Answer:

90-15 and you have your answer

Answer:

75

Step-by-step explanation: it is a right angle so you do 90-15 which is 75 degrees.

PLEASE HELP MATH QUESTION 99 POINTS ASAP
Function A and Function B are linear functions. Compare the two functions and choose all that are correct.

Answers

Answer:

 2 .The slope of Function A is less than the slope of Function B

A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)

The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)

_____

More detailed working

The slope of Function A can be figured easily between the points with x-values that differ by 1:

 m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.

The slope of Function B is the coefficient of x in the equation: 3.

__

The y-intercept of Function A can be found starting with point-slope form:

 y -22 = 2(x -9)

 y = 2x -18 +22

 y = 2x +4 . . . . . . . slope-intercept form

The intercept of +4 is the same as that of Function B.

Step-by-step explanation:

mrk me brainliest plz

Answer:

2 .The slope of Function A is less than the slope of Function B

A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)

The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)

_____

More detailed working

The slope of Function A can be figured easily between the points with x-values that differ by 1:

m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.

The slope of Function B is the coefficient of x in the equation: 3.

__

The y-intercept of Function A can be found starting with point-slope form:

y -22 = 2(x -9)

y = 2x -18 +22

y = 2x +4 . . . . . . . slope-intercept form

The intercept of +4 is the same as that of Function B.

Step-by-step explanation:

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What is the degree measure of FEG?
A 20°
B 31°
C 56°
D
124°

Answers

Answer:

C) 56

Step-by-step explanation:

DEG and FEG are on a straight line forming 180 degree.

Set your formula up as

180 = (3x+31)+(2x-6)

180 = 3x +2x +31 - 6

180 - 31 + 6 = 5x

155 = 5x

155/5 = x

31 = x

Now substitute 31 in place of x

FEG = (2*31-6)

FEG = 56

Find the missing side. Round to the nearest tenth

Answers

Answer:

We know Cot51 = x/17

=> 0.809784 × 17 = x

=> 13.753 = ×

.°. The value of x = 13.753 ~~ 14.000 (Ans)

plzzzzzzzz help for a brainly

Answers

Answer:

246

Step-by-step explanation:

Write in the equation for the slope intercept form and please no links or I will report you

Answers

Answer:

y = 3/2x + 8

Step-by-step explanation:

using points (-2,5) and (0,8),

we find slope, by using rise/run aka the y's/x's. so 8-5/0--2= 3/2 for slope. (8,0) is an intercept, so b out y=mx +b has been found!

From the equation below, where is the center of the circle located and what is the radius?
(x – 4)2 + (y + 8)2 = 16
A) Center: (4, -8) Radius = 4
B) Center: (-4, 8) Radius = 4
C) Center: (4, -8) Radius = 16
D) Center: (-4, 8) Radius = 16

Answers

Answer:

B Center: (-4, 8) Radius = 4

Step-by-step explanation:

Sequences:
Determine the first five terms of the following sequences:

A. [tex]a_{n} = \frac{2n+3}{4}[/tex]

B. [tex]a_{n} = \frac{n-3}{n-2}[/tex]

Answers

Answer:

A.

aₙ = (2n + 3)/4

The first 5 terms:

a₁ = (2*1 + 3) / 4 = 5/4a₂ = (2*2 + 3) / 4 = 7/4a₃ = (2*3 + 3)/ 4 = 9/4a₄ = (2*4 + 3) / 4 = 11/4a₅ = (2*5 + 3) / 4 = 13/4

B.

aₙ = (n - 3)/(n - 2)

The first 5 terms:

a₁ = (1 - 3) / (1 - 2) = 2a₂ = (2 - 3) / (2 - 2) = undefineda₃ = (3 - 3)/ (3 - 2) = 0a₄ = (4 - 3) / (4 - 2) = 1 / 2a₅ = (5 - 3) / (5 - 2) = 2 / 3
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