A sheet of cardboard 12 inches square is used to make an open box by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest possible volume

Answers

Answer 1

Answer:

[tex]x=6+3\sqrt{2}[/tex] is the size of the square

Step-by-step explanation:

Let the side of the square cut from the cardboard be “x”

Size of the square base = [tex]12 -2x[/tex], height of the box = x

Volume of square box = Area * height = [tex](12-2x)^2 * x[/tex]

Differentiating the above equation and equating it to zero, we get –  

d/dx [tex]((12-2x)^2 * x)[/tex]

d/dx[tex]{(144 + 4x^2 -48x)*x}[/tex]= d/dx [tex](144x + 4x^3 -48x^2)[/tex]

d/dx [tex](144x + 4x^3 -48x^2) = 0[/tex]

[tex]144+8x^2-96X= 0\\18 +X^2-12X = 0[/tex]

On solving above equation, we get –  

[tex]x=6+3\sqrt{2} \\ x=6-3\sqrt{2}[/tex]


Related Questions


When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?

Answers

Answer:

Step-by-step explanation: 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you  

NO LINKS PLEASE ..Solve for x

Answers

Answer:

x = 42.5

Step-by-step explanation:

all triangles inscribed into a circle like in the picture must have a 90 degree angle.

so, 90 = 2x + 5, 85 = 2x, x = 85/2 = 42.5

PLEASE HELP DUE IN 5 MINUTES!! NO LINKS! HELP PLEASE!!

Answers

Answer:

Step-by-step explanation:

its about 263.08!

Answer: about 263.08 sq meters (choice C)

====================================================

Explanation:

We'll use this formula

S = (x/360)*A

where,

S = area of pie slice, aka sectorx = central angle in degreesA = area of full circle

We'll plug in S = 85.5 and x = 117 to find solve for A.

S = (x/360)*A

85.5 = (117/360)*A

85.5*(360/117) = A

A = 85.5*(360/117)

A = 263.076923076923 which is approximate

A = 263.08 square meters (choice C)

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

Side note: As the formula suggests, the x/360 portion is the fractional portion of the full area A. For example, if x = 180 degrees, then x/360 = 180/360 = 1/2, meaning we'll take half of the full circle area to get S.

Simplify : (3-3y+y)
ANSWER ?

Answers

it should be the answer- 3-2y

what number is equal to 3 thousands+ 7 tens+ 5 ones

Answers

Answer:

3075

Step-by-step explanation:

There is 3 thousands so 3,000 no hundreds so 0 then 7 tens,70, then 5 one,5, so 3075

Answer:

3,075

Step-by-step explanation:

3 thousands = 3,000

0 hundreds = 0

7 tens = 70

5 ones = 5

Solve for x.
2x + 4
4x - 88
x = [?]

Answers

Solve for x.
2x + 4= 8
4x - 88 = -352
x = [?]

explain how you can determine if a triangle is a right triangle. (make it look like a middle schooler wrote it :) )

Answers

Answer:

if one of the angles is 90°

Step-by-step explanation:

when it has an angle that is 90° that means that it is a right triangle

let me know if you need more b/c I wasn't sure whether to make it more advanced for middle school lol

Hope this helps! :)

Solve the problem and enter your solution for the variable below. Do not include units in your answer. The scale below shows the weight, in grams, of two identical blocks. How many grams does one of the blocks weigh?​

Answers

Answer:

1) 100+10+10 = 120

2) 120 : 2 = 60

1 block — 60

During a bean flipping experiment Fiona modeled her data using the function

f(t) = 4.127 (1.468) and Karl modeled his data with the function

k(t) = 0.897 (1.992) where t represents the number of trials and f(t) represents

the number of beans.

At what number of trials would Fiona and Karl have the same number of beans?

A.3

B4

C.5

0.6

Answers

Answer:

C.5

Step-by-step explanation:

Fiona:

After t trials, she would have:

[tex]f(t) = 4.127(1.468)^t[/tex]

Karl:

After t trials, he would have:

[tex]k(t) = 0.897(1.992)^t[/tex]

At what number of trials would Fiona and Karl have the same number of beans?

