Building a Storage Container
You are being asked to design an enclosed water storage container. You are given a budget of
$100 to build the container. It has been determined that the best material to make the container
costs $10 per m². (In other words your surface can not cost more than $100.) What is the
largest amount of water your container can hold? You will need to explain to your boss the
reasoning because they have a business degree and do not really remember any of their
geometry work from school.

Answers

Answer 1

Answer:

  2973.5 liters

Step-by-step explanation:

You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.

__

area

The available area is ...

  ($100) / ($10/m²) = 10 m²

diameter

The area of a sphere with diameter d is ...

  A = πd²

Then the diameter for the given area is ...

  10 m² = πd²

  (10/π) m² = d² . . . . . divide by π

  √(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere

volume

The volume of a sphere is given by ...

  V = 4/3πr³ = (π/6)d³

For the diameter found above, the volume of the sphere will be ...

  V = (π/6)(1.78412 m)³ ≈ 2.97354 m³

There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...

  2.97354 m³ × (1000 L/m³) = 2973.54 L

The largest amount of water the container can hold is about 2973.5 liters.


Related Questions


Which values complete the function? f(x)=_(x-_)(x+_)

Answers

Answer:

the answer is b

Step-by-step explanation:

just took the test

Answer:

Step-by-step explanation:

-1

3

4

In a right triangle, a and b are the lengths of the legs and c is the length
of the hypotenuse. If a = 2 feet and b = 1 foot, what is c? If necessary,
round to the nearest tenth.
c =
feet

Answers

c=2.2feet

The solution in the attached file

2,994 divided by 128 i need help

Answers

23.390625
That is your answer

Answer:

Divide 320 by 128 to get 2

23.39062

128| 2994.00000

256

____

434

384

_____

500

384

_____

1160

1152

____

80

0

___

800

768

_____

320

256

_____

64

Stopping at 5 decimal places

The solution for Long Division of 2994/128 is 23.39062

23.39062

I ALWAYS GIVE BRAINLIEST!!!!!!COME AND GET IT IF YOU WANT IT! ~20 POINTS AT STAKE!

Answers

Answer:
3rd answer
Step-by-step explanation:
because for the width of the first rectangle (27 cm) it is just 3 times larger for the width of the second rectangle (9 cm)

same for the length, 33cm is 3 timer larger

also sorry if its the other way around, i just call the ones that are like "______" length

Answer: C

Step-by-step explanation:

How many combinations without repetition are possible if n = 6 and r = 3? 56 20 27 18

Answers

Answer:18

Step-by-step explanation:

n+r=9

n×r=27

r²=9

n²=36

n+n=12

r+n=9

r+r=6

Can someone try to help me I’m trying to get to a 91

Answers

In most ovens, the lowest the temperature can go is 170°F. So, the most reasonable answer would be 200°F.

Help pleasseeeee!!!!


Which of the following statements is TRUE about using a quadrilateral to construct a parallelogram?

A. All sides of the quadrilateral must be congruent and all angles must be congruent?

B. Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.

C. The sides of the quadrilateral can be any length and the angles can be any measure.

D. Adjacent sides of the quadrilateral must be perpendicular and adjacent angles must be congruent.

Answers

Answer:

B. B. Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.

Answer: Opposite sides of the quadrilateral must be parallel and opposite angles must be congruent.

Step-by-step explanation:

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

The sum of three consecutive integers is 90. Find the integers. If the smallest integer is x, the equation will be. I NEED HELP PLS SOLVE THIS QUICKLY I BEG YOU.

Answers

Answer:

x = 29

Step-by-step explanation:

Take the smallest integer as x. The next one as (x+1) and the last one as (x+2)

x + (x+1) + (x+2) = 90

x + x + x + 3 = 90

3x = 87

x = 29

Hence, x = 29

Hope this helps out. Feel free to mark me as brainliest! :)

Which function is represented by the graph?

Answers

Answer:

cos(x-[tex]\frac{pi}{4}[/tex])-2

Step-by-step explanation:

The function is cos(x).

The horizontal shift is caused by (x- pi/4) so it would go to the right a distance of pi/4. If it was positive the entire thing would go left (x + pi/4).

The vertical shift is caused by the negative 2. Unlike horizontal shifts, negative moves it down and positive moves it up.

The x-axis is in radians. Desmos has option to change it to radian.

short answer: Write an equation in the form y=ax2+bx+c for a parabola that intersects the x-axis at -6 and 2 and passes through the point (1,-14) (2 points). Show you work.

