A box is to be made out of a 12 by 20 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L , width W , and height H of the resulting box that maximizes the volume.

Answers

Answer 1

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43


Related Questions

22 - 8x = -5x - 14
Find x
Please help this is due today

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The answer is x=12 I hope I helped

what’s 818*426 (multiplication)

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Answer:

348468

Step-by-step explanation:

Answer:

348,468

Step-by-step explanation:

Hope it's help you !!!!:)

Brainly to whomever solves for x and y. Will report scams and the unhelpful "what" answers!

Answers

Answer:

[tex]x=\frac{125}{6},\\y=11[/tex]

Step-by-step explanation:

The angles marked [tex]7x-15[/tex] and [tex]5x-5y[/tex] are co-interior angles. Since all co-interior angles are supplementary (add up to 180 degrees), we have the following equation:

[tex]7x-15+5x-5y=180[/tex]

The two angles marked [tex]4x+4y[/tex] and [tex]2x+y[/tex] are also co-interior angles, thus must also add to 180 degrees.

Therefore, we have the following system of equations:

[tex]\begin{cases}7x-15+5x-5y=180,\\4x+4y+2x+y=180\end{cases}[/tex]

Combine like terms:

[tex]\begin{cases}12x-5y-15=180,\\6x+5y=180\end{cases}[/tex]

Divide the first equation by -2 and add both equations to get rid of [tex]x[/tex]:

[tex]\begin{cases}-6x+2.5y=-97.5,\\6x+5y=180\end{cases},\\-6x+6x+2.5y+5y=82.5,\\7.5=82.5,\\y=\boxed{11}[/tex]

Now substitute [tex]y=11[/tex] into any equation with [tex]x[/tex]:

[tex]6x+5y=180,\\6x+5(11)=180,\\6x+55=180,\\6x=125,\\x=\boxed{\frac{125}{6}}[/tex]

Verify that these two solutions work:

[tex](7(\frac{125}{6})-15)+(5(\frac{125}{6})-5(11))=180\:\checkmark,\\\\(4(\frac{125}{6})+4(11))+(2(\frac{125}{6})+11)=180\:\checkmark[/tex]

How do I fill this out I need to pass this class to move up a grade

Answers

Answer: x = 8,-2

Step-by-step explanation:

x^2-6x-16=0

x =[ -(-6)+-sqrt(-6)^2 - 4x1x(-16)/2x1

x = [6+-sqrt 36+64]/2

x = 6+-sqrt 100/2

x = 6 +-10/2

x = 6+10/2, 6-10,2

x = 8, -2

Answer:

Step-by-step explanation:

This is the quadratic equation formula for the roots.

x^2 - 6x - 16 = 0

x = [- (-6) +/- √( (-6)^2 - 4*1*-16) / 2*1

x = (6 +/- √(36 + 64) / 2

x = (6 +/- √(100) / 2

x = (6 +/- 10) / 2

x =  16/2 = 8

x = -4/2 = -2

In a community of 9,400 people the number of women exceeds the number of men by 1,500.Find the ratio of men to women in the community

Answers

Answer:

Step-by-step explanation:

x +(x+1500) = 9400

2x + 1500 = 9400

2x = 7900

x=3950 (men)

y = 5450 (woman)

5450 :3950

109:79


Helpppppppppppppppp

Answers

I think last one is correct

i’ll give you brainliest

Answers

Answer:

the answer you want is number 2

Suppose 1757 grams of sugar is 31.69% of 5544 grams of jam. How much jam would there be if there were 2500 grams of sugar?

Answers

7889 grams of jam

Step-by-step explanation:

In 5544 grams of jam, 1757 grams of sugar ==> 31.69%

let x be the grams of jam

2500 grams of sugar ==> 31.69%

x grams of jam ==> 100%

[tex]x \times 31.69\% = 2500 \\ x = 2500 \div 31.69\% \\ x = 7888.92 \: grams \\ x = 7889 \: grams \: (nearest \: whole \: number)[/tex]

What is m angle A? Enter your answer in the box.​

Answers

Answer:

ANSWER: 22

Step-by-step explanation:

hope it helps thankks

Answer:

I agree with the person above

pls help me !!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

9.89 m

Step-by-step explanation:

AC is the hypotenuse (H)

x is the opposite (O)

O and H are in sine

sin=O/H

H=O/sin

H=7.9/sin(53)

=9.89187169943418

3 SF

9.89 m

Answer:

AC= 13.144

Step-by-step explanation:

cos ∅ =  Adjacent/ Hypotenuse

cos (53°) = x/AC

cos (53°) = 7.9/AC

(0.601).(AC)=7.9

AC=(7.9)/(0.601)

AC=  13.144 (3 S.F)

can you help answer these:

