Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x inches, from each
corner and then fold each side up to form the box. If Jeremy wants the volume of the box to be 432 cubic inches, what should the minimum length
of the sides of the squares cut from each corner be? Find the volume of the box as a function of x. Given: V = length x width x height

Jeremy Wants To Construct An Open Box From An 18-inch Square Piece Of Aluminum. He Plans To Cut Equal

Answers

Answer 1

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.

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Related Questions

A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
Find a mixture that will make the different shade of green that is more yellow.

Answers

Answer:

Use 1.75 cups of blue and 1 cup of yellow

Step-by-step explanation:

The given problem can be placed in the category of ratios and proportions. There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too. Hence adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

I hope this helps have a great day :)

explain why 256 + 4 is equivalent to (200 + 4) + (40+4) + (164)​

Answers

The expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

Given the expression 256 + 4. This can be solved using the partial sum expressed as:

256 + 4

256 + 4

= (200 + 40 + 16) + 4

According to the commutative property, A+B = B+A

The arrangement does not affect the result. Hence;

(200 + 40 + 16) + 4 = 4 +  (200 + 40 + 16)

Using the distributive law;

4 +(200 + 40 + 16) = (200 + 4) + (40 + 4) + (16 + 4)

Hence the expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

​Learn more on  partial sum  here: https://brainly.com/question/6958503

helppp please needed before tomorrow!!!!!!!!!!​

Answers

Answer:

The function is 200+50t (t= # of months)

Step-by-step explanation:

The best way to do this is to look at the question, and see no matter what, we have to pay 200 dollars to start. After which, they charge 50 bucks a month. Knowing this, we can make a function using f(x). Let C(t)= cost. Included is that graph. So for these questions, we need to see that there is an independent and a dependent variable, and we need to see that cost is affected by time. Hope this helps.

If f(x) = 4x − 1 and g(x) = −3x + 2 (a) Find ℎ(x) = f(x) + g(x)

Answers

Answer:

x+1

Step-by-step explanation:

4x - 1 + (-3x) + 2 = x + 1

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Even after that large purchase at Best Buy, you decide to go to Target to grab a few things that you missed. You purchase WWE 2K21 for $49.99, Starbucks Vanilla Coffee for $13.99, the new Keurig K550 for $179.99, and a pair of jeans for $17.99. The state sales tax is 6%.

What is the total selling price before tax?

How much is sales tax did you pay?

What was your total cost?

Answers

The total selling price before tax is $261.96.

The sales tax paid is $15.72.

The total cost is  $277.68.

The total selling price before tax is the sum of the prices of the WWE 2K21, Starbucks Vanilla Coffee,  new Keurig K550 and the jeans

$49.99 + $13.99 + $179.99 + $17.99 = $261.96.

Sales tax is the amount of money levied when a good or service is purchased. It is a percentage of the price of an item

Sales tax = tax rate x cost

6% x $261.96 = $15.72

The total price paid is the sum of the sales tax and the  total selling price.

$15.72 +  $261.96 = $277.68

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Using the scale 1/2 inch = 100 miles, figure out the number
of actual miles represented by 1/4 inches.

Answers

Answer:

  50 miles

Step-by-step explanation:

Multiply the given scale numbers by 1/2 to find your answer:

  1/2 in = 100 mi

  (1/2)(1/2 in) = (1/2)(100 mi) . . . . multiply the ratio values by 1/2

  1/4 in = 50 mi

At Store A, a game system sells for $150.The same system sells for $175 at Store B.Use a ratio to compare the price at Store A to the price at Store B.

Answers

Answer:

6:7

Step-by-step explanation:

=store A:store B

=150:175

=6:7

1) -88 ≤ -8(x+6)

2) 43 > -5k + 3 ≥ 8

Please show work :)

Answers

[tex](1)\\\\-88\leq -8(x+6)\\\\\implies -88\leq -8x -48\\\\\implies -88+48 \leq -8x\\\\\implies -40 \leq -8x\\\\\implies \dfrac{-40}{-8} \geq x~~~~ ;[\text{Dividng by a negative number so, reverse the inequality}]\\\\\implies 5 \geq x\\\\\implies x \leq 5\\\\\text{Interval solution,}~ (-\infty,5]\\\\\\(2)\\\\43 > -5k+3 \geq 8\\\\\text{Now,}\\\\43>-5k+3\\\\\implies 43-3 > -5k\\\\\implies 40 >-5k\\\\\implies - \dfrac{40}5 <k\\\\\implies -8<k\\\\\implies k>-8\\\\[/tex]

[tex]-5k+3 \geq 8\\\\\implies -5k \geq 8 -3\\\\\implies -5k \geq 5\\\\\implies k \leq -1\\\\\text{Combine solutions,}\\\\-8<k\leq -1\\\\\text{Interval solution,}~ (-8, -1][/tex]

Please help me solve this problem ASAP

Answers

Quadrant 4
Hope this helps!

