Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volume of each configuration. Does it appear that there is a maximum volume

Answers

Answer 1

Answer:

) See annex

b) See annex

x  =  0,5 ft

y =  2 ft   and

V = 2 ft³

Step-by-step explanation:  See annex

c) V = y*y*x

d-1) y = 3 - 2x

d-2) V = (3-2x)* ( 3-2x)* x   ⇒ V = (3-2x)²*x    

V(x) =( 9 + 4x² - 12x )*x    ⇒   V(x) = 9x + 4x³ - 12x²

Taking derivatives

V¨(x) = 9 + 12x² - 24x

V¨(x) = 0              ⇒   12x² -24x +9 = 0     ⇒  4x² - 8x + 3 = 0

Solving for x (second degree equation)

x =[ -b ± √b²- 4ac ] / 2a

we get    x₁  =  1,5       and    x₂ =  0,5

We look at y = 3 - 2x    and see that the value x₂ is the only valid root

then

x  =  0,5 ft

y =    2 ft   and

V = 0,5*2*2

V = 2 ft³


Related Questions

Factor this expression. 3x² - 6x O A. 3x(x - 2) B. 3x(x2 - 2) O C. 3(x-2) D. 3072 - 2)​

Answers

The answer is A. 3x(x-2).

Answer:

A. 3x (x-2)

Step-by-step explanation:

Question:

To factorise

3x² - 6x

Solution:

3x² - 6x

[Taking common term out]

= (3x × x) - (3x × 2)

= 3x ( x - 2)

Result:

Hence, factorised answer of 3x² - 6x is 3x (x-2) (Ans)

A 20 in wagon wheel has 6 spokes. What is the outside distance between the end of the spokes if they are spaced evenly(arc length)?

Answers

Answer:

10.47 inches

Step-by-step explanation:

circumference = πD = 3.14(20) = 62.8 inches

62.8 inches/6 spaces = 10.47 inches per space

Solve these equations.

Answers

Answer:

no solution

Step-by-step explanation:

|x-33| = -33

An absolute value must be greater than or equal to zero

The right hand side is a negative number.

There is no solution

Answer:

No solution

Step-by-step explanation:

When you do the absolute value, it is equal to a negative number. Which does not make sense so no solution

A researcher posts a radio advertisement offering $35 in exchange for participation in a short study. The researcher accepts the first eight people who respond to the advertisement. Which of the following statements is true about the sample? (5 points)
A. It is a valid sample because the first eight people were selected to participate.
B. It is not a valid sample because it is not a random sample of the population.
C. It is a valid sample because money was offered to participants.
D. It is not a valid sample because it is only a short study.

Answers

Answer:

B.

Step-by-step explanation:

Its meh best guess

Answer:

B.

Step-by-step explanation:

I think it is B

What is the area of the triangle?​

Answers

Answer:

11 ½ * 4* 5.52 *5.5=11.....….

QUESTION
The first four terms of a quadratic sequence are 8; 11; 16; 23; .-
Write down the next two terms of the quadratic sequence.
J. 2 Calculate the nth of the quadratic sequence.
i: 5.3 Determine the position of the term 2311 in the sequence.
(1)
(4)
(3)
[8]​

Answers

Answer:

b

Step-by-step explanation:

Kylie is a psychologist who studies memory. She wants to see whether background music affects memorization.
Kylie randomly sorts 40 subjects into two groups. The 20 subjects in one group are given five minutes to memorize a list of words while background music is playing. The 20 members of the other group perform the same task without any background noise. Afterward, Kylie records how many words from the list each subject could remember.
Words memorized with background music
92914927282011132325162226141421131812
Mean: 18.2 words
Words memorized without background music
2824282427261371512276292022262220179

How much lower is the average for the treatment group than the average for the control group?

Answers

Answer:

14,96

Step-by-step explanation:

Help me to convert the following to redian (1) 300° (2)18° (3) 105°​

Answers

Answer:

(1) 5.23599

(2) 0.314159

(3) 1.8326

Plz help me this very important

Answers

The answer will be 31 hope it right

Please help me i cannot understand these Questions

Answers

Answer:

In the last task, the result is 17+3x/6

Step-by-step explanation:

X+5/3 - 2x-7/6 + x/2

2(x+5)-(2x-7)+3x /6

2x+10-2x+7+3x /6

17+3x/6

I dunno this task above, I hope this one is correct :))

D = L ( m/k + v^2/25)

Make v the subject of the formula.

Answers

Answer:

Answer and steps in picture.