Answers

Answer:

y = 2x^2 + 8x - 24

Step-by-step explanation:

This is a "working backwards" kind of a problem. You know the solution (the x-intercepts) and work backwards to find the equation. See image.

What is the product? startfraction x squared minus 16 over 2 x 8 endfraction times startfraction x cubed minus 2 x squared x over x squared 3 x minus 4 endfraction

Answers

The product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]

Simplifying fractions

From the question, we are to determine the product of the given expressions

The given expressions are

[tex]\frac{x^{2} - 16}{2x+8}\times \frac{x^{3}-2x^{2} +x}{x^{2} +3x-4}[/tex]

[tex]\frac{(x+4)(x-4)}{2(x+4)}\times \frac{(x^{2} -x)(x-1)}{(x-1)(x+4)}[/tex]

[tex]\frac{(x-4)}{2}\times \frac{(x^{2} -x)}{(x+4)}[/tex]
[tex]\frac{(x-4)}{2}\times \frac{x(x-1)}{(x+4)}[/tex]

[tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex]

OR

[tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex]

OR
[tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]

Hence, the product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]

Learn more on Simplifying fractions here: https://brainly.com/question/27038950

Here is the complete and correct question:

What is the product? StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction

#SPJ4

Answer:

A. StartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFraction

Step-by-step explanation:

correct on edge :)

Pls help will give brainilist

Answers

Answer:

$16.37

Step-by-step explanation:

They want to raise $463.72 and they already have $218.22 so if we subtract it

$463.72-$218.22=$245.50

we get $245.50 left to raise.

We have 15 teachers so we do

$245.50/15

we get 16.36 but we round it so we get $16.37.

Which line is the best model for the data in the scatter plot?

Answers

Answer:

the top right (2) answer is probably what you'll want to go for, if this is incorrect then you have my deepest apologies

Step-by-step explanation:

Quadrilateral abcd is a parallelogram if both pairs of opposite angles are congruent. prove that quadrilateral abcd is parallelogram by finding the measure of the opposite angle pairs?

Answers

Answer:

you how are doing please study and work hard

HEY GUYS THIS IS MY FINAL MATH ASSIGNMENT OF THE YEAR... PLS JUST HELP ME FIND THE DOMAIN AND RANGE THANK YOU

Answers

Answer:

domain: all real numbers (-∞,∞)

range: y ≤ 64

Step-by-step explanation:

since the domain is arn,

and range is the coordinates

coordniate (top or bottom-most point)

downward facing so the top

(2, 64)

since it is downward facing we use ≤ instead of ≥

y value is 64 (just as x is 2)

your answer is y ≤ 64

hope this helps:)

Answer:

[tex]D=[x E R | {x = \infty} ][/tex]

[tex]R = [yER| y\leq 64][/tex]

Step-by-step explanation:

1) Identify whether the [tex]x[/tex] and [tex]y[/tex] values are continuous

2) Since [tex]x[/tex] will continue below the [tex]x[/tex]-axis, it will approach infinity.

   Therefore [tex]D=[x E R | {x = \infty} ][/tex]

3) Since [tex]y[/tex] ONLY continues below 64, [tex]R = [yER| y\leq 64][/tex]

What is the value of z, rounded to the nearest tenth? use the law of sines to find the answer. 2.7 units 3.2 units 4.5 units 5.3 units

Answers

The triangle is a shape with 3 sides and angles. The value of z from the given figure to the nearest tenth is 3.2

Sine rule of triangle

The triangle is a shape with 3 sides and angles

From the given triangle, we will use the expression below to determine the value of z

2.6/sin51= z/sin76

simplify

z = 2.6sin76/sin51
z = 2.5227/0.7771

z = 3.246

Hence the value of z from the given figure to the nearest tenth is 3.2

Learn more on sine rule here: https://brainly.com/question/27174058

#SPJ4

A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.
Is this a matched pairs design for this experiment?
Yes, the company used 24 different vehicles.
Yes, both types of tread were randomly assigned to each vehicle.
No, the vehicles were not put into groups of two.
No, the tires with the different types of tread were not randomly assigned to each vehicle.

Answers

This is a matched pairs design because both types of tread were randomly assigned to each vehicle.

What is matched pairs design?

The term matched pairs design has to do with the situation in which participants are randomly assigned to an experiment or a control group. For each participant assigned to an experimental group, another is assigned to the control group.