Robert graded his friend Sam's practice test and a him a 72% Sam checked it again in found that he really made a 80% Robert said relax i only made an error of 8%Is robert correct

Answers

Answer:

No

Step-by-step explanation:

Use the formula, difference/original. The difference is 8%. The original is 72%.

The equation would be: 8/72

Which is 1/9

1/9 = 11.1%

So he made a mistake of 11%

bro can anybody please help :(!!

Answers

Answer:

This is what i got

I really need the answer to this

Answers

Answer:  14.2

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

Explanation:

Let point N be at the intersection of the horizontal line and segment JM.

We can prove the right triangles JNK and MNK are congruent using the hypotenuse leg (HL) rule. This in turn means JN = NM through the use of CPCTC.

In other words, JN = NM because the horizontal line is the perpendicular bisector of JM.

So,

JM = JN + NM

JM = NM + NM

JM = 2*NM

JM = 2*7.1

JM = 14.2

Answer:

JM = 14.2

Step-by-step explanation:

Given JK = MK then Δ JKM is isosceles.

The line through K is a perpendicular bisector of JM , so

JM = 2 × 7.1 = 14.2

I need to find the missing angles

Answers

Can you explain well


Which expression shows a way to find 22 X 46?

Answers

Answer:A. (22)(40)+(22)(6)

Step-by-step explanation: (22)(40)+(22)(6)

880+(22)(6) 880+132 1012

Christian buys a two-gallon bottle of juice for $18.16.


1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounce

How many fluid ounces of juice did Christian buy?

Answers

Answer:

256 fluid ounces

Step-by-step explanation:

2 gallons = 8 quarts

8 quarts = 16 pints

16 pints = 32 cups

32 cups = 256 fluid ounces

Directions- If each quadrilateral below is rectangle, find the missing measures ​

Answers

Answer:

1) 59

2) 31

3) 59

4) 31

5) 31

6) 59

7) 118

8) 62

9) 62

10) 118

11) 31

Step-by-step explanation:

The angle marked 59 degrees is congruent to angles 1, 3, and 6. The angle marked 59 + angle 11 is 90 degrees because the shape is a rectangle, so 90-59=31. Angle 11 is congruent to angles 2, 4, and 5. Now that we know that the triangle on the left has two angles of 59 degrees and that the angle measures of a triangle add to 180, 59+59=118 and 180-118=62, so angle 9 is 62 degrees. Angles 8 and 9 are vertical angles and therefore are congruent. To find angles 10 and 7, we can use the same method: angles 4 and 5 are both 31 degrees, 31+31=62, so we subtract 62 from 180 to get 118. Angles 7 and 10 are also vertical angles, so they are both 118 degrees. I hope this helps!

(-3x+4)+(x-9) help please.​

Answers

Answer:

- 1 · (2×±5)

Step-by-step explanation:

Answer:

−2−5

Step-by-step explanation:

(-3x+4)+(x-9)

−3x+4+x−9

Subtract

−3x+4+x−9

-3−5+

Combine terms

−3x−5+x

−2−5

PLEASE HELP GIVING POINTS

Answers

Answer: You are correct, the slope 2, is the slope of the present line displayed on the graph.

Step-by-step explanation:

To find slope, you use the formula/term; [tex]\frac{rise}{run}[/tex].

This means to rise up ___ amount of numbers and run __ amount of numbers.

Rise is moving along y, and x is moving along x.

-Additional info:

positive slope (when lines go uphill from left to right) negative slope (when lines go downhill from left to right) zero slope (when lines are horizontal) undefined slope (when lines are vertical)

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

#TeamTrees #TeamSeas #PAW #Spread_Positivity

I hope this helps,

-Oceanbreeze24

There are 30 kilograms of 10 percent apple juice how much more aplle juice does it need to get to 25 percent?

Answers

Answer:

45 kg of apple juice

Step-by-step explanation:

Divide 25% by 10%

The answer you get multiply it by 30

Take the answer you get subtract the 30 kg

The volume of a room is 640 cubic feet. If the length is 10 feet and the width is 4 feet, find the height

Answers

Answer:

16

Step-by-step explanation:

Divide 640 by 40.