This is t for which:

[tex]f(t) = k(t)[/tex]

So

[tex]4.127(1.468)^t = 0.897(1.992)^t[/tex]

[tex]0.897(1.992)^t = 4.127(1.468)^t[/tex]

[tex]\frac{(1.992)^t}{(1.468)^t} = \frac{4.127}{0.897}[/tex]

[tex](\frac{1.992}{1.468})^t = 4.6[/tex]

[tex](1.35695)^t = 4.6[/tex]

[tex]\log{(1.35695)^t} = \log{4.6}[/tex]

[tex]t\log{1.35695} = \log{4.6}[/tex]

[tex]t = \frac{\log{4.6}}{\log{1.35695}}[/tex]

[tex]t = 5[/tex]

So the correct answer is 5 trials, option C.

A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs Rs 15 per litre, a. Write a numerical expression for the given statement. B. Which property of whole numbers would you use to form a numerical expression for the given statement? C. How much money he gets per day for the supply?

Answers

Answer:

a) (15 × 32) + (15 × 68)

b) Distributive property

c) $1500

Step-by-step explanation:

A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs Rs 15 per litre,

a. Write a numerical expression for the given statement.

The numerical expression for the given statement is written as:

$15 × 32 liters + $15 × 68 liters

15 × 32 + 15 × 68

B. Which property of whole numbers would you use to form a numerical expression for the given statement?

The property that I would use to form a numerical expression is a distributive property

a × (b + c) = (ab + ac)

Where a = $15

b = 32 liters

c = 68 liters

Hence:

15 (32 + 68) = (15 × 32) + (15 × 68)

C. How much money he gets per day for the supply?

The amount he gets per day:

15 (32 + 68) = (15 × 32) + (15 × 68)

= $1500

How do you find the area of a circle???

Answers

The area of a circle is pi times the radius squared
A= π r2 Depending on what the value is in “r”

Divide 78 in the ratio 8 : 1 : 4

Answers

Answer:

78×8/13=48

78×1/13 =6

78×4/13=24

8:1:4

48:6:24

The topic is about secant tangle angles

Answers

Answer:

41

Step-by-step explanation:

360-(104+104+111)=41

Can someone help me with this ?

Answers

Answer:

Step-by-step explanation:

the side opposite of K is JL.

answer: the side opposite is JL

explanation:








A rental car company charges $62.47 per day to rent a car and $0.09 for every mile driven. Ariana wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $320 to spend.

What is the maximum number of days that Ariana can rent the car while staying within her budget?

Answers

Answer:

only 11 days

Step-by-step explanation:

Check all that apply. is the reference angle for:
A.
1277
4
B.
1577
4
D C
1977
4
D.
777

Answers

Answer:

B. C. and D.

Step-by-step explanation:

The value of a house has increased by 5% the house is now valued at £609000 what is the value of the house before the increase? I found a post that answered the question but it didn't explain how they got the answer.

Answers

Answer:

[tex]Current \ price = 609000\\\\Let \ the \ original \ price \ be = x\\\\\% increase = 5 \% \ of \ x = \frac{5}{100} \times x = \frac{5x}{100}\\\\Price \ after \ increase, current\ price = \frac{5x}{100} + x\\\\[/tex]

[tex]=> 609000 = \frac{5x}{100} + x\\\\=>609000 = \frac{105x}{100}\\\\=> x = \frac{609000 \times 100}{105}\\\\x = 580000[/tex]

Therefore original price = $580,000

Combine like terms.

y + 2 + 8(y + 7) =

Answers

Answer:

Step-by-step explanation:

y+2+8(y+7)

y+2+8y+56

9y+58

please someone help me with this

Answers

Answer:

260 cm³

Step-by-step explanation:

Full surface area:

S = 3(6*10) + 2(1/2*8*10) = 260 cm³

Answer:

Surface Area = Surface Area of triangle + SA of rectangle

Surface Area = 3 × (6 × 10) + 2 × ½ × 8 × 10

Surface Area = 3 × 60 + 80

Surface Area = 180 + 80

Surface Area = 260 cm ³

[tex] \\ [/tex]

Find missing measure

Answers

Answer:

x = 40°

Step-by-step explanation:

using the angle sum theorem...

