A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 123 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)

Answers

Answer 1

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

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Related Questions

3x - 2y= 5, 4x + 3y= 1​

Answers

Answer:

x=17 and y=23 DONT SUE ME IF I GET THIS WRONG PLZZ ;-;

Step-by-step explanation:

Answer:

(1, - 1 )

Step-by-step explanation:

Given the 2 equations

3x - 2y = 5 → (1)

4x + 3y = 1 → (2)

Multiplying (1) by 3 and (2) by 2 and adding the result will eliminate y- term

9x - 6y = 15 → (3)

8x + 6y = 2 → (4)

Add (3) and (4) term by term to eliminate y

17x + 0 = 17

17x = 17 ( divide both sides by 17 )

x = 1

Substitute x = 1 into either of the 2 equations and solve for y

Substituting into (2)

4(1) + 3y = 1

4 + 3y = 1 ( subtract 4 from both sides )

3y = - 3 ( divide both sides by 3 )

y = - 1

solution is (1, - 1 )

Help me it is an hw due soon please

Answers

Answer:

1st is 1/4 and 2nd is 1/10

the number of magazine subscriptions decreases by 8% each year.If there are 225,000 this year,how many will there be 7 years from now

Answers

Answer:

I got 147107

Step-by-step explanation:

If the subscriptions decrease by 8% each year then you would times 225000 by 0.08 then take the number you get from that and subtract it from 225000. And repeat until you get to the seventh year.

Plz help me with this

Answers

B is the correct answer

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y=47(0.63)
x

Answers

It represents decay because the term inside the parentheses (which is “b”) is less than one. To find the percentage rate, subtract b from 1 and multiply it by 100.

1-0.63=0.37
0.37(100)=37

So the final answer is 37% decrease.

Answer:

decay function

percent rate of decrease is 37%

Step-by-step explanation:

I assume the x is the exponent.

[tex] y = 47(0.63)^x [/tex]

The number raised to the exponent x is 0.63 which is between 0 and 1. That means that as x increases, (0.63)^x decreases. That means it is an exponential decay function.

Each unit more in x results in 0.63 being multiplied by the number.

Since 1 - 0.63 = 0.37, the percent rate of decrease is 37%.

Answer:

decay function

percent rate of decrease is 37%

HELP ME!!!!!!!!!!! Its the one in the middle

Answers

Answer:

[tex]\frac{x3(p+5)}{10p(p-1)}[/tex]

Step-by-step explanation:

BRAINLIEST PLEASE

Helia invested 4000 AED for 3 years with a compound interest rate of 1.5%, Calculate the worth of her investment at the end of this time period

Answers

4000(1+1.5\100)to the power of 3

Choose the statement that describes a way to solve the equation x – 23 = 18.

Answers

Answer:

x-23=18

x=18+23

x=41

Step-by-step explanation:

go to - 23 on the other side after equal to the changed sign and find x

You have to solve the problem \frac{3}{4}-\frac{1}{8} ​4 ​ ​3 ​​ − ​8 ​ ​1 ​​ . After you make the denominators the same, what do you do?


FOR ALL MY POINTS

Answers

Answer:

If you are doing subtraction with fractions you need to make a common denominator and subtract the numerators from each other

ex. 1/2 - 1/3

make a common denominator (or find the least common multiple)

3/6 - 2/6

subtract the numerators

take 2 from 3 and put that on top.

Solution 1/2-1/3= 3/6-2/6= 1/6

Si tenemos un cuadrado cuyos lados miden 1/3 en 7 partes iguales, ¿Cuál es su área?

Answers

Answer:

English please?

Step-by-step explanation:

...........

what is the area of a square yards of a rectangle with a length of 9 yds and a width of 4 yds?

Answers

[tex]a = lw[/tex]

[tex]a = (9)(4)[/tex]

[tex]a = 36 \: {yds}^{2} [/tex]

Answer:

Here we can understand that the shape is a rectangle as length is not equal to width.