D/L = m/k + v^2/25
-m/k -m/k
25(D/L - m/k) = v^2/25(25)
Sqrt 25(D/L - m/k) = sqrt v^2
Sqrt 25(D/L - m/k) = v

Tomas drew a rectangle with an area of 6 square centimeters.what is the greatest possible perimeter of this rectangle?Explain please. i want 20 answers please

Answers

The answer is 14. Hope it helps!

solve this question 5/8÷15/16=?​

Answers

Answer:

Hellou our answer is 2/3

Step-by-step explanation:

5/8 ÷ 15/16 = 2/3

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

what is the value for θ: sin (θ+20) = cos θ

Answers

Answer:

Step-by-step explanation:

Bob earns $10 per hour plus a
15 percent commission on his sales. Last week he worked h hours and had s dollars in sales. Write an equation that represents his total earning, in dollars, last week?


O 10.15hs
O 10.15(h +s)
O 10h+0.15s
O 10(h + 0.15s)

Answers

Answer:

C, 10h + 0.15s

Step-by-step explanation:

he earns 10 dollars per hour so 10h

he earns 15% or .15 per sale so .15s

add them together to get 10h + 0.15s

Anyone knows the answer???

Answers

Answer:

351.9 m²

Step-by-step explanation:

[tex]SA=2\pi r^2+2\pi rh[/tex] where r is the radius of the base and h is the height of the cylinder

We're given the diameter of the base, which is 8 m. Therefore, the radius is 4 m (after dividing by 2).

Plug in 4 as r and 10 as h

[tex]SA=2\pi (4)^2+2\pi (4)(10)\\SA=2\pi (16)+2\pi (40)\\SA=32\pi +80\pi \\SA=112\pi[/tex]

Therefore, the surface area of the cylinder is approximately 351.9 m² after rounding to the nearest tenth.

I hope this helps!

351.9 to the power of 2

help me please :(*********​

Answers

Answer:

These will be equal, so the answer is 7

Step-by-step explanation:

Set 2x+42 and 9x-7 equal to each other, then solve.

2x+42=9x-7

-2x +7 -2x +7

49=7x

x=7

help, please will give Brainliest

Answers

9514 1404 393

Answer:

  A.  57 7/9 ft³

Step-by-step explanation:

The volume of a rectangular prism (cuboid) is the product of its dimensions.

  V = LWH

  V = (4 1/3 ft)(3 1/3 ft)(4 ft)

If you drop the fractions, this becomes ...

  V = (4 ft)(3 ft)(4 ft) = 48 ft³

You know the fractions add some amount to this, so you know the volume will be somewhat larger than 48 ft³. The only reasonable choice is A: 57 7/9 ft³.

__

If you feel the need to compute the volume exactly, you can do so using improper fractions.

  V = (13/3 ft)(10/3 ft)(4 ft) = 520/9 ft³ = 57 7/9 ft³

This is hard for me but easy for you so what’s the answer ?

Answers

Step-by-step explanation:

112=35+d

112-35=d

d=77

The ratio of dogs to cats at the local
shelter is 2 to 5. There are 20 dogs at
the shelter. What is the total number
of cats and dogs at the shelter?
A. 28
B. 50
C.
70
D. 8
Need

Answers

Answer:

B 50

Step-by-step explanation:

Option 1) 2/5 = 20/x  |  20/2 = 10 so x = 10  |  5 times x 10 =50

Option 2) dogs 2 to cats 5  |  2/5 = 20/x  |  .40 = 20/x  |  .40x = 20  |  x = 50

Option 3) you can look and see that 20 is 10 times more than 2 and therefore infer that x is 10 times more than 5 which is 50

An individual can win a prize by drawing the highest numbered card out of five cards. After each draw, the card is replaced and the cards are shuffled for another chance. If the prize is not won, the card is again replaced and mixed in with the other cards. If a prize is won, the highest card is replaced and the five cards are shuffled for a new game. If an individual makes seven draws, what is the probability the individual will win a prize exactly two times

Answers

Answer:

[tex]\frac{1}{25} =0.04[/tex] (Unusual)

Step-by-step explanation:

1/5 for one drawing

1/5 chance to win once, if there is only one game.

Then multiply them together to get 1/25.

If you need in decimal form 1/25 = 0.04 (unusual)

If an individual makes seven draws, what is the probability the individual will win a prize exactly two times is 0.2753

What is Permutation and Combination ?

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

An individual can win a prize by drawing the highest numbered card out of five cards.