180 - 90 - 91 - 51 = 40

Answer:

Step-by-step explanation:

51+x+90+91=360(sum of four angles is always 360 degree)

232+x=360

x=360-232

x=128

The Atlanta Journal Constitution conducted a survey of 900 registered voters to determine which voting method they prefer. The AJC found 60% favored voting on paper ballots they filled themselves (as opposed to voting with a computer). Find a confidence interval for the proportion of all registered voters that favor at 85% confidence level. a) (0.576, 0.624) b) (0.376, 0.424) c) (0.583, 0.617) d) (0.586, 0.614)

Answers

Answer:

a) (0.576, 0.624)

Step-by-step explanation:

Given that the sample proportion (p) = 60% = 0.6, sample size (n) = 900, confidence (C) = 85%

α = 1 - C = 1 - 0.85 = 0.15

α/2 = 0.075

The z score of α/2 (0.075) corresponds with the z score of 0.425 (0.5 - 0.075) which is equals to 1.44, hence [tex]z_\frac{\alpha }{2} =1.44[/tex]

The margin of error (E) is:

[tex]E=z_\frac{\alpha }{2} *\sqrt{\frac{p(1-p)}{n} } =1.44*\sqrt{\frac{0.6(1-0.6)}{900} } = 0.024[/tex]

The confidence interval = p ± E = 0.6 ± 0.024 = (0.576, 0.624)

When rolling a pair of dice, what is the probability (as a percent) that each die will land on an even number?

Answers

Answer:

The probability of getting an even number at the first die is 1/2 (as the probability of even = the probability of odd = 1/2); 2. The probability of getting a total of 8 is 5/6^2, as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4);

Step-by-step explanation:

Someone help me! I have a pic down below.

Answers

that last one doesnt equal to the expression
the 3rd one, 3^-3/3^4

How many distinct "pieces" are in this graph?

Answers

Answer:

2

Step-by-step explanation:

the first point and where the line turns

74,308 Problem: Round the number above to the nearest ten.

Answers

Answer:

74,310

Hope this helped! ^^

Answer:

[tex] = 74,310[/tex]

step by step explanation:

Solve for x

|2x+1| + |3x-4| = 5

Answers

Answer:

0, 8/5

Step-by-step explanation:

You can use the app photo math you just take a picture of the problem and it gives you the answer and shows the steps:)

Mr. Roundtree had 20 tickets. He gave 10 to his family and 8 to his friends.​

Answers

He has two tickets left

MATH PLEASE HELP ! PLEASE

Answers

Answer:

wait I am solving this

Step-by-step explanation:

mark it as the brainliest to get the answer

If you doubled joes age and added 10 years he would still be younger than his uncle. His uncle is 51. Use inequalities to find how old Joe is.

Answers

Answer:

He is 20 at oldest, or [tex]x\leq 20[/tex]

Step-by-step explanation:

The first step in finding a possible age is:

Subtract 10 from 51, and you get 41. Divide by 2, and you get about 20.5.

This means Joe is younger than or 20 years old.