Thus, this is a matched pairs design because both types of tread were randomly assigned to each vehicle.

Learn more about matched pairs design:https://brainly.com/question/17144039

#SPJ1

Identify coordinate point A.

(0, 2)
(6, 7)
(1, 5)
(7, 3)

Answers

i need to see the image

Answer:

(0, 2)

Step-by-step explanation:

it right I got 100% on my quiz

And… here are others that are right in the quiz

Identify coordinate point B.

(1, 5)

Identify coordinate point D.

(7, 3)

Identify coordinate point C.

(6, 7)

Hope it helps! :)

The quotient of 7 and the difference of a number and 8.

Answers

                    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]      

      ➪  What is the quotient of 7 and the difference of a number and 8?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

         ➪ First, the word "quotient" indicates that we divide.

   ✳︎ Here, we are asked to divide 7 by the difference of a number and 8.

➪ The word "difference" indicates that we subtract.

        ✳︎ Here, we are asked to subtract  a number minus 8.

     

Let the number be x.

Since the difference of x and 8 means we subtract x minus 8, this expression looks as follows:-

         [tex]\texttt{x-8}[/tex]

  ◈     Now, we are also asked to find the quotient of 7 and the difference of a number and 8, which equals [tex]\bold{x-8}[/tex].

As I said earlier, the "quotient" means we divide, so we divide 7 by [tex]\bold{x-8}[/tex].

So we conclude that the expression is:-

7÷(x-8)

Good luck.

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

If you get a $50.00 raise in pay per month and your taxes also increase about $50.00 per month, how would you probably feel?

appreciated because you are getting rewarded for your hard work

satisfied because you broke even

proud because the government needs your money more than you do

resentful because it seems unfair

Answers

Answer:

i would say satisfied because you broke even. Because then you still work the same as you did, because before that you were breaking even every month. So you are not getting paid any extra

Step-by-step explanation:

Order the following integers from least to greatest: -32, -43, -28, -22 and 13

Answers

Answer:

-22, -28, -32, -43, 13

Step-by-step explanation:

If it is after the digit 0 it will be less than any number above itself.

Russ walks 710 mile to school. How far has he walked when he has covered 58 of the distance to school?\

Answers

Answer: [tex]\frac{7}{16}[/tex]

Step-by-step explanation: Distance to school = [tex]\frac{7}{10}[/tex] mile

Distance covered = [tex]\frac{5}{8}[/tex] of [tex]\frac{7}{10}[/tex]

                      = [tex]\frac{5}{8}[/tex] x [tex]\frac{7}{10}[/tex]

                       = [tex]\frac{35}{80}[/tex]

                      = [tex]\frac{7}{16}[/tex]

list all the possible order you can have

Answers

wala ako pake sau

Step-by-step explanation:

wala ako pake sau

I need this solved now

Answers

Answer: Opposite

Detailed Explanation:

If both pairs of Opposite sides of a Quadrilateral are equal, then it is a Parallelogram. These are the basic properties of a Parallelogram.

A rectangular pyramid has a volume of 492 cubic yards. if the base has a length of 18 yards and a width of 4 yards, what is the height of the pyramid?

Answers

Answer:

h = 20.5 yards

Step-by-step explanation:

Volume of Rectangular Pyramid: lwh/3

492 = (18) * (4) (h) /3

Multiply 3 on both sides

1476 = (18) (4) (h)

1476 = 72h

Flip the equation.

72h = 1476

h = 41/2 or 20.5 yards

ignore the numbers on top of the fruits but can someone help solve this?

Answers

Step-by-step explanation:

I don't know what the 3rd fruit is. let's call it an apple.

so,

1 apple + 3 cherries = 3 bananas

1 apple = 3 bananas - 3 cherries

1 banana + 2 cherries = 1 apple = 3 bananas - 3 cherries

5 cherries = 2 bananas

1 apple + 1 banana = (1 banana + 2 cherries) + 1 banana =

= 2 bananas + 2 cherries =

= 5 cherries + 2 cherries =

= 7 cherries

the numbers did not help, as they were wrong.

e.g. if you assume the apple = 5, a cherry = 1 and a banana = 2, you would get 8 = 6 on the first scale.

if you change the apple to a 3, that would make the first scale true (6 = 6), but the second scale wrong (4 = 3).

funny enough, the other answer got 7 nevertheless (but the wrong way - actually 2 mistakes balanced each other out).

it is 7 cherries, though !

the actual numbers would be e.g.

a cherry = 1

then

1 banana = 5/2 = 2.5

1 apple = 3×5/2 - 3 = 15/2 - 6/2 = 9/2 = 4.5

to get whole numbers, we could multiply all by 2 :

cherry = 2

banana = 5

apple = 9

and then the first balance :

9 + 3×2 = 3×5

9 + 6 = 15

15 = 15 correct

the second balance

5 + 2×2 = 9

9 = 9 correct.

