A rectangular box without a top is have a volume of 12 cubic feet. Find the dimensions of
the box that will have minimum surface area.​

Answers

Answer 1
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.

We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.

Therefore the box has length and breadth as 4 ft each and a height of 2 ft.

Related Questions

Aspen has 10 pairs of white socks and 1 pair of red socks. What is the chance that Aspen wears a pair of black socks?

Answers

Answer:

no chance

Step-by-step explanation:

he doesn't have any black socks

Answer:

Step-by-step explanation:

Of the ten socks,

10/11 chance of wearing white socks

1/11 chance of wearing red socks

0/11 chance of wearing any OTHER color

Black socks fall into the final row, which is the OTHER color, meaning there is no chance he can wear black socks.

CAN SOMEONE PLEAASSSEE HELP ME WITH THIS TRIGONOMETRIC FUNCTION PROBLEM? I AM REALLY STRUGGLING AND IT WOULD MEAN A LOT

Answers

Answer:

the sine Is 5/13

Step-by-step explanation:

use the trigonometric identity : sin^2+ cos^2 = 1

so the sine Is sqrt(1-(12/13)^2) = 5/13

sqrt means Square root btw

a system of equations is shown on the graph below. what is the solution to the system of equations?

Answers

Answer:

Step-by-step explanation:

solution is the point of intersection, (0,1)

Solution of the system of equations is, (0, 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A system of equations is shown on the graph.

Now, We have seen that;

Both the graph intersect at a point (0, 1), which is solution of the graph.

Hence, Solution of the system of equations is, (0, 1)

Thus, Solution of the system of equations is, (0, 1)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

1. Escribe dos semejanzas dadas en la estructura de la
circunferencia y la elipse.​

Answers

Un círculo es una forma curva cerrada que es plana. Es decir, existe en dos dimensiones o en un plano. En un círculo, todos los puntos del círculo están igualmente lejos del centro del círculo. Una elipse también es una forma curva cerrada que es plana.

~~Espero que esto ayude~~

What additional information must be known to prove the triangles similar to SAS?

Answers

Answer:

Option A) is the right answer because for SAS property we need to verify that the sides are equal to each other in the triangles.

Find the measure of the indicated angel.

A) 30 degrees
B) 35 degrees
C) 25 degrees
D) 40 degrees

Answers

Answer:

D

Step-by-step explanation:

44+32=76

180-76=104

104+36=140

180-140=40

D)40

find the slope of the line that passes through (1, 2) and (10, 6). mplify your answer and write it as a proper fraction, improper fraction, or integer.​

Answers

y2-y1/x2-x1 then plug in numbers so 6-2/10-1 which gives 4/9

When plotting points on the coordinate plane below, which point would lie on the x-axis?



(6, 0)
(0, 2)
(3, 8)
(5, 5)

Answers

Answer: (6,0)

Coordinate points are always written in pairs of the x- and y-coordinate: (x, y). Knowing this, the point would need to have a y-value of 0 in order to lie on the x-axis (otherwise, it would be on a random spot on the grid). The only coordinate point with a y-value of 0 is (6, 0). Therefore, the coordinate point (6, 0) lies on the x-axis.

Please refer to the attached graph below to see all the coordinate points.

describe a family member in 3-5 sentences (use nouns) make it easy and simple please!!

Answers

Ok! ———- is ———- because of ————. They have ———- hair color and ———— eye color. I think they are ———— because of ————. They like to —————- because —————.

Solve (y–3)2 – 32 = 0, where y is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click "No solution."
y = 0
Х

Answers

Answer:

[tex] \sqrt{32} + 3[/tex]

[tex] - \sqrt{32} + 3[/tex]

Step-by-step explanation:

Use foil method

[tex](y - 3) {}^{2} [/tex]

[tex](y - 3)( y - 3)[/tex]

First multiply y and y

[tex]y \times y = {y}^{2} [/tex]

Next Multiply Outer term y and -3.

[tex]y \times - 3 = - 3y[/tex]

After that ), Multily inner tern -3 and y

[tex] - 3 \times y = - 3y[/tex]

Finally multiply -3 and -3 and you get 9.

Then combine all

[tex] {y}^{2} - 6y + 9 - 32 [/tex]

[tex] {y}^{2} - 6y - 23[/tex]

Now I'm going to complete the square. First get only the y value on the left side so we first set this equal to zero then move add 23 on both sides.

[tex] {y}^{2} - 6y - 23 = 0[/tex]

Add 23

[tex]y {}^{2} - 6y = 23[/tex]

Apply formula

[tex] (\frac{b}{2} ) {}^{2} [/tex]

where b is the coefficient.

plug it in

[tex]( \frac{ - 6}{2}) {}^{2} [/tex]

Which is -3 squared which equal 9.