(GIVING BRAINLIEST). Daria earns $17.50 per customer when she gives haircuts. If she gave x haircuts on Monday and y haircuts on Tuesday, which expression
shows the amount of money she earned? A) 17.50/x+y B) 17.50 (x+y) C) 17.50x+y. D)17.50xy

Answers

Answer:

B. 17.50(x + y)

Step-by-step explanation:

So lets find the equation for monday:

It would be 17.50 times x

or:

17.50(x)

For Tuesday:

17.50 times y

17.50(y)

17.50(x) + 17.50 (y) = 17.50(x+y)

Or B.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Other Questions
make a table where the constant rate of change is 6 inches for every foot How many distinct triangles can be drawn by using three of the seven dots below? (Twotriangles are considered different if they dont share the same three vertices.) supported "any means necessary" to secure civil rights Solve the equation d divided by 1.2 is equal to 6 PLS HELPP Which question is a statistical question?A. How tall is the oak tree?B. How much did the tree grow in one year?C. What are the heights of the oak trees in the schoolyard?D. What is the difference in height between the oak tree and the pine tree? 11) What is the perimeter of the object *15 mm7 mm12 mm8 mm42 mmO70 mm65 mm47 mm 3. Three resistors with values of 3 , 4 and 5 are connected to a 12 V battery.a. Draw the circuit.b. Calculate the equivalent resistance of the circuit.c. Calculate the current through the battery.d. How much current is passing through each resistor?e. Calculate the voltage drop across each resistor.f. How does the voltage drop across each resistor compare to the voltage of the battery?4. Three resistors with values of 12 , 24 and 6 are connected in series to one another and a 24 V power supply. Draw the circuit and fill in the data table. The energy of the sun is transferred through plants and given toA. producers. B. consumers. !!20 POINTS!!Human use a (an) ____________ circulatory system to remove waste. A. OpenB. ClosedC. CapillariyD. Continuous ou are going to write 5 sentences using the following verbs and the vocabulary:Verbs: I do/make=Yo hago, I put/place=Yo pongo, I leave/go out=Yo salgo, I give=Yo doy, I come=Yo vengoVocabulary: helado=ice cream, dulcera=candy store, la moneda=coin, la mesa=table, la farmacia=pharmacy, el dinero=money, la juguetera=toy store, la peluquera-hair salon, barato=cheap, el crdito=credit, la tarjeta de crdito=credit card, el precio=priceExample: Yo hago pan en la panadera - (I make bread in the bakery)1.Yo hago_______________2.Yo pongo_______________3.Yo salgo______________4.Yo doy________________5.Yo vengo_____________ Luke randomly selects 25 students from his school and asks each of them how many minutes they read each night to find out how much, on average, students at his school read. This represents which type of data collection Which of the following are properties of dictionaries? (check all that apply) nestable accessed by key iterable ordered I need help on this it would really make my day The term divine rights is best defined as a. A) revolution to gain political rights and freedoms B) philosophy that encourages religious toleration C) belief that a ruler's authority comes from God D) system in which a monarch has limited power Give me 1-5 words for the theme of a song. And I will write a song based of the theme. Also i will do no more than 5 songs then i will finish and post them on this thread (50 points) Subtract. (8.3x+4)(3.2x5) Enter your answer, in simplified form, in the box. (Combine and simplify the equation.) Explique a importncia da Corte Francesa ao se reunir em Versalhes e como era a poltica de favores que l aconteciam.DO NOT ANSWER IF YOU ARE GOING TO TROLL Please help I dont understand! Giving brainliest! HELP IS NEEDED ASAPInstructions: The following argument argues for spending taxpayer money to colonize the moon. Read the argument and answer the question that follows:Topic and QuestionSpace Travel: Should our society spend taxpayer money to colonize the moon?Ineffective ArgumentI love space. It rocks.It is super important to colonize the moon because we will run out of room on earth. My neighbor who grows organic vegetables says that we are ruining the earths environment and we will need a new place to live. I totally agree.I think that another reason we should colonize the moon is that it would be cool. Can you imagine living up there and being able to see the earth? Wow. My best friend says that living on the moon would be an awesome experience for anyone.The moon is great!Why is the argument ineffective? In a paragraph of 710 complete sentences, explain why the following parts of the argument are ineffective, and how they can be improved:ClaimSupportConclusion ClincherPoint of ViewTransitionsSubmit your review of the argument. Do not write a complete argumentative essay. Help, pleaseThe function f(x) = 2x 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?Replace the values of h and k in the equation.g(x)=2x+h+k