Assume that you want to construct a box with a square base (closed top) and a volume of 1000 cm3 . Find the dimensions of the box to minimize the surface area of the box.

Answers

Answer 1

Answer:

[tex]x=10\sqrt[3]{2}[/tex]

Step-by-step explanation:

The Volume of a box with a square base  

x by  x  cm and height  h  cm is  

V =x^2h

The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.

The surface area of the box described is  

A = x ^2 +4 x h

We need  

A  as a function of  x  alone, so we'll use the fact that

V= x^2h = 1000 cm^3

This imples  [tex]h=\frac{1000}{x^2}[/tex]

This makes

[tex]A= x^2 + 4x(1000/x^2)\\A= x^2+4000/x[/tex]

Differentiating A w.r.t. x

[tex]A' = 2x-4000/x^2[/tex]

Now, A'=0

[tex]x=10\sqrt[3]{2}[/tex]

Therefore, minimum value x = [tex]x=10\sqrt[3]{2}[/tex]


Related Questions

A sound wave is given by the
following equation:
y = 6 sin(324pi t)
where t = time in seconds
How many cycles will occur
between t= 3 and t = 5.5 seconds?

Answers

Answer:

405 cycles

Step-by-step explanation:

We have the equation:

y = 6*sin(324*π*t)

For the properties of the sin function, we know that the period is 2π.

So between:

Sin(x) and Sin(x + 2*pi)

we have a cycle.

between:

Sin(x) and Sin(x + 6*pi)

we have 3 cycles.

and so on.

Now we want to find how many cycles will occur between t = 3 s, and t = 5.5 seconds

Between these times, the difference in the argument of the sin function is:

324*π*5.5 - 324*π*3 = 324*π*(5.5 - 3) = 324*π*2.5

Now, the number of cycles that we will have between these times is equal to the number of times that "2*π" is in 324*π*2.5

That number is just the quotient between 324*π*2.5 and 2*π

N = (324*π*2.5)/(2*π) = (324*2.5)/(2) = 405

There are 405 cycles between 3 seconds and 5.5 seconds.

Which expressions simplify to 2x - 3?

Answers

Answer:

-5

Step-by-step explanation:

x=-3-2

x=-5

+2 GOES ON RIGHT AND IT BECOMES -2 And then -×-is=+but 3 is greater so the sign becomes-

Towns X, Y, and Z are on the same straight road. Town Y is between Town X and Town Z. Town X is 57 miles from Town Z, and Town Y is 28 miles from Town Z. What is the distance from Town X to Town Y? A. 21 miles B. 28 miles C. 29 miles D. 30 miles

Answers

Answer:

c

Step-by-step explanation:

distance between town X and Z = 57 MILES

distance between y and z = 28 miles

distance from x to y = 57 - 28 = 29 miles

please check the attached image for a diagram that would help better understand the question

find the missing side​

Answers

Answer:

x = 27.6907 units

Step-by-step explanation:

cos (62) = 13/x

x cos (62) =13

13 / cos(62)=x

x is 27.6907 units

Which of the following is a classified as a trinomial

Answers

Answer:

A

Step-by-step explanation:

theres 3 ( x³, -3x, 3)

Answer:

A) x² - 3x + 3

Step-by-step explanation:

A trinomial is an algebraic expression consisting of three terms, which usually include a quadratic variable, a coefficient multiplied by a variable, and an integer.

In other words, a trinomial is a polynomial consisting of three monomials.

Help me ! Jdkdjdjdb almost due

Answers

Answer: B

Step-by-step explanation

p^2+q, use p=5 and q= -3

All you have to do for this problem is fill in for p and q.

5^2+-3 = 22

Answer:

B) 22

Step-by-step explanation:

Plugging in the values we can solve the equation:

(5)^2 + (-3)

25 + (-3)  -- Evatuate exponents first

25 - 3 = 22 -- Simplify to receive answer

What is the value of the following expression? (8 + 5 x 9) - 2
Topic: PEMDAS
Please provide an explanation to be rewarded brainly.
Worth: 20 Points

Answers

Answer:

51

Step-by-step explanation:

Parenthesis exponents multiplication division addition subtraction

(8+5x9)-2

(8+45)-2

53-2

51

What is an equation of the line that passes through the points (-3, -5) and
(-5, -3)?

