If 2000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
volume=------------cm^3

Answers

Answer 1

Answer:

8586.7cm^3

Step-by-step explanation:

We can denote the side of the base square as "x" in cm

We can also denote the height as "y" in cm

(x^2 * y) = V(x,y)

The surface area can be written as

(x^2 + 4xy = 2000)

We can make "y" as subject of the formula

4xy = 2000 - x^2

y=( 2000 - x^2)/ 4x----------eqn(*)

Substitute "y" into V(x,y)

(x*y)= x^2 * (2000-x^2)/4x = V(x)

We can divide the numerator by the denominator

y= x^2 (500/x - x/4)----------eqn#)

We can take the derivatives

V'(x)= 500 - 3/4x^2

If we set V'(x)=0 we have

500=3/4x^2

2000=3x^2

x^2=666.7

x=√666.7

x=25.8cm

From eqn(*)

y=( 2000 - x^2)/ 4x

y=(2000 - 25.8^2)/(4×25.8)

y=12.9cm

(x^2 * y) = V(x,y)

25.8^2 × 12.9

V(x,y)= 8586.7cm^3

Hence find the largest possible volume of the box is 8586.7cm^3


Related Questions

I need help please. This is due in 40 minutes:(
Given the diagram below, solve for x and y.

Answers

Answer:

x=14, y=37

Step-by-step explanation:

We know that (4y-10)° and 3x° are supplementary angles, meaning the total sum of the angles add up to 180°. (4y-10)° is also corresponding to the blank angle below (9x+12)°, making it a vertical angle. Since (4y-10)°=(9x+12)° because they are vertical angles, then that means we can solve for x:

Original Equation: (4y-10)°+3x°=180

New Equation: (9x+12)°+3x°=180

9x+12+3x=180

12x+12=180

12x=168

x=14

So x is 14

Because x=14, then y is:

4y-10+3(14)=180

4y-10+42=180

4y+32=180

4y=148

y=37

So y is 37

r(x)=x^2-5x-13, s(x)=-3x+5. find r(s(-1)

Answers

Wow that looks rlly hard

How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?



A. 12 m
B. 4 m
C. 133 m
D. 245 m

Answers

Answer: C

Step-by-step explanation: I took the test!!

The required distance that the ladder foot away from the base of the wall is √133  meters. Option C is correct.

What are Pythagorean triplets?  

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and base is Pythagorean triplets.

Here,
Let the base length be x,
According to the question, a 13-meter ladder reach, the foot of the ladder is 6 meters.
So, applying the Pythagoras theorem,
13² = 6² + x²
x = √169 - 36
x = √133

Thus, the required distance that the ladder foot away from the base of the wall is √133  meters.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ2

Which of the following represents the measures of all angles coterminal with a -220° angle?
O 360 + 140n, for any whole number n
O 360 + 140n, for any integer n
O 140 + 360n, for any whole number n
O 140 + 360n, for any integer n

Answers

Answer n 9 Explanation 140 degrees is the measure of each angle and the sum of ... So degrees and radians are related by the following equations 360 2 ... Measure angles in whole number degrees using a protractor.

The measurement of all angles co-terminal with a -220° angle is represented by 140+ 360 n, for any integer number n.

What are Co-terminal angles?

These are the angles which shares the same initial line or terminal side. They are obtained by adding or subtracting 360° from the given angles.

Given, angle is -220° then its one positive co-terminal angle= -220°+360 = 140°

So, 140° is a positive co-terminal angle of -220°.

Therefore, co-terminal angle must be the type of 140°+360° n,

Learn more about  Co-terminal angles.

https://brainly.com/question/14692520

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9) Eva can knit of a scarf in an hour. Her sister takes 3/4 of the time she takes. How long will her sister take to knit 8 similar scarves?

Answers

Answer:

it would take 360 minutes or 6 hours

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

3/4 of an hour is 45 mins, 45 minutes times 8= 360

Convert to hours and you get 6 hours.

