If 1700 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.

Answers

Answer 1

Answer:

[tex]V = 6746.30cm^3[/tex]

Step-by-step explanation:

Given

[tex]Surface\ Area = 1700cm^2[/tex]

Required

Determine the largest possible volume

Represent the dimension with:

[tex]Height = h[/tex]

[tex]Sides = x[/tex]

Surface Area with an open top is:

[tex]Surface\ Area = x^2+ 4hx[/tex]

Substitute 1700 for Surface Area

[tex]1700 = x^2+ 4hx[/tex]

Make h the subject

[tex]4hx = 1700 - x^2[/tex]

[tex]h = \frac{1700 - x^2}{4x}[/tex]

The volume (V) is calculated as:

[tex]V = x^2h[/tex]

Substitute value for h in [tex]V = x^2h[/tex]

[tex]V = x^2*\frac{1700 - x^2}{4x}[/tex]

[tex]V = x*\frac{1700 - x^2}{4}[/tex]

[tex]V = \frac{1700x - x^3}{4}[/tex]

[tex]V = \frac{1700x}{4} - \frac{x^3}{4}[/tex]

[tex]V = 425x - \frac{x^3}{4}[/tex]

[tex]V = 425x - \frac{1}{4}x^3[/tex]

Differentiate and equate to 0, afterwards

[tex]V' =425 - \frac{3}{4}x^2[/tex]

[tex]425 - \frac{3}{4}x^2 = 0[/tex]

[tex]\frac{3}{4}x^2 = 425[/tex]

Solve for [tex]x^2[/tex]

[tex]x^2 = 425 * \frac{4}{3}[/tex]

[tex]x^2 = 566.67[/tex]

Take the square root of both sides

[tex]x = \sqrt{566.67[/tex]

[tex]x = 23.80[/tex]

Substitute 23.80 for x in [tex]h = \frac{1700 - x^2}{4x}[/tex]

[tex]h = \frac{1700 - 23.80^2}{4*23.80}[/tex]

[tex]h = \frac{1133.56}{95.20}[/tex]

[tex]h = 11.91[/tex]

So, the largest possible volume is:

[tex]V = x^2h[/tex]

[tex]V = 23.80^2 * 11.91[/tex]

[tex]V = 6746.30cm^3[/tex]


Related Questions

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Step-by-step explanation:

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Answers

Answer:

15

Step-by-step explanation:

Answer:

the measure of an angle that is the supplement of angle C=180-165=15

What is tan K?

please show your work

Answers

Since it’s angle K, 51 will be the hypotenuse, 45 will be the adjacent, and 24 will be the opposite. And since we’re looking for tan, which is the opposite over the adjacent, 24 is the opposite, and 45 is the adjacent. In conclusion, tan K = 24/45

a ladder is 6 ft 9 in tall how tall is it in inches​

Answers

6ft 9 is 81 inches.

Answer:

81 in

Step-by-step explanation:

1 ft=12in

12x6=72in

72+9=81

An artist is creating tiles to use in a project. Each tile is to be in the shape of a right triangle. One of the legs of the tile is to be 3 Inches long. The hypotenuse is to be z Inches long.
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Answers

Answer:

???

Step-by-step explanation:

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Answers

Answer:

98

Step-by-step explanation:

the exterior angle is equal to the sum of the opposite interior angles

-Sumin <3

Answer:

98

Step-by-step explanation:

53+45+x = 180

53+45=98

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82+98=180

x = 98

Which of these is equivalent to x + 1 + x + 2 + x + 3 + x + 4?

Answers

Answer:

what are the options?