Answers

Answer: y = -x-8

Step-by-step explanation:

(-3,-5) (-5,-3)

Slope (m) = (y-y)/(x-x) = (-3- -5)/(-5- -3) = (-3+5)/(-5+3) = 2/- 2 = - 1

m = - 1

Point (-3,-5)

y-y=m(x-x)

y- -5= -1(x- -3) = y+5 = -1(x+3)

y+5 = - x -3

y+5= - x - 3 (substract 5 from both sides)

y = - x - 8

When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 72 days by 10 workers. How many days would it take to build a similar house with 20 workers?​

Answers

Hopes this helps

Answer: 102

If it’s right please mark as brainlist and if it’s not than I am so sorry I couldn’t help you.


[tex]\huge \mathcal\color{orange}\boxed{\colorbox{purple}{Question}}[/tex]

Use Euclid's division lemma to show that the square of any positive integer is either of
the form 3m or 3m + 1 for some integer m.



Answers

Answer:

let us consider a positive integer a

divided the positive integer a by 3, and let r be the remainder and B be the quotient and such that.

a=3b+r.........(1)

where =0,1,2,3

case 1:consider r=0

equation (1)becomes

a=3b

on squaring both the side

a²=(3b) ²

a²=9b²

a²=3 x 3b²

a²=3mwhere m=3b²case 2: Let R=1

equation (1) become

a=3b+1

squaring on both the side we get

a²=(3b+1)²a²=(3b) ²+1+2x(3b)x1a²=9b²+6b+1a²=3(3b²+2b) +1a²=3m+1

where m=3b²+2bcase3:let r=2equation (1)becomesa=3b+2squaring on both the sides we get a²(3b+2)²a²=9b²+4(12x3bx2a²9b²+(12b+3+1)a²3(3b²+4b+1)+1a²3m+1

where m=3b²+4b+1

: square of any positive integer is of the form 3M or 3M + 1

: hence proved.

Answer:

It is the correct answer.

Step-by-step explanation:

Hope this attachment helps you.

Mhanifa please help! This is late and I need to get it done ASAP or I will fail

Answers

Answer:

Use the ratio of corresponding sides of similar triangles.

#1

50 / x = x / 25x² = 50*25x = 25√2

#2

63 / x = x / (112 - 63)x² = 63*49x = 21√7

#3

100 / x = x / 8x² = 100*8x = 20√2

#4

x / 18 = 18 / 16x = 18*9/8x = 81/4

I need this in 10 mins I’m BEGGING HELP

Answers

Answer:

148.5 in^2

Step-by-step explanation:

First, get the area of the rectangle

A = 15*12

A = 180

Now the area of the triangle, with the base at 3.5

A = h b/2

A = 9 * 3.5/2

A = 15.75

Since you have 2 halves, add them together., 31.5

Substract 31.5 from 180

Answer:

180 in

Step-by-step explanation:

Because if you multiply 15×12 it gives you 180

Properties of Triangles (Math please help meee its worth 100 points in my grade)

Answers

First off all angles within a triangle added to together add up to 180 degrees.

Also an isosceles triangle has two sides of equal length (as shown by the two lines drawn through the sides of the triangle)

Since you are given the angle B as 46 degrees that means that angle C is also 46 degrees (since they both share the same base and since both sides of the triangle are equal).

When added together you can subtract this from 180 degrees.

So...

180-92=88

88 is your answer.

I don't like doing math help if you know :)

Answers

Answer:

Step-by-step explanation:

-(2x+1)

-2x-1

write -2 in that bos and 1 after "-"

HELP PLEASE !! which right prism would have the same volume as a square prism with a base area of 36 m 2 and a height of 3 m ?

Answers

Answer:

3 x 36 = 108 (square prism's volume)

3 x 9 = 27, 27 divided by 2 ( x 1/2) = 13.5, 13.5 x 4 = 54

2 x 18 x 3 = 108

6 x 3 = 18, 18 x 2 = 32

Your answer is b, because it has the volume of 108 which matches the square prism's volume.

Find the value of x
Please help out !!

Answers

Answer:

x = 8

Step-by-step explanation:

These are corresponding so they are congruent.

Your equation is: 14x-4=12x+12

x=8

Step-by-step explanation:

these numbers are corresponding angle to each other

so =>14x–4=12x+12

14x–4=12x+12collect like terms

=>14x–12x=12+4

=>2x=16 divide both side by 2 you get

=>x=8

Find the surface area of
the prism.
12 in.
7 in.
4 in.
The surface area is
in. 2.

Answers

There is no photo sorry

Frances and Joyce decided to take a shortcut through the woods to go to their friend's house. When they went home they decided to take the long way around the woods to avoid getting muddy shoes. If the length of the shortcut is equal to the square root of the sum of the squares of the other two sides, what total distance did they walk?

