A manufacturer wants to construct a box whose base length is 4 times the base width. The material to build the top and bottom cost 8 dollars per ft.2 and sides 5 dollars per ft.2. If the box must have a volume of 72 ft.3, determine the dimensions that will minimize cost.

Answers

Answer 1

Answer:

width = 1.77845 ft

length = 7.1138 ft

height = 5.691 ft

total cost = $759.09

Step-by-step explanation:

volume = length x width x height

length = 4 width

base of the rectangle = 4 x 1 w = 4w²

72 (volume) = 4w²h

18 = w²h

f(c) = (2 x 4w² x $10) + (2 x wh x $5) + (2 x 4wh x $5)

f(c) = 80w² + 10wh + 40wh

f(c) = 80w² + 50wh

since we need only 1 variable (width), we have to substitute h:

h = 18/w²

f(c) = 80w² + 50w(18/w²) = 80w² + 900/w

f'(c) = 160w + 900/w²

0 = (160w³ + 900)/w²

0 = 160w³ + 900

0 = 20(8w³ + 45)

0 = 8w³ + 45

8w³ = -45

w³ = -45/8

w = ∛-45/8 = -1.77845 and 1.77845

since w cannot be negative, then it must be 1.77845


Related Questions

12points I will give pls help

Answers

Answer:

[tex]\\ m=3[/tex]

Step-by-step explanation:

[tex]\\ m=\frac{y_2-y_1}{x_2-x_1}\\\\ m=\frac{2-(-1)}{0-(-1)}\\\\ m=\frac{2+1}{1}\\\\ m=3[/tex]

Hope this helps you. Have a nice night.

The sum of 6 consecutive even numbers is 126.
What is the fourth number in this sequence?

Answers

Answer:

The 6 numbers are: 16, 18, 20, 22, 24, and 26 so the answer would be 22.

Renzi can type 50 words per minute. Samuel can type 45 words per minute. If Renzi and Samuel each type for 20 minutes, about how many more words can renzi type?

Answers

Answer:

100

Step-by-step explanation:

(50-45)*20

=5*20

=100

PLEASE GIVE BRAINLIEST

Answer:

Renzi can type 100 more words than Samuel

Step-by-step explanation:

PLZ MARK BRAINLIEST!!!

A bag of marbles contains 3 red marbles, 5 green marbles, and 7 blue marbles. If joseph reaches in pulls out one marble, what is the probability that the marble will not be red?

Answers

Answer:

the answer is 12/15, or 4/5. That's also 80%.

Step-by-step explanation:

List the angles in order from shortest to longest.
De, CE, CD

Answers

Answer:

CE, CD, DE

Step-by-step explanation:

Answer:

The angles in order will be CE, CD, DE

Hope this helped!

May i have brainliest !

Least to greatest -5.9, 23/4, 5.9, 58%,

Answers

Answer:

-5.9,58%,23/4,5.9

Step-by-step explanation:

-5.9,5.75,5.9,0.58

Answer:

-5.9, 0.58, 5.75, 5.9

Step-by-step explanation:

Begin by writing all four numbers into the same form.  

We'll start with -5.9.

Next, 23/4 = 5 3/4 or 5.75

Next:  5.9 stays as such

Finally, 58%, a percentage, changes to 0.58

Then the four numbers are:

-5.9, 5.75, 5.9 and 0.58

-5.9 is the smallest (and is positioned furthest from the origin to the left.  

0.58 is the next smaillest; it's positive, whereas -5.9 is negative.

The next two numbers are

5.75 and

5.9

Least to greatest, we  have -5.9, 0.58, 5.75, 5.9

Which answer choice shows sixty-one ten thousandths in standard form?

A
61,000
B
0.061
C
0.0061
D
0.00061

Answers

Answer:

The answer is C. 0.0061

Step-by-step explanation:

because sixty-one ten thousandths in standard form is 0.0061

You work in a restaurant. Your hourly wage is $5.25. One evening you work from 5:30 to 9:30 and make $34.20 altogether. How much do you make in tips that evening?
Your answer

Answers

9514 1404 393

Answer:

  $13.20

Step-by-step explanation:

Working h hours and earning t in tips, your earnings (e) are ...

  e = 5.25h +t

Solving for t, we get ...

  t = e - 5.25h

Filling in the given values, we have ...

  t = 34.20 -5.25(4) = 34.20 -21.00 = 13.20

You made $13.20 in tips that evening.

What is the slope of the line.