Given that an individual makes 7 draws

p = 1/5  =  0.2

q = 1-P =0 .5

5 times corresponds to B( 7 , 0.2)

P(x = 2) = 7 C₂ (0.7)² (0.8)⁵

= 21 * 0.04 * 0.3277

= 0.2753

Therefore If an individual makes seven draws, what is the probability the individual will win a prize exactly two times is 0.2753

To know more about Permutation and Combination

https://brainly.com/question/13387529

#SPJ2

Need help quick!!! Karl set out to Alaska in his truck the amount of fuel remaining in the trucks tank in liters as a function of distance driven in kilometers is graphed how fast did the truck consume its fuel

Answers

Answer:

I think it's 40 . I'm not sure

Answer:

0.6 liter per kilo

Step-by-step explanation:

Question 4
The results of the Woodlands Middle School poll show that 20% of
the students prefer the aquarium and 50% of the teachers the
aquarium.
Which of the following statements is true?
There is evidence that teachers at Woodlands Middle may prefer the aquarium
more than students.
There is not enough evidence to support a relationship between destination
preference (aquarium or amusement park) and school role (student or teacher).
Woodlands Middle may prefer the aquarium
There is evidence that students
more than teachers.

Answers

Answer:

There is evidence that teacher at Woodlands Middle May prefer the aquarium more than students

Step-by-step explanation:

There is evidence that teachers at Woodlands Middle may prefer the aquarium (Option A) is the true statement from all the available options.

Why do we do sampling?

We do sampling so that we don't have to work on entire population of items but only on that sample in a way that we can predict information about population.

Most of the times, it isn't possible in real world to work on entire populations. Samples come out for rescue by assumptions that they will have some properties of the population pertained in them.

Thus, the sample should be taken out such that it includes data of the population as much  as it can in unbiased way so as to imitate population.

Poll oftenly uses sampling.

The data obtained from the poll shows that:

20% of the students prefer the aquarium and 50% of the teachers the

aquarium.

That means, from the poll, we found that out of total students, 20% prefer aquarium whereas 50% of total teacher prefer aquarium.

Since we conclude from sampling only as this is the usual way we do conclusion about population, and since percentage shows that less students' proportion prefer aquarium than the proportion of teachers prefering aquarium, thus,

There is evidence that teachers at Woodlands Middle may prefer the aquarium (Option A) is the true statement from all the available options.

Learn more about sampling here:

https://brainly.com/question/24842573

Determine the intercepts of the line I need help quick!!!!!

Answers

Answer:

x-inter = (-40,0), y-inter= (0,15)

Step-by-step explanation:

the fitnessgram pacer test is an automated aerobic capacity test that progressively gets more difficult as it continues.

What is the contrapositive of the following conditional? If a number is divisible by 10, then it is divisible by 5.

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: No because that is not always true.

Explanation:

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Which of these sets of numbers contains no rational numbers?
NEED ANSWER NOW!​

Answers

Answer:

the first option

Step-by-step explanation:

for a number to be rational, it should be able to be expressed as a fraction.  Non terminal decimals must have a repeating pattern. Square roots of random numbers aren’t rational. Just like the first rule with decimals, the third number cannot be expressed as a fraction

Answer:

Step-by-step explanation:

it’s the first one

please help me i can't figure this out

A 6 meters per second

B 5 meters per second

C 4 meters per second

D 7 meters per second​

Answers

Answer:

B 5 meters per second

Step-by-step explanation:

Pick two points on the graph, and find the slope.

For example, you can use the points

(0, 8500) and (1700, 0)

slope = (difference in y)/(difference in x)

slope = (0 - 8500)/(1700 - 0) = -8500/1700 = -5

The slope is negative because the plane was losing altitude as it descended.

It descended at a rate of 5 meters per second.

Answer: B 5 meters per second

Answer:

B. 5 meters per second

Step-by-step explanation:

slope=8500÷1700=5

Plane descended at the rate of 5 meters per second.

hope it helps

have a great day!!

To find the value of the following expression, which task should be completed first?

Answers

Answer:

subtract inside the parentheses

Step-by-step explanation:

According to pemdas. It is parenthesis first so you subtr what’s inside first

Answer:

Subtract inside the parenthesis

Step-by-step explanation:

For this problems you have to follow PEMDAS which stand for

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

in that order

what is 1086.3961 rounded to the nearest square foot?

Answers

I believe the answer would be 1086.4

Please give a like if I’m right and tell me in the comments if I’m wrong.
Hope this helped :)

Solve the following inequalities and give the solutions in both set and interval notations.

-2x + 5 < -x + 25

Answers

4y + 3 > 23 subtract 3 from both sides
4y > 20 divide both sides by 4
y > 5

-2y > -2 divide both sides by -2 (the order changes)
y < 1

(-oo, 1) ∪ (5, oo)
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