Answers

Answer:

Length of shortcut  = 15 km

Step-by-step explanation:

Given that;

Length of shortcut is equal to square root of the sum of the squares of the other two sides.

So,

We can find length of shortcut.

Assume:

Length of other two side area 12 km and 13 km

So,

H = √P² + B²

Length of shortcut  = √12² + 13²

Length of shortcut  = √144 + 169

Length of shortcut  = √225

Length of shortcut  = 15 km

You buy 11 bagels with a $20 bill. How much change do you receive?

Answers

Answer:

You would receive $13.75

Step-by-step explanation: What i did was divided 7.50 by 6 so it would give me the price of 1 bagel(1.25).I subtracted 11 and 6 which would give me 5 so I know how much I need to calculate with the discount. Then I multiplyed 5 times 1.25 (6.25) so I could get the price for 5 bagels. After I added 7.50 and 6.25 which would give you your answer of $13.75.

I hope this helps and makes sense to you. Please mark brainlist!

Step-by-step explanation:

Answer:

You would receive $13.75

Step-by-step explanation:

What i did was divided 7.50 by 6 so it would give me the price of 1 bagel(1.25).I subtracted 11 and 6 which would give me 5 so I know how much I need to calculate with the discount. Then I multiplyed 5 times 1.25 (6.25) so I could get the price for 5 bagels. After I added 7.50 and 6.25 which would give you your answer of $13.75.

Hope u understand

Please mark brainliest

Thank You

Find the volume of this cone.
Use 3 for TT.
V = T12h
3
V ~ [?]in3
sin
3in
HELP
EMEEEEEE

Answers

Answer:

18 is the answer

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What is the probability of a baseball player getting three hits in a row if his batting average is 17.9%?
0.57%
53.7%
6.0%
17.9%

Answers

Step-by-step explanation:

Here batting average is 17.9% = 0.179

In baseball, a batting average is the probability of the number of hits divided by the number of t... do the rest

The area of the base of this right rectangular prism is 14 square centimeters, and the height is 3 centimeters. What is the volume, in cubic centimeters, of this prism? I NEED THIS ANSWER IN LIKE NOW

Answers

Answer:

42cm^3

Step-by-step explanation:

Given data

Area of base= 14 square centimeters,

Height= 3 centimeters

Volume = Area* Height

Volume= 14*3

Volume= 42 cm^3

Hence the volume of the prism is 42cm^3

The spinner is spun 48 times. What is a reasonable prediction for the number of times the spinner will land on an even number?

Answers

Answer:

18 times

Step-by-step explanation:

Number of even numbers on spinner = 3

Total number of sections on spinner = 8

Probability of obtaining an even number on one spin = 3/8

Number of times an even number can be obtained from 48 spins = 3/8 * 48 = 18 times

How many subset of (a, b, c, d, et, h, i) are there?
show how you determined it.

Answers

Answer:

6

Step-by-step explanation:

hope this helped

Are the ratios 10:2 and 20:4 equivalent

Answers

Answer:

Yes, they are equal

Step-by-step explanation:

To see if a ratio is equal, multiply the first numbers of each ratio to the second numbers. If they equal the same, they are equivalent.

In this case, 10*4 = 40

20*2 = 40

El concepto calidad de vida varía de persona a personas correcto o incorrecto

Find the principal that will yield a simple interest of Rs 9000 in 5 years at a rate of 6% per annum.

Answers

9514 1404 393

Answer:

  ₹ 30000

Step-by-step explanation:

The simple interest formula is ...

  I = Prt . . . . . . principal P invested at rate r for t years

Fill in the values you know, and solve for the one you don't know.

  9000 = P(0.06)(5)

  9000/0.30 = P = 30000

The principal that will give ₹9000 in interest is ₹30000.

A =?

P= 9000

t = 5 yrs

r = 6% = 0.06

A = p(1+r)^t

A = 9000(1+0.06)⁵

A = 9000× 1.338

A = 12044 Rs.

Please help please please please helppp

Answers

Answer:

m∠3 = 73°

Step-by-step explanation:

Vertical angles are equivalent in measure. Complement angles add up to 90°, so subtract 17° from 90° to get your answer.

Help me please thank you for

Answers

Answer:

I don't know

Step-by-step explanation:

Sorry

Answer:

Just at a glance I'm pretty sure it would be B.

What is the volume of this triangular right prism?

Answers

Do u have a picture? Because there isn’t any number or equation I can solve for u ?

Find the area of the shape shown below.

Answers

Answer:

10

Step-by-step explanation:

2x2=4

1x2=2

2x2=4

4+2+4=10

write this down if u need to show work

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