Then add 9 on both sides

[tex] {y}^{2} - 6y + 9 = 23 + 9[/tex]

23+9=32

Now let factor the left side

the only number that adds to -6 and multiply to 9 is

-3 so we would rewrite the left side as

[tex](x - 3) {}^{2} = 32[/tex]

Now take the sqr root of 32

[tex] \sqrt{(x - 3) {}^{2} } = \sqrt{32} [/tex]

Then add 3 on both sides

[tex]x + - 3 + 3 = \sqrt{32} + 3[/tex]

A sqr root of a number can be positive or negative so

the answer is

[tex] - \sqrt{32} + 3[/tex]

[tex] \sqrt{32} + 3[/tex]

Find the length of line AC. Use that length to find the length of line CD. What is the length of line CD? Round to the nearest tenth.
a. 2.3 cm
b. 4.0 cm
c. 10.7 cm
d. 18.6 cm

Answers

Is it either C or D not 100% but it is one of those hope this helped

Answer:

C on edge 2021

Step-by-step explanation:

Lines a and b are parallel.

What is the measure of angle s?

Enter your answer in the box

S=


Answers

Answer:

22 degrees

Step-by-step explanation:

The angle that measures 158 degrees and angle u are supplementary angles, meaning they add up to 180 degrees.

Angle s and angle u are corresponding angles, meaning that they are congruent.

This means that the angle that measures 158 degrees and angle s are supplementary as well. Knowing this, we can construct the following equation:

[tex]180=158+s[/tex]

Subtract both sides by 158

[tex]180-158=158+s-158\\22=s[/tex]

Therefore, angle s has a measure of 22 degrees.

I hope this helps!

c. (4 points) The p-value for this study is 0.0002. Provide an interpretation of this p-value
("the p-value is the probability that...)

Answers

Answer: yes

Step-by-step explanation:

Leeza’s aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Which inequality can determine out how many more gallons she might put in the tank?

Answers

Answer:

The inequality that will be used would be

x + 22 <= 55

find the x and y-intercept of this function: 2x+y=-2

Answers

Answer:

x- intercept:(-1,0)

y-intercept:(0,-2)

Step-by-step explanation:

IS THIS A FUNCTION ? YES OR NO ????

ILL GIVE 40 POINTS DONT LIE !!

Answers

Answer:

no it is not a function. .

Answer:

Step-by-step explanation:

No, it does not pass the  vertical line test

Find the area:
HELP PLEASE

Answers

Answer:

Area = 30.3 ft²

Step-by-step explanation:

Area = area of a semicircle + area of a rectangle

= (½*πr²) + L*W

Where,

radius (r) = ½ of 4 = 2 ft

Length (L) = 6 ft

Width (W) = 4 ft

Plug in the values

Area = (½*π*2²) + (6*4)

Area = 30.3 ft² (nearest tenth)

Given that IG FT which of the following statements is true

Answers

Answer:

C

Step-by-step explanation:

Please solve for y in this equation!
0.5y -2 2/5 = 1/2y +2.4

Answers

Answer:

No solution

Step-by-step explanation:

Move all the variables to one side and all the numbers to the other side.

0.5y-2*2/5=1/2y+2.4

-2*2/5=1/2y+2.4-0.5y

-2*2/5-2.4=0

thus there is no solution

Write a word description of the set.
{10, 11, 12, 13, ...}

Answers

this set of numbers counting by ones or the addition of one each time
It would be the addition of one.

The total length of a beach towel is 28 inches. If there are 6 beaches towels laid right next to each other side-by-side, what is the total length of the towels?

Answers

Answer:168 inches

Step-by-step explanation:

the answer is 168 inches because 28 times 6 is equivalent to 168 and then u have to put the inches on the end.

find the slope of the line​

Answers

Answer:

1/2

Step-by-step explanation:

(2,1)(4,2)

x1-y1/x2-y2

slope:m=1/2

10 Six years ago Jon was one-sixth the age of his mother
and in four years time his age doubled and increased
by 10 will match his mother's age. How old is Jon
now?​

Answers

Answer:

Jon is 11 years old

Step-by-step explanation:

We write the following equations describing the sentences of the problem, using the letter M to represent Jon's mom's current age, and j to represent his current age.

First sentence: "Six years ago Jon was one-sixth the age of his mother."

translates into:

J - 6 = (M - 6) / 6

Second sentence: "in four years time his age doubled and increased

by 10 will match his mother's age."