PLEASEEEEE

Match the expressions with their simplified versions.

Answers

Answer:

1. [tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]

2. [tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]

3. [tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]

4. [tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]

Step-by-step explanation:

The Radical Rules by Lial et al. (2017) state that:

Product rule: [tex]\large \textsf{$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$}[/tex]

"The product of two roots is the root of the product."

Quotient rule: [tex]\large \textsf{$\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$}\ \ \textsf{$(b \neq 0)$}[/tex]

"The root of a quotient is the quotient of the roots."

1.

[tex]\implies \normalsize \textsf{$4\sqrt{2}\cdot\sqrt{2}$}\\\\\normalsize \implies \textsf{$4\sqrt{2\cdot2}$}\\\\ \implies \normalsize \textsf{$4\sqrt{4}$}\\\\ \implies\normalsize \textsf{$4\cdot 2 = 8$}[/tex]

[tex]\normalsize \boxed{\textsf{$4\sqrt{2}\cdot\sqrt{2}$}} \implies \boxed{8}[/tex]

2.

[tex]\implies \normalsize \textsf{$3\sqrt{7}-2\sqrt{7}$}\\\\ \implies\normalsize \textsf{$(3-2)\sqrt{7}$}\\\\ \implies\normalsize \textsf{$1\sqrt{7}$}\\\\ \implies\normalsize \textsf{$\sqrt{7}$}[/tex]

[tex]\normalsize \boxed{\textsf{$3\sqrt{7}-2\sqrt{7}$}} \implies \normalsize \boxed{\textsf{$\sqrt{7}$}}[/tex]

3.

[tex]\implies \normalsize \textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1\sqrt{7}}{2\sqrt{7}}$}\\\\\\ \implies\normalsize \textsf{$\dfrac{1}{2}$}\\\\[/tex]

[tex]\normalsize \boxed{\textsf{$\dfrac{\sqrt{7}}{2\sqrt{7}}$}} \implies \normalsize \boxed{\textsf{$\dfrac{1}{2}$}}[/tex]

4.

[tex]\implies \normalsize \textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}\\\\ \implies\normalsize \textsf{$2\cdot2\sqrt{5\cdot5}$}\\\\ \implies \normalsize \textsf{$4\sqrt{25}$}\\\\ \implies \normalsize \textsf{$4\cdot5=20$}\\\\[/tex]

[tex]\normalsize \boxed{\textsf{$2\sqrt{5}\cdot 2\sqrt{5}$}} \implies \boxed{20}[/tex]

Reference:

Lial, M., Hornsby, J., Schneider, D., & Daniels, C. (2017). College Algebra and Trigonometry, Global Edition (6th ed., p. 94).

What multiplies to 4 and adds to 6​

Answers

Answer: 2

Step-by-step equation: 2 x 2= 4
2 + 4= 6

It takes Imani seven hours to dig a 10 ft by 10 ft hole. Stefan can dig the same hole in five hours. If they worked together how long would it take them

Answers

Answer:

2 hours and 44 min. or 2.7273 hours

Step-by-step explanation:

Ryan: 1 hole per 5 hours

Castel: 1 hole per 6 hours

x = time if working together then

x(1/5 + 1/6) = 1

x(6 + 5) = 30

11x = 30

x = 30/11

x = 2.7273 hours

or

x = 2 hours and 44 minutes

1.Judy put 50 cents and 1 quarter into a vending machine to buy a bottle of fruit juice. She got 2 dimes and 1 nickel back from the vending machine. How much did the bottle of fruit juice cost

Answers

Nickel - 5 cents

Dime - 10 cents

Quarter - 25 cents

Judy put in: 50 + 25 = 75 cents

The machine gave back: 10 + 10 + 5 = 25

Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents

Answer:

Nickel - 5 cents

Dime - 10 cents

Quarter - 25 cents

Judy put in: 50 + 25 = 75 cents

The machine gave back: 10 + 10 + 5 = 25

Subtract the two numbers to find the difference (what the fruit juice cost): 75 - 25 = 50 cents

Step-by-step explanation:

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