Answers

-4/5 is the skip of the graph

Answer:

-4/5

Step-by-step explanation:

The slope of the graph is -4/5. The slope is the change in y over the change in x. The y-value decreases by 4 and the x-value increases by 5. So the slope is -4/5. One visual way to check this is to remember that slopes that are fractions will make the line flatter, while numbers with absolute values greater than 1 make the slope steeper.

The slope of the line is

Answers

Answer:

(-1,1)(2,-8)

Step-by-step explanation:

-1-2=-3

1-8=-7

the slope of the line is (-3,-7)

correct me if i am wrong and also refresh your screen because i had changed my answer after i had noticed the second plotted point

PLS HELP! WILL GIVE BRAINLIEST! 70 PTS! pls only answer if you know
Completing the Square
Solve the equation by completing the square. Show your work.
x2 – 30x = –125
Step 1: Add to both sides of the equation. (2 points)







Step 2: Factor the left side of the equation. Show your work. (2 points)
Hint: It is a perfect square trinomial.









Step 3: Take the square root of both sides of the equation from Step 2. (1 point)







Step 4: Simplify the radical and solve for x. Show your work. (1 point)

Answers

Answer:

25, 5

Step-by-step explanation:

x^2-30x=-125
x^2-30x+225=-125+225
x^2-30x+225=100
(x-15)^2=100
First answer:
x-15=+10
x=25
Second answer:
x-15=-10
x=5

Determine the area of the sector of a circle in the following diagram (round to the nearest tenth):

A =

Answers

Answer:

1,848 units²

Step-by-step explanation:

360° ÷ 120° = 3

A = πr²

A = [tex]\frac{22}{7}[/tex] × 42² = 5,544

The area of the sector of a circle is 5,544 ÷ 3 = 1,848 units²

La rueda delantera de una moto mide 50cm de diámetro. ¿Qué distancia ha recorrido la moto si la rueda ha dado 120 vueltas? ¿Cuántas vueltas ha dado la rueda trasera si su diámetro es de 60cm?Trace la gráfica del problema.

Answers

Answer:2.8333333

Step-by-step explanation:

Which of the following are square roots of –8 + 8iStartRoot 3 EndRoot? Check all that apply.
Negative 2 + 2 I StartRoot 3 EndRoot
Negative 2 minus 2 I StartRoot 3 EndRoot
2 + 2 I StartRoot 3 EndRoot
Negative 4 + 4 I StartRoot 3 EndRoot
4 minus 4 I StartRoot 3 EndRoot
4 + 4 I StartRoot 3 EndRoot

Answers

Answer:

the answer is the 2nd and 3rd option

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The square root of -8 + 8i√3 have

√2(-4 + 4i√3)

or

√4(-2 + 2i√3)

Options A and D is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The square root of -8 + 8i√3

This means,

= √(-8 + 8i√3)

= √2(-4 + 4i√3)

or

= √4(-2 + 2i√3)

Thus,

The square root of -8 + 8i√3 have

√2(-4 + 4i√3)

or

√4(-2 + 2i√3)

Options A and D is the correct answer.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

a basketball team won 60% of their games this season. If the team won 18 games this season, how many games did they play?
A.16 games
B.30 games
C.42 games
D.78 games

Answers

Answer:

B) 30 games

Step-by-step explanation:

All you need to do is divide the games won by the percent won (make sure to change the percent into a decimal)

18/ 0.6 = 30

Answer:

66666666666666666666666666666666

Step-by-step explanation:

Which inequality is represented by this graph

Answers

Answer:

The answer is C

Step-by-step explanation:

The points (-1, -3) and (2, r) lie on a line with slope 3. Find the missing coordinate r

Answers

Answer:

6

Step-by-step explanation:

y+3/2+1= y+3/3

what can be divided by 3 to then equal 3? 9

9-3+6

6+3/2+1=9/3

9/3=3


Erin goes to a pumpkin patch and picks out a pumpkin that weights 4.250 grams. How many kilograms does the pumpkin
weigh?

Answers

Answer:

0.0043

Step-by-step explanation:

Answer:

0.00425 kilograms

Solve the following:
-12 = 6(-3) + 8

Answers

Step-by-step explanation:

the left -12 does not equal to right side -28 which means that the given statement is false.

which expression is equivalent to
(2m+3)(4m-1)

Answers

Answer:

8m^2+10m-3

Step-by-step explanation:

8m^2+10m-3

The function shown is reflected across the y-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.

Answers

Answer:

its b friends :)

Step-by-step explanation:

If the function shown is reflected across the y-axis create a new function. Both the range and domain stay the same.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, the function shown is reflected across the y-axis to create a new function. We have to state the domain and range of each function.

