5

Remaining Time: 52 minutes, 50 seconds _Question Completion Status:0 B (x I)x - 3) (x + 2)(x - 3) 0 D (x)(x - 3)QUESTION 2box without top to be constructed by cutti...

Question

Remaining Time: 52 minutes, 50 seconds _Question Completion Status:0 B (x I)x - 3) (x + 2)(x - 3) 0 D (x)(x - 3)QUESTION 2box without top to be constructed by cutting ~inch squares from each of the four corners ofa square piece of cardboard. Assuming the box is to hold 480 cubic inches write the quadratic equation used to find the length of the original piece of cardboard_ 480 (x-S)(x-5)(10) 480 = (x-1O)(x -10J(10) 0 € 480 (x-1OJlx-10J(5)QUESTION 3Find the solution to the equation: 130

Remaining Time: 52 minutes, 50 seconds _ Question Completion Status: 0 B (x I)x - 3) (x + 2)(x - 3) 0 D (x)(x - 3) QUESTION 2 box without top to be constructed by cutting ~inch squares from each of the four corners ofa square piece of cardboard. Assuming the box is to hold 480 cubic inches write the quadratic equation used to find the length of the original piece of cardboard_ 480 (x-S)(x-5)(10) 480 = (x-1O)(x -10J(10) 0 € 480 (x-1OJlx-10J(5) QUESTION 3 Find the solution to the equation: 130



Answers

Answer each question.
A rectangular piece of metal is 5 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 64 in. ${ }^{3} ?$ A. $(x+1)(x-4)(2)=64$ B. $x(x+5)(2)=64$ C. $(x+1)(x-4)=64$ D. $x(x+5)=64$

In this problem. We have a rectangular sheet of metal, so let's draw that here. And we're told that the length of this, uh, of this rectangular sheet, it's five inches longer than it's with So we can denote the with of this rectangle by X, So its length is then X plus five. And we're also told that there are squares that have sides that have side links of two inches that are cut out in the corners of this rectangle. And that's so eso that we are able to turn this rectangle into a box. And we are also told that the volume of the box is 64 inches cubed, and what we want is a formula for the volume of this box. So we know that the volume of a box is given by height, times, length, times with and the height will be equal to two. And that's because when we fold these pieces up, they'll have. They'll have a height of two because we have to fold each side and then the links That's equal to X plus five. But we have to subtract four, and the reason we subtract for is because we're actually cutting into the length when we make our corners, so the length is X plus one and then finally the with is X minus four, and that's for the same reason. So we get that the volume is equal to the height, which is to times the length, which is X plus one times the width, which is X minus four. And we'll also use the fact that the volume is equal to 64. So when we compare our answer choices, we get that the solution is a and that completes the problem.

57 Question number e, then equally two x question number. B week equals X is given and land east. Why the wits? A given condition so with equal X minus four and length equal to X minus four when X is bigger than four. Question number C Cutting to ah inch of each corner Results is cutting in cutting a total of four inch on each side so volume equal to X squared minus 12 X plus 16 Question. Number me length. Equal X minus four and with equal to X minus four height equal to so volume equal to multiply by x minus four multiplied by two x minus four, then weeks equal eat and length equal 20. What's your number? E volume equal to multiply by x minus four multiplied by two x minus four equals 320 four, multiplied by X minus. School multiplied by X minus two equals 320 then six minus four. Multiply point X minus two Equal 30 320 over four equals 80. Then X squared minus six x minus 72 Equal. See you if X equal six. All X equals 12. Uh, as we solve this equation, then if X equals six, the volume will be 32 and exa quint when the volume will be 3 300 20 therefore, X equal. Right? An ex it's bigger than 17.2 and listening 18.8. Okay, when volume is bigger than four 100. Volume equal two X squared minus 12 x plus 16 is bigger than 400. It's squared minus six. X minus. 192 equals you then X equal. 17.2 old minus 12.11 point two. But X is bigger than zero. Therefore, it's equal 17.2. Okay, actually, equal is a lesson. 500 going home equal to X squared minus 12 x close to clean his lesson. 500. Then it's a squared. Find a six x minus 242 is less than you X squared minus uh, x minus. If x squared minus six x minus 242 equals you, then X equal 18.8 or x equal minus 12.2. But X is bigger than zeros. Therefore, X equals 9 18.8. Swimming go. Summing up is X is bigger than 17.2 and less than 18.8