1) (-3 ) * ( + 3 ) = ___

2) ( - 3) * ( - 3)= ______

3) ( + 20 ) ( + 5) = ____

4) ( + 21 ) ( - 3 ) )= ___

5) (-2) * (+3) * (- 4) = ___

Answers

Answer:

1) -3 x 3=-9

2) -3x-3=9

3)20x5=100

4) 21x-3=-63

5) -2x3x-4=24

note: negative x positive= negative

negative x negative=positive

positive x positive= positive

Step-by-step explanation:

hope this is helpful

Step-by-step explanation:

(-3)*(1+3) = -9 (-3)*(-3) = 9(+20)(+5) =100(+21)(-3) = -63(-2)*(+3)*(-4) = 24

What is the perimeter of the figure shown to the right.
Plss HELP MEE

Answers

Answer:

perimeter=a+b+c+d+e+f+g+h+I

x+13+3x+2+x+5+2+8+3x

CLT

x+x+3x+3x+13+2+5+2+8

8x+30

WILL MARK BRANLIEST
When describing a rotation, what
information must you include?

Answers

Answer:

The point you are rotating at (also called the centre of rotation)

The angle of rotation (usually in degrees but I don't know your school)

Direction of the turn

Step-by-step explanation:

if a triangle has one angle that measure 81 degrees and another that measures 47 degrees, what is the measure of the third angle?

Answers

Answer: 52

Step-by-step explanation:

81 + 47 is 128.

180 - 128 =52 degrees.

:)

You want to nail your 4 championship plaques onto a wooden
plank. The plaques are each 5 inches wide, and the plank
measures 33 inches in length. If you have 2 inches of space on
both ends of the plank and want to space out your plaques
evenly, how much space should there be between each
plaque?

Answers

Answer:  3 inches

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

Explanation:

The overall plank is 33 inches long. Subtract 2 copies of 2 inches off to represent those left and right 2 inches of space at each end.

33 - 2*2 = 33 - 4 = 29

So we have 29 inches to work with.

There are 4 plaques to hang up, and each is 5 inches wide. So that accounts for 4*5 = 20 inches of space just for the plaques themselves. We have 29-20 = 9 inches left for the gaps between plaques.

Since we have 4 plaques, there are 4-1 = 3 gaps between the adjacent plaques. The gap width is 9/3 = 3 inches.

See the diagram below. The values in black are the widths of each championship (5 inches each). The values in red are the gaps either between the plaques or between the plaque and the edge of the plank.

As a check, the values in that diagram should add to 33.

2+5+3+5+3+5+3+5+2 = 33

So the answer is confirmed.

What is the factorization of 49b2 − 81?

(7b – 9)(7b – 9)
(7b – 9)(7b + 9)
(7b2 – 9)(7b2 – 9)
(7b2 – 9)(7b2 + 9)

Answers

(7b-9)(7b+9)

explanation:
I learned in math last year

Answer:

B. (7b – 9)(7b + 9)

Step-by-step explanation:

got 100% on my quiz

If the inverse of a function is also a function, then
The function is said to be ….?

Answers

Answer: Invertible

Step-by-step explanation:

If inverse of a function exists, then the function is said to be invertible. A unique value exits for each given input.

Inverse of a function can be obtained by expressing the given function in terms of y and then replace y by x.

In the circle shown below, The length of chord AB is 24 and the length of OC is 5. What is the radius of the circle with center O

Answers

Answer:

radius = 13

Step-by-step explanation:

OC is a perpendicular bisector of AB , then AC = 12

OA is the radius of the circle

Using Pythagoras' identity in right triangle OAC

OA² = OC² + AC²

OA² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

OA = [tex]\sqrt{169}[/tex] = 13

The radius = 13 units

Answer:

13

Step-by-step explanation:

AB is bisected by perpendicular OC so AB is divided into intwo two equal halves.

if AB = 24

AC =[tex]\frac{1}{2} *AB[/tex]

=[tex]\frac{1}{2} *24[/tex]

=12

no join OA and name its length as x

OA = X

OC = 5

AC = 12

when u join O and A it forms a triangle . SO to find OA lets find pythagoras theorem

OC^2 + AC^2 = OA^2

5^2 + 12^2 = OA^2

25 + 144 = OA^2

169 = OA^2

[tex]\sqrt{169}[/tex] = OA

13 = OA

radius is the line joining the centre and any point on the circumference.So here since O is the centre and A is the points on the circumference and they are joined so the line can be named as radius of a circle.