The domain and/or range of a function will change when it is transformed. Only the domain will change if the inputs are only transformed. Only the range will change if the transformation only affects the outputs. The domain and range will change if the inputs and outputs are transformed simultaneously.

Thus, if the function shown is reflected across the y-axis creates a new function. Both the range and domain stay the same.

Learn more about the function here:

brainly.com/question/5245372

#SPJ6

complete the statements below about the graphs of y=-2x and y=x

Answers

Answer:

Compared to the graph of y = x, the graph of y = -2x is steeper.

Compared to the graph of y = x, the graph of y = -2x intersects the y-axis at the same point.

Compared to the graph of y = x, the graph of y = x + ⅔ is equally steep.

Compared to the graph of y = x, the graph of y = x + ⅔ intersects the y-axis at a higher point.

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiStep-by-step explanation:

PLS PLS PLS PLS PLS I GIVE ALL MAH POINTS

Answers

125 = 5³, and the given expression reduces to

[tex]\left(\sqrt{125}\right)^{\frac13}\cdot\left(\sqrt[3]{125}\right)^{\frac12}=\left(125^{\frac12}\right)^{\frac13}\cdot\left(125^{\frac13}\right)^{\frac12}=125^{\frac16}\cdot125^{\frac16}=125^{\frac13}[/tex]

so it has a value of 5.

Now:

• the first choice is equivalent, since 625 = 25², so

[tex]\dfrac{\sqrt[3]{625}}{5^{\frac13}}=\dfrac{25^{\frac23}}{5^{\frac13}}=\dfrac{5^{\frac43}}{5^{\frac13}}=5[/tex]

• the second choice is not equivalent, since

[tex]5 \cdot 25^{\frac13} = 5 \cdot 5^{\frac23} = 5^{\frac43}[/tex]

• the third choice is also equivalent, since

[tex]\dfrac{\left(\sqrt[4]{5}\right)^7}{125^{\frac14}}=\dfrac{5^{\frac74}}{5^{\frac34}}=5[/tex]

• the fourth choice is also equivalent, since

[tex]\dfrac{5^{\frac12}\cdot25^{\frac13}}{\sqrt[6]{5}}=\dfrac{5^{\frac12}\cdot5^{\frac23}}{5^{\frac16}}=\dfrac{5^{\frac76}}{5^{\frac16}}=5[/tex]

write the equation of the line in slope intercept form .

Answers

Answer:

Step-by-step explanation:

Points are (0,-2)(3,0)

Slope intercept form is y=2/3x-2

WILL MARK BRAINLIEST PLEASE HELP!!!!!!!!!!!!!!!!!

Answers

Answer:

its c

Step-by-step explanation:

find the value of x in the triangle shown below , please help

Answers

Answer: 55°

Step-by-step explanation:

Isosceles Triangle

Give an example of two integers that make a zero pair. Explain how they are additive inverses.

Answers

Answer:

-6+6=0

-10-(-10)=0

Step-by-step explanation:

Hope that helps!

An example of two integers that make a zero pair is 6 and -6.

They are additive inverses because they sum up to zero

For two integers to make a zero pair:

They must be equal in magnitudeThey must have opposite signs

Let the first number be represented by x

For one to be the additive inverse of the other, the second number must be -x.

x  +  (-x)  

=  x  -  x

=  0

An example of integers that make a zero pair 6 and -6

6  +  (-6)

=  6  - 6

= 0

Learn more here: https://brainly.com/question/18453268

hi can someone do this and explain how to do it

Answers

The equation in slope intercept form is f(x)=-3x-7

Hope this helps!

Five more than a number is 25. What is this number?

Answers

Answer:

5

Step-by-step explanation:

let the number be a.

5a=25

divide both sides by 5

5a=25

5divide by 5a is a.

5divided by 25 is 5

therefore,a=5.

the number is 5

What is the area of this shape?
units squared

Answers

Answer: 19 units squared

Step-by-step explanation:

1) Use Area= 1/2bh to get the area of the two triangles, 15 and 4

2) Add the areas together

Answer:

19 units squared

Step-by-step explanation:

I have attached an image that explains the process.

Essentially we split the shape into 3 triangles, and solve the area of each, and add them up.

The top right triangle is 3 x 5. So A = (3 x 5) / 2 = 7.5

The bottom right triangle is a copy of the top right. So that A = 7.5

The triangle on the left is 4 long and 2 high. So A = (4 x 2) / 2 = 4 units.

Total area is:

7.5 + 7.5 + 4 = 19 units squared.

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