[tex]640 = x \times 10 \times 4[/tex]

[tex]640 = 40x[/tex]

Divide both sides by 40

[tex] \frac{640}{40} = \frac{40x}{40} \\ [/tex]

[tex]x = 16[/tex]

Thus the height would be 16 feet .

5(2x-2)=8x: what is the value of x?

Answers

Answer:

5

Step-by-step explanation:

First, you multiply the 5 by 2x to get 10x, then multiply the 5 by -2 to get -10. After that, you should get:

10x-10=8x

And here’s how you find x:

10x-10=8x

-10x     -10x

-10x=-2x

/-2x   /-2x

x=5

What is the distance between the points (5, 1) and (-3, -5)?

Answers

Answer: 10

Step-by-step explanation: d = √(x^²-x^₁)^2+(y^²-y^₁)^2 d = √ (-3-5)^2+ (-5-1)^2 d = √(-8)^2 + (-6)^2 d = √64+36 d = √100 d = 10

ABCD is a square of side 4cm. In each of the following loci, the point p moves only inside the square. Sketch the locus in each case. AP=BP

Answers

The sketch of the locus AP = BP  shows an equal distance between AP and BP which can be seen in the image attached below.

A square is a plane figure that has four sides with each side adjacent to each other and they make a right angle of 90° to one another.

A locus is a point that satisfies a constraint on the square of the distances between two lines.

The sketch of the locus AP = BP given an intersection between lines A and B and that intersection is point P.

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Carlos can read 30 pages per hour in the 270 page book he is reading. At this rate, how long will it take him to finish his book?

Answers

Answer:

9 hours

Step-by-step explanation:

270/30=9

Do Now 13.2:
Green light has a frequency of 5.71 x 10' Hz.
Calculate the energy of a green light photon.
(SHOW ALL WORK for FULL CREDIT!)

Answers

Answer:

Not Step-by-step explanation:

Not enough info

my Christmas present to you​

Answers

Answer:

thankss

Step-by-step explanation:

Can someone help me out with this?

Answers

Answer:

-7.5x -12.5, x < -17.5x +2.5, x ≥ -1

Step-by-step explanation:

The absolute value function changes slope at its vertex. Here, that vertex is translated to x = -1. To the left of that point, the function is equivalent to one that negates its argument:

  |x| = -x . . . for x < 0

  |x| = x . . . for x ≥ 0

for (x+1) < 0

  y = -7.5(x +1) -5 = -7.5x -12.5

for (x+1) ≥ 0

  y = 7.5(x +1) -5 = 7.5x +2.5

This means we can write the piecewise function as ...

  [tex]y=\begin{cases}-7.5x-12.5,&\text{if }x<-1\\7.5x+2.5,&\text{if }x\ge-1\end{cases}[/tex]

Shira’s Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold. How many shoes did the company sell in June? Analyze Emily’s calculations. What error did she make? StartFraction part Over whole EndFraction = StartFraction 70 times 8,750 Over 100 times 8,750 EndFraction = StartFraction 612,500 Over 875,000 EndFraction.

Answers

Answer:

1,250,000

Step-by-step explanation:

875,000 sandals account for 70% of the total pairs sold.

875,000/7 = 125,000

125,000 accounts for 10%.

125,000 * 10 = 1,250,000.

1,250,000 accounts for 100%.

The company sells pairs of shoes in June is 612,500

In Emily's calculation the error she makes in the second last steps she forgets to write the term 70.

Given that,

Shiras Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold.

We have to determine,

How many shoes did the company sell in June? Analyze Emily's calculations. What error did she make?

According to the question,

Shiras Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold.

Then,

The shoes did the company sell in June is,

[tex]= \dfrac{70} {100}\times 875,000\\\\=8750 \times 70 \\\\= 612,500[/tex]

Hence, The company's sells pair of shoes in June is 612,500.

For more details refer to the link given below.

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What is the slope of the following line?

Answers

the answer is y= - (1/2) x +2

Answer:

1/2

Step-by-step explanation:

becase 1(0,0) 2(2,1) = 1/2

When finding ratios, did it matter whether you used the values for 3 lawns mowed or the values of 4 lawns mowed? ​

Answers

No it doesn’t actually because it’s the same thing there for the rates are equivalent ratios are equivalent if you turn them into fractions They would both be the same 696969696969
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