Answer:

x + 1 + x + 2+ x + 3 + x + 4

4x + 10

2( 2x + 5)

hope it helps

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Answers

The surface area is 1000 and the volume is 49

A = 1
2 × (15 + 20) × 16
B = 1
2 × 15 × 20 × 10
C = 1
2 × (15 + 20) × 10
D = 1
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Answers

Answer: a

Step-by-step explanation:

Which equation represents a slope of 4 and (5,-2)?

y-2=4(x-5)
y-5=4(x-2)
y+2=4(x+5)
y+2=4(x-5)

Answers

Answer:

Step-by-step explanation:

the formula is named the point slope formula for a reason.   and  you have show both of them in the question , the slope and the point are given

y - y1 = m(x-x1)

so for your answer

y-(-2) = 4(x-5)

y+2 = 4(x-5)    is the right answer

michalle bought a new tablet for 360 last month now it priced at 280 what is the percent of change in price of the tablet

Answers

Answer:

Step-by-step explanation:

%change=100(280-360)/360

%change=-200/9%

%change=-22.22% (to nearest hundredth)

How much will 9 pencils cost if 6 pencils cost $1.68?

Answers

Answer:

$2.52

Step-by-step explanation:

1.68/ 6 = $0.28 each pencil

0.28 x 9 = $2.52

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Answers

Answer:yutu

gdffg

Step-by-step explanation:

uytyuytuyuyu dfgdgdg

Answer: the answer is b on the forum

Step-by-step explanation:

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Answers

Answer:

Point Form: 8,2

Equation Form: x = 8, y = 2

Step-by-step explanation:

solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

(8,2)

Step-by-step explanation:

write 16 + 32 = as a product of two factors using GCF and the distributive property

Answers

Answer:

16 (1+2)

Step-by-step explanation:

factors of 16: 1,2,4,8,16

factors of 32: 1,2,4,8,16,32

16 x 1 = 16

16 x 2 = 32

Solve the following system in any
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4x + 8y = -3
6x + 12y= -7
Can someone please help me with this?

Answers

Answer:

No Solution.

Step-by-step explanation:

4x+8y=-3

6x+12y=-7

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

3(4x+8y)=3(-3)

-2(6x+12y)=-2(-7)

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

12x+24y=-9

-12x-24y=14

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

0=5

no solution.

3. Jessie is looking for the volume of the cone
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Which of the following is the value of “B”?

Answers

Answer:

A

Step-by-step explanation:

The base is the circle.

To find the area of the circle, use pi*r^2

pi = 3.14

r = 6

Area = 3.14 * 6^2Area = 3.14 * 36Area = 113.04

Answer:

C. 414.48

Step-by-step explanation:

1/3 x 3.14 x 6² x 11 = 4.14.48

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Answers

Answer:

416.23

Step-by-step explanation:

A=a2+2aa2

4+h2=102+2·10·102

4+152≈416.22777

Answer:

find the areas of the individual triangles then add those ares

together.

Step-by-step explanation:

-6 x (1/3 + 1/3)What is the answer?

Answers

Answer:

−4

Step-by-step explanation

Answer:

−4

Step-by-step explanation:

-6 x (1/3 + 1/3)

Since 1/3 and 1/3 have the same denominator, add them by adding their numerators.

-6 x (1+1/3)

Add 1 and 1 to get 2.

-6 x (2/3)

Express -6 x (2/3) as a single fraction.

-6 x 2/3

Multiply −6 and 2 to get −12.

-12/3

Divide −12 by 3 to get −4.

−4

How to round 8.6023 in the nearest tenth?

Answers

Answer:

8.6

Step-by-step explanation:

https://www.you.tube.com/watch?v=32gDF10ZXOA

( it might be wrong pls dont report me just let me kno y its wrong )

Answer:

8.6

Step-by-step explanation:

First of all consider the thousands in the decimal which is 2. Since 2 is not greater than 5 we have to remove the number 2 and 3 from the 8.6023.

We're left with 8.60. Now we see that there's a 0 in the hundredths so since it's not greater than 5 we remove it.

Now we're left with 8.6 which is to the nearest tenth.

f – 5.2 1.6

answer pls

Answers

Answer: what u mean

Step-by-step explanation:

Answer:

huh what do you mean picture?