Mark me brainiest

The average combined SAT score for students at Brookstone High was 1000 in 2003, 1100 in 2004, 1210 in 2005, and 1331 in 2006. Predict the SAT score for Brookstone seniors in 2007. Explain your answer.

Answers

1, 441 in 2007 because it is going in a pattern add 100 plus 10 to get your 2005 answer so then I add 100 plus 10 plus 11 for 12,10 to get 1331 . so the answer is 1,441

find a number such that five more than one half the number is three times the number​

Answers

Answer:

0.5

Step-by-step explanation:

THE CORRECT ANSWER IS 12 FAVORS!!

Answers

Answer:

yes the answer in 12 fpavers

Step-by-step explanation:

wa

mary will spin the spinner below 150 times. about how many times should mary expect the spinner to land on a number greater than 5

Answers

Answer:

where is the spinner at least attact an attachment so i can see the spinner and how the odds of likely it can turn out

Step-by-step explanation:

What is 21 1/4% expressed as a fraction?
a) 13/200
b) 17/80
c) 21/80
d) 17/40

Answers

Answer:

B. 17/80

Step-by-step explanation:

The decimal form is 0.2125.

To make sure if 17/80 is 21.25 percent divide 17÷80=0.2125=21.15 percent

Find the measure of angle A.
3)
74
16x + 1
19x
A
A) 82°
C) 57°
B) 69°
D) 49°

Answers

Answer:

I think its 69* but I be wrong so good luck

Step-by-step explanation:

i would believe it’s 69

Derek has 6 feet of ribbon that he needs to cut into 2/3 feet pieces. How
many pieces of ribbon can Derek cut?

Answers

Answer:

The correct answer is 9 pieces of ribbon.

Step-by-step explanation:

9 is correct because if you do 6 divided by 2/3 you equal 9, therefore 9 is the correct answer

HAVE A GOOD DAY!

Help please! This has to do with the Pythagorean theorem.

Answers

Answer:

x = 11.49

Step-by-step explanation:

Apply the pythagorean theorem to find x

Thus:

a² + b² = c²

Where,

a = x = ???

b = 8

c = 14 (hypotenuse)

Plug in the values

x² + 8² = 14²

x² + 64 = 196

x² = 196 - 64 (subtraction property of equality)

x² = 132

x = √132

x = 11.49 (approximated to nearest hundredth)

HELPP ASAP
The ratio of boys to girls in the sixth grade is 3:4. If there are 48 girls, what is the total number of sixth graders?

36

55

60

84​

Answers

Set up two ratios: 3:4 and x:48. The ratio always stays the same, so the value that you increased the girls by will be equal with the boys. To get from 4 to 48, you need to multiply by 12. So, to get a proportional number of boys, multiply 3 x 12.

The ratio of boys to girls is 36:48. The question is asking how man total, so add. 36 + 48 = 84.

There are 84​ total sixth graders.

Answer:

Step-by-step explanation:

I believe it is 84

#11 PLEASE HELP!!! URGENT!! NEED ASAP!!!

Answers

Answer:

See bolded answers

Step-by-step explanation:

Since 1=100%, then 1.15=115%, meaning x increased by 15% is correct

Since 1=100%, then 0.15=15%, meaning 15% of x is correct

Since 1=100%, then 0.85=85%, meaning x decreased by 15% is correct

What is the slope of the line?

Answers

Answer:

c.  1/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (0, -1)

Point (3, 0)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]:                    [tex]m=\frac{0+1}{3-0}[/tex]Add/Subtract:                      [tex]m=\frac{1}{3}[/tex]

The sum of two integers is 9 their difference is 5 what are the 2 integers

Answers

the two integers are 7 and 2

Which equation can be used to solve for x in the following diagram?
(6z- 15)°
Choose 1 answer.
z= (6z-15)
O z-(6z-15) = 90
O z+(6z- 15) = 90
4 of 7

Answers

Answer:

I'm answering this for points

can someone help me with this geometry problem?