Area of the rectangle in square yards when length is 9 yds and width is 4 yds will be,

Area of Rectangle = LENGTH × WIDTH

⇒ 9*4

⇒ 36 sd yds

Thus the are will be  36 sd yds

On a triangle, one side measures 4x2−2x and another side measures 2x2 −5x+1. If the perimeter of the triangle is 9x2 + x+6, what is the measure of the third side of the triangle? (Your answer will be an expression)

Answers

Answer:

3x² + 8x + 5

Step-by-step explanation:

Subtract the sum of the 2 given sides from the perimeter, that is

9x² + x + 6 - (4x² - 2x + 2x² - 5x + 1)

= 9x² + x + 6 - (6x² - 7x + 1 ) ← distribute parenthesis by - 1

= 9x² + x + 6 - 6x² + 7x - 1 ← collect like terms

= 9x² + 8x + 5

PLEASE HELP! ANSWER FOR 20 POINTS PLS PLS

Answers

Answer:

5³ = 125

Step-by-step explanation:

5³ = 5 × 5 × 5 = 25 × 5 = 125

Answer:

5³ = 15 because the ³ mean 3 left over 5's like if i had 2² the ² = 2 so 2²=4

5+5+5=15

Answer : 15

When a rocket is launched, it climbs 50 feet for every 13 feet it travels horizontally. Estimate the rocket's distance (Find the missing side of triangle).​

Answers

Answer:

About 51.6 feet

Step-by-step explanation:

50^2+13^2

Square root of 2669 is 51.66236541

Which expression is represented by the model?


4X43
-4X-3
-4x+3

Answers

4x43 im pretty sureeeeeeeeeeeeee
4x43 I think yeppppppppp

What is the positive value of “x”?
x(x+5)=387
Hint: Use the quadratic formula

Answers

Answer:

x= −5−11√13/2, −5+11√13/2

Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

Exact Form:

x= −5−11√13/2, −5+11√13/2

Decimal Form:

x=17.33053201…,

−22.33053201…

Step-by-step explanation:

x(x+5)=387

Simplify

x(x+5).

x^2+5x=387

Subtract 387 from both sides of the equation.

x^2+5x−387=0

Use the quadratic formula to find the solutions.

−b±√b^2−4(ac)/2a

Substitute the values a=1, b=5, and c= −387 into the quadratic formula and solve for x.−5±√5^2−4⋅(1⋅−387)/2⋅1

Simplify.

x=−5±11√13/2

The final answer is the combination of both solutions.

x=−5−11√13/2, −5+11√13/2

The result can be shown in multiple forms.

Exact Form:

x=−5−11√13/2,−5+11√13/2

Decimal Form:

x=17.33053201…,

−22.33053201…

Hope it is helpful....

Answer:

[tex]\displaystyle x=\frac{-5+11\sqrt{13}}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define

x(x + 5) = 387

Step 2: Identify Variables

Rewrite

[Distributive Property] Distribute x:                                                               x² + 5x = 387[Subtraction Property of Equality] Subtract 387 on both sides:                  x² + 5x - 387 = 0Part:                                                                                                                 a = 1, b = 5, c = -387

Step 3: Solve for x

Substitute in variables [Quadratic Formula]:                                                [tex]\displaystyle x=\frac{-5\pm\sqrt{5^2-4(1)(-387)}}{2(1)}[/tex][√Radical] Evaluate exponents:                                                                    [tex]\displaystyle x=\frac{-5\pm\sqrt{25-4(1)(-387)}}{2(1)}[/tex][√Radical] Multiply:                                                                                         [tex]\displaystyle x=\frac{-5\pm\sqrt{25+1548}}{2(1)}[/tex][√Radical] Add:                                                                                               [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2(1)}[/tex][Fraction - Denominator] Multiply:                                                                  [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2}[/tex][Fraction - √Radical] Simplify:                                                                        [tex]\displaystyle x=\frac{-5\pm 11\sqrt{13}}{2}[/tex]

If the formula for finding the area of a rectangle is A=bh, then how could you describe the formula for finding the area of a triangle

Answers

Answer:

A=LxW

Step-by-step explanation:

Answer:

El perímetro de un triángulo es igual a la suma de sus tres lados.

b   x h

 2

I am going to repeat myself ONE LAST TIME. Please help!