2 * (J + 4) + 10 = M + 4   which removing parentheses gives: 2 J + 18 = M + 4

We solve for "M" in the first equation

6 (J - 6) = M - 6

6 J - 36 = M - 6

M = 6 J - 30

and now use this result to substitute for M in the second equation

2 J + 18 = (6 J - 30) + 4

and work on solving for J

2 J + 18 = 6 J - 30 + 4

18 + 26 = 6 J - 2 J

44 = 4 J

J = 44 / 4

J = 11

Simplify the expression please with step
[tex] \sqrt{13 - 4 \sqrt{3} } [/tex]

Answers

Answer:

[tex] \huge \boxed{ \boxed{ \red{2 \sqrt{3} - 1}}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:redicalsimplifying redicalPEMDASgiven:[tex]\tt \sqrt{13-4\sqrt{3}}[/tex]to do:

simplificationtips and formulas:(a-b)²=a²-2ab+b²√(a)²<=>|a|let's do:

[tex]step - 1 : define [/tex]

[tex] \tt \sqrt{13 - 4 \sqrt{3} } [/tex]

[tex]step - 2 : simplify[/tex]

[tex] \tt use \: the \: 1 \: formula : \\ \tt \sqrt{ 1 + 12 - 4 \sqrt{3} } \\ \tt \sqrt{1 - 4 \sqrt{3} + 12} \\ \tt \sqrt{ {(1)}^{2} - 2.1.2 \sqrt{3} + {(2 \sqrt{3}) }^{2} } \\ \sqrt{ \tt (1 - 2\sqrt{3} {)}^{2} } [/tex][tex] \tt use \: the \: 2 \: formula : \\ \tt |1 - 2\sqrt{3} | \\ \tt - (1 - 2 \sqrt{3} ) \\ - 1 + 2 \sqrt{3} \\ 2 \sqrt{3} - 1[/tex]

if paul rode at a constant speed, how fast did he travel in miles per hour(please help me i will give brainliest i promise)​

Answers

Answer:

Raul traveled 31.25 miles an from 1:50 to 4:20. So, subtract those, you get 2:30. Turn 2:30 into a decimal (2.30) and now divide 31.25 by 2.30. the answer is 13.59 rounded That number turned into a Fraction is about 13 miles an hour.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

the difference between the start time and end time is 2hrs and 30mins

So this means we have to multiply the number and add half of it.

12[tex]\frac{1}{2}[/tex] + 12[tex]\frac{1}{2}[/tex]+ 6[tex]\frac{1}{4}[/tex]= 31[tex]\frac{1}{4}[/tex]

(now can get a brainliest lol)

someone help me lol..

Answers

Answer:

1/3x + 3 is the correct answer, hope it help

PLEASEEEE HELPPP
Ben Frank is an electrician who installs lighting fixtures. He charges (in dollars) his clients 15h +40f
where h is the number of hours worked and f is the number of fixtures installed.
How much does Ben Frank charge when he works 7 hours and installs 9 fixtures?

Answers

Answer:

465 Dollars

Step-by-step explanation:

15h+40f = Amount Charged

if: h = 7

   f = 9

15(7)+40(9) = Amount Charged

105 + 360 = Amount Charged

465 = Amount Charged

He will charge 465 dollars.

Answer:$465Steps and explanation of why:

Ben works 7 hours installing 9 fixtures. This tells us that h = 7, and f = 9. So, let's substitute h = 7 and f = 9 into the expression and evaluate:

Step 1:

15h + 40f

Step 2:

= 15(7) + 40(9)

Step 3:

= 105 + 360

Step 4:

= $465

Hope this helps!! Remember to get good grades, and to stay safe :))

Also, please mark as brainliest..I'm trying to get to, "Virtuoso," which is a level on here that's really important to me.. But- I'm not forcing you so..don't feel pressured into doing it, but if you do, then, thanks so much!! I love you!!

Caleb bought raisins in bulk $2.50 per round. He spent a total of $5.75. How many pounds of raisins did he buy?

Answers

$5.75 divided by $2.50= 2.3 pounds

Answer:

2 1/3 I believe

Step-by-step explanation:

PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((

Answers

Answer:

B is the answer

Step-by-step explanation:

not staright line so not linear. but it is a function

Answer:

Step-by-step explanation:

it is non-linear; function

A standard six-sided die is rolled.
What is the probability of rolling a number greater than or equal to 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Tables
Keypad

Answers

Answer:

Step-by-step explanation:

There are six sides on the die...

1, 2, 3, 4, 5, 6

Greater than or equal to 3 includes 3, 4, 5, 6

This means 4 out of 6, or 4/6

4/6 simplified is 2/3

Hope this helps!

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