Answers

Answer:   VW < UW < UV

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

Explanation:

The exterior angle is 137, so the interior angle adjacent to that is 180-137 = 43. This is interior angle U of triangle UVW.

Let's find the missing angle W

U+V+W = 180

43+68+W = 180

111+W = 180

W = 180-111

W = 69

We have three three interior angles of triangle UVW

U = 43V = 68W = 69

The longest side is opposite the largest angle, so the longest side is UV

The shortest side is opposite the smallest angle, so the shortest side is VW

The order of the sides from smallest to largest is

VW < UW < UV

Refer to the diagram below.

Determine the type of triangle that draw below ASAP

Answers

I think scalene acute
Hope help but not 100% sure yet

What is the predicted value of fuel efficiency (in miles per gallon) for a car with a 2.5 cubic liters engine? Round your answer to two decimals, if needed.

Answers

Answer:

25.92

Step-by-step explanation:

Fuel efficiency is the measure or effort that is required to convert the chemical energy in the fuel to the kinetic energy which the cars needs to move. It is meant by how good or effectively the fuel is utilized by the vehicle. It is the ability of the engine to extract more energy from the fuel.

In the context, the size of the engine is 2.5 cubic liters. Then the predicted value of the fuel efficiency will be 25.92 miles per gallon.

Need help with these 2

Answers

Answer:

1)(6,4)

11+1=12/2 =6

6+2=8/2=4

8. A skateboard ramp is 5ft tall and is 12ft from the base of the ramp to the end. What is the length from the top of the ramp to the end?

Answers

Answer:

iacbsc kakwc s s k kd sdidv d lm vdfj

Step-by-step explanation:

please help me asap​

Answers

Answer:A, C, C

Step-by-step explanation:

Answer:

rueiwiejr rjrjrjrjrjrrjriirjrjrjrrj

Brandi wants to participate in an after-school program. She has to choose between one art class, three dance classes, bwo gymnastics classes, or three sports casses. She cannot decide, so she writes the name of each class on a slip of paper and draws one slip out of a bag. What is the probability that she does not draw a dance class?​

Answers

Answer:

Step-by-step explanation:

Its 1/3 just put that it will be right I promise

Please, can someone help me on math? Struggling a bit.

Answers

to find the perimeter you just multiply the numbers for example

for number one just multiply 4 and 6 which is 24

You are buying bottles of glue for Mrs. Perro's class. A bottle of glue is $0.74. Which equation can be use to find the number bottles she purchased for $12.58?

Answers

15.75$$


She used all the money up so that’s how much she has

the figure consists of a quarter circle and a parallelogram. what is the area of the composite figure? use 3.14 for . Round to the nearest whole number.
70in.²
84in.²
154in.²
224in.² ​

Answers

Answer:

224

Step-by-step explanation:

the area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex], so for the circle plug in your numbers:

(3.14)([tex]14^{2}[/tex]) = 615.44

divide this by 4 because t=in the picture you only have a fourth of a circle:

615.44 / 4 = 153.86

the formula for area of a trapezoid is [tex]\frac{a + b}{2}[/tex] × h

so plug in your values: [tex]\frac{14+14}{2}[/tex] × 5

you get 70

add 70 and 153.22

70 + 153.22 = 223.22

this can round to 224

10. Doug has added two decimal numbers. His work is shown.
14.2
+ 6.25
7.67
Doug's answer is incorrect. What did he do wrong? What should his sum be?
hurry please .

Answers

Doug didn’t line up the decimals, so his answer would be incorrect. His answer should be 20.45

Brandon has been studying a lot and got 12 questions correct out of 15 on his Unit test. What
percentage of questions did Brandon get correct?

Answers

Answer: he got 80% correct

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