What is the domain of the function y = StartRoot x EndRoot?

Answers

It’s C!

Hope this helps :)

A community builds a sandbox section and a playground section at one of the local parks. The area of the playground
section is 1,675 square feet. It is 100 square feet more than 4.5 times the area of the sandbox section.
• Write an equation that can be used to determine the area, A. of the sandbox section.
. What is the area of the sandbox section? Show all work.
Enter your equation, answer, and work in the box

Please help worth 25 points

Answers

9514 1404 393

Answer:

A + (100 +4.5A) = 1675A ≈ 286.4 square feet

Step-by-step explanation:

The problem statement tells us that the area of the sandbox and playground together is 1675 square feet. Using A as the area of the sandbox section, the playground section is said to be (100 +4.5A). Then the total area is ...

  A + (100 +4.5A) = 1675 . . . . . . an equation to determine A

  5.5A = 1575 . . . . . . . . . . . . . . . subtract 100, collect terms

  A = 1575/5.5 = 286 4/11 . . . . . divide by 5.5

The area of the sandbox section is about 286.4 square feet.

Logan ran a 200-meter rase in 25.24 seconds, and Scott ran 0.4 kilometer in 52.77 seconds. Who ran faster, Logan or Scott? And at what rate did they run meters per second

Answers

Neither Logan or Scott ran farther than the other they were in the same miles at the same time.

Is the absolute value of -29 less than 29?

Answers

Answer:

no

Step-by-step explanation:

The absolute value is EXACTLY 29, so.

Andrei ,Aura,Dorin,și Emilia calculează media geometrică a numerelor √32;3√2 și obțin rezultatele din tabelul:Andrei 6√2.
Aura 4√3.
Dorin 2√6
Emilia6.

Answers

Answer:

this is the way we calculate it ♡♡♡

Find the values of the variables in the parallelogram. The diagram is not to scale.

Answers

Step-by-step explanation:

option B is the correct answer of this question.

x = 29, y = 49 and z = 102 .

plz mark my answer as brainlist plzzzz vote me also .

hope this will be helpful to you.

Answer:

B

Step-by-step explanation:

x is 29 because the inverse opposite of angles are the same.

z is 102 because opposite parallelogram angles are the same.

y is 49 through process of elimination.

Which of the relations has a domain of {-5, 0, 5}?

A. {(-5, 5), (0, 5), (5,5)}
B. {(0, -5), (0, 0), (0, 5)}
C. {(-5, 0), (0, 5), (1, 0)}

Answers

Answer:

B

Step-by-step explanation:

its that how you would look like if you were anime sorry was looking at your pf. have a nice day

[tex]\sqrt{2x-3} =5[/tex]

Answers

X=14

How to:
Square both sides then solve the equation

I really need help really fast!!!

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Answer:

-3 sqrt 2 or -4.242640687

Step-by-step explanation:

PLEASE HELP!!!!!!!! Identify the angle of elevation.

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Answer:

8

Step-by-step explanation:

Hope it helps you in your learning process.

5y=2x+5 Y=-x +6
( x, y)

Answers

Answer:

Step-by-step explanation:

6/5 + 2x/5= y

3+ 5y/2 = x

If you give me the correct answer I will give you brainliest plz help

Answers

It’s 1 and 2.
Comment if you need clarification.

libro de matemáticas 1 de secundaria pag 108

porfavor es para hoy ಠ﹏ಠ​

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con repuesta y todo para mi friend, no mas que las demas no pude contestarlas ya que estava en clase y ahorita estoy haciendo tarea ok

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