He's off guard would is twice as long as it's one it just made into a ball with open door got into into squares from each corner and falling off the site. The first represent learned of the old piece of cardboard. Incomes are fixed. Lynn composing a piece of cardboard baby, it is stated. 6 65th on the card did God and two weeks is the limit next year, asking us to find the dimensions of the recruitment of books and restrictions on the same. So the dimensions. My mentions. Car X minus four, comma two X minus four and the restrictions are it should reach from zero to x 24 because the maximum is X minus four Syrians actually do for you. Don't mind a function being that represents the walled him off the ball in terms of sex. So while you is equally, toe Exline us for into two X minus four into do, which will give us four X squared minus 24 X plus 30 for what damages of the bottom off the walls. With William B. 3 20 the value is given us 3 20 so we will be quick, pretty windy will be equal to four x squared minus 24 x past 30. That will be excess square minus six. X minus 72 is equal to deal that will be X managed well into X plus 6 40 people. Zero thanks is a 4 to 12 comma minus six. So since my innocence is not in the normal, rates will be no in the graph, we'll see. Then just see that the graph Xing do X minus four into its going to explain its foreign people X minus four. This is graft and they asked us to find a William between the 400 line and the 500 line. The red color is a forward line in the Black Sea. 500 li. So let's see the intersection point. So the intersection point maybe so well rewarded the Intersect entered in the foot second coldly Sprinkle. And Billy, I guess the answer. Just 13.0 fight so well, right? This is 13 point and then mixed came to sit this blue life in the black light infusing into. And then that's the and then the decision point is 14 point. Next On the other side of the graph, It will be well finally into sick, this guy on the other side and present off in the red light percent off who gets and the answer is minus 7.4 and then the last one, which is black point. It is the loophole, indeed, black or just feeling that which we lived in the second point ls minus 8.24 So I find the Williams between these two holes, Dude off made at least two points. This is the This is the limit off the value in between the two life and this will be the wall you between little what's

For this problem, we're going to create an open topped box, starting with a flat sheet off plate metal. Now, from this sheet metal, we're going to cut out a square from each corner. That is three inches on a side. Okay, now we're told a few things about this piece off this rectangular piece of sheet metal. First, we're told that the short side is X, and we know that the longer side is 2.5 times its width. So if the shorter side is X than the full longer side, before we cut out the squares is going to be 2.5 times X. It's 2.5 times as long as it is wide. Are there any restrictions on the size of this rectangular piece of metal? Well, we don't have an upper limit. We've even. This could be an enormous square for all we know, but we do have a lower limit, since I'm taking out three inches for each of these two squares in the corner, X has to be big enough to take out six inches, so X has to be greater than six inches. Like I said, there's no upper limit excessive have to be smaller than a certain amount, but it has to be at least a big as six inches. Okay, With that in mind, let's figure out what the volume of our resulting box will be. Well, I know that the base of the box and I'm gonna draw this in blue on my picture here. When I fold up the sides on those blue dotted lines, that's going to be the base of my box. So the short side is going to be X minus What I've removed from those corners X minus six. The long side is gonna be what I started with 2.5 and I'm going again. Subtract 63 for each of those squares in the corners. So I'm going to have 2.5 look. Sorry, not 2.52 point five X is what I started with 2.5 X minus six. And the height of my box will be three, cause that's what I'm cutting out. When I fold up those size, they're gonna be up three units from the base of my box. So let's multiply this out if I multiply those first two numbers all use foil to expand that out. I get 2.5 x squared, minus six x minus 15 X plus 36 and I'll be molting multiplying all of that by three. So that gives me off resulting volume equation of 7.5 x squared well, six x and 15 x is negative 21 x and then multiplying that by three. So naked is 63 x +108 This is my volume equation for this box. Now, the last piece I want to know. I want to end up with a volume somewhere between 608 100 cubic inches. This is an easy thing to find. If we graph our equation, whether you use a graphing calculator or a graphing application, you can see what this is going to look like at the very bottom you can tell. I said X had to be at least six. If X was less than six, we'd end up with negative, um, negative volume. We can't have that. That's impossible for a real life box. So we're going to really be looking from six x equal six and larger now. I have graft on here our volume equaling 600 want an 800. I will reach a volume of 600 when X is 13.3 and albeit 800 when X is 14.7, rounding to the nearest 10th. So if X is between 13.3 and 14.7, I will end up with a desired volume for my box.


Similar Solved Questions

5 answers
Which reagent would yQu use accomplish the transformation shown here?Brz H-O 01, then (CHw)SHyWilkinson catalyst BH; THF, then HzOz; HzO: NaOH Hg(OAc)z and HzO, then NaBH:
Which reagent would yQu use accomplish the transformation shown here? Brz H-O 01, then (CHw)S HyWilkinson catalyst BH; THF, then HzOz; HzO: NaOH Hg(OAc)z and HzO, then NaBH:...