Therefore radius of a circle is 13

the gravitational acceleration on Earth is 9.8m/s^2 what is the weight of a car on earth if the mass is 1360

Answers

Answer:

13328 N

Step-by-step explanation:

9.8 m/s^2 • 1360 = X

13328 N = X


Assignment - 3. Deductive Reasoning

State a true conclusion.
1) If two planes intersect, their intersection is a line.
2) Plane Rand plane S intersect.
Conclusion:
WRITER

Answers

Answer:

the answer is the intersection is a line

Which of the following equations is of a parabola with a vertex at (0, 6)?

y = ( x + 6) 2
y = ( x - 6) 2
y = x2 + 6
y = x2 - 6

Answers

Answer:

y = x² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, 6) , let a = 1 , then

y = (x - 0)² + 6 , that is

y = x² + 6

expression of three power of five rational number with a negative exponent is?
answer with step by step explanation​

Answers

Answer:

[tex]\frac{1}{243}\\[/tex]

Step-by-step explanation:

The expression of three power of five rational number with a negative exponent is;

Please answer quickly

Answers

Answer:

10

Step-by-step explanation:

given :

length WX ≅ (congruent means equal) length XY

therefore ,  WX = 3

WZ = WX + XZ

WZ = 3 + 7

WX = 10

What is the next term in the sequence below?

0.25, 0.75, 2.25, 6.75, …
A. 6.25
B. 10.25
C. 20.25
D. 60.75

Answers

It would be B. 10.25

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {C. \:20.25}}}}}}[/tex]

[tex]0.25, 0.75, 2.25, 6.75,20.25,..[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]0.25, 0.75, 2.25, 6.75,20.25 \\ \\ ➺ \: 0.25 \times 3 = 0.75 \\ \\ ➺ \: 0.75 \times 3 = 2.25 \\ \\ ➺ \: 2.25 \times 3 = 6.75 \\ \\ ➺ \: 6.75 \times 3 = 20.25[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Can someone help me with this.

Answers

Answer:

A' (-1, 1), B' (-2,1), C'(-2, 2), D'(-1, 3)

Step-by-step explanation:

Rotate all of the points 90 degrees clockwise and move them to the second quadrant.

find the outer perimeter of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate π.​

Answers

Answer:

19.42 ft.

Step-by-step explanation:

The diameter of the semicircle is 6, so 3.14 x 6 = 18.84. Since it is a semicircle, we divide that by 2 to get 9.42.

The hypotenuse of the right triangles only matter for the perimeter. 5 + 5 = 10, and 9.42 + 10 = 19.42 ft.

The outer perimeter is 19.42 ft.

What is perimeter?

Perimeter is the distance around the edge of a shape.

Given:

radius= 3 ft

height= 4 ft

slant height= 5 ft

diameter of the semicircle is 6 feet.

So,

= 3.14 x 6 = 18.84.

Since it is a semicircle,

=18.84/2

=9.42 feet

Now, the perimeter.

= 5 + 5 +9.42

= 19.42 ft.

Hence, the perimeter is 19.42 feet.

Learn more about perimeter here:

https://brainly.com/question/20759336

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Which expression is equivalent to 2^-3/2^-5

Answers

Answer:

2^2

Step-by-step explanation:

2^-3/2^-5

We know that a^b / a^c = a^(b-c)

2^-3/2^-5 = 2^( -3 - -5) = 2^(-3+5) = 2^2

The locksmith is 82.9 miles west of the bakery. The pet store is 44.5 miles west of the bakery. The toy store is 38.6 miles east of the bakery. The coffee shop is 71.5 miles east of the bakery. The library is 57.0 miles south of the bakery. The magic shop is 75.7 miles south of the bakery. How far apart are the toy store and the locksmith?

Answers

Answer:

82.9+38.6=121.5 miles far away.

f(x) = x2. What is g(x)?
5
[ f(x)
g(x)
(3,3)
X
-5
5
x2
O A. g(x)=1
-02-G
B.
X
O c. g(x) = 3²
O D. g(x)=-* x2
Please help :/

Answers

The function g(x) = x²/3

Given that graph of the function f(x) = x²,

Since, the graph of f(x) is transformed to form the g(x).

We see that g(x) is passing by (3, 3)

Here, the scale factor is 1/3,

So, we can say that the equation of the function g(x) is g(x) = x²/3

Therefore, the required function is g(x) = x²/3

Learn more about function click;

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-y-22-13




6< X/2-2


I need help solving both

Answers

Answer:    The first one is y≤11 and the second question is x>16 Hope that helps Goodbye!

Step-by-step explanation:  1. Add 22 to both sides.

-13+2

−y≥−13+2

2 Simplify  -13+2−13+2  to  -11−11.

-y\ge -11

−y≥−11

3 Multiply both sides by -1−1.

y\le 11

y≤11

1 Add 22 to both sides.

6+2<\frac{x}{2}

6+2<  

2

x

 

2 Simplify  6+26+2  to  88.

8<\frac{x}{2}

8<  

2

x

 

3 Multiply both sides by 22.

8\times 2<x

8×2<x

4 Simplify  8\times 28×2  to  1616.

16<x

16<x

5 Switch sides.

x>16

x>16

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