Mr. Armstrong went to Target to buy four pairs of dress socks. There was a 30% off sale
on the socks, and his total bill before tax was $14. What was the price of each pair of socks
before the sale?

Answers

Answer: $5

Step-by-step explanation:

We should note that since there was a 30% off sale, it means that he paid for 70% (100% - 30%) of the sales price.

Therefore, let the price of the socks be represented as x.

70% of x = 14

70/100 × x = 14

0.7 × x = 14

0.7x = 14

x = 14 / 0.7

x = 20

Therefore, the price of the socks was $20. Since there are 4 pairs, each pair will be:

= $20 / 4

= $5

I will give Brainliest or a Cookie, your choice

Answers

Answer: x= 10??
I hope this is correct
And I want the brainliest

A ball is thrown into the air with an upward velocity of 44 ft/s. It’s height h in feet after t seconds is given by the function h=-16t^2 +44t+5. How long does it take the ball to reach its maximum height? What is the balls maximum height?

Answers

9514 1404 393

Answer:

1.375 seconds35.25 feet

Step-by-step explanation:

A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).

Here, we have ...

  h = -16t^2 +44t +5

  t = -44/(2(-16)) = 11/8 = 1.375

It takes 1.375 seconds for the ball to reach its maximum height.

The height at that time is ...

  h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25

The maximum height is 35.25 feet.

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Answers

Answer:

7^2

Step-by-step explanation:

Which pairs of expressions are equivalent

More the 1 answer

Answers

Answer:

The first 3 pairs of expressions are equivalent.

Step-by-step explanation:

Determine whether each expression is equivalent to 100t^2-0.5t

Answers

Answer:

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{10^{t^{2}}}{100^{t}}[/tex].

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex].

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex].

Step-by-step explanation:

The expression to be evaluated is [tex]100^{t^{2}-0.5\cdot t}[/tex], we find by algebraic means the equivalent expression:

Possibility 1:

[tex]100^{t^{2}-0.5\cdot t}[/tex]

[tex]\frac{100^{t^{2}}}{100^{0.5\cdot t}}[/tex]

[tex]\frac{100^{t^{2}}}{(100^{0.5})^{t}}[/tex]

[tex]\frac{100^{t^{2}}}{10^{t}}[/tex]

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{10^{t^{2}}}{100^{t}}[/tex].

Possibility 2:

[tex]100^{t^{2}-0.5\cdot t}[/tex]

[tex]\frac{100^{t^{2}}}{100^{0.5\cdot t}}[/tex]

[tex]\frac{(50\cdot 2)^{t^{2}}}{(25\cdot 4)^{0.5\cdot t}}[/tex]

[tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex]

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}}\cdot 2^{t^{2}}}{25^{0.5\cdot t}\cdot 4^{0.5\cdot t}}[/tex].

Possibility 3:

[tex]100^{t^{2}-0.5\cdot t}[/tex]

[tex]\left(\frac{500}{5} \right)^{t^{2}-0.5\cdot t}[/tex]

[tex]\frac{500^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex]

[tex]100^{t^{2}-0.5\cdot t}[/tex] is not equivalent to [tex]\frac{50^{t^{2}-0.5\cdot t}}{5^{t^{2}-0.5\cdot t}}[/tex].

It is dinos birthday today. She is 9 years older than tyger. Altogether, their ages add up to 23 years. How old is dino?

Answers

Answer:

7

Step-by-step explanation:

Tyger = x

Dinos = x + 9

Total = 23

x + x+9 = 23

2x + 9 = 23

2x = 23 - 9

2x = 14

x = 14/2 = 7

I hope im right!!

Determine the domain of the following graph:

Answers

Answer:

[0,11)

Step-by-step explanation:

the function is defined over {0,11) because it includes x=0, but has an open dot at x=11.

Pls help reward the brainiest to right answers

Answers

Answer:

1. y=(4, 1)

2.y=(1/2, 2)

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Step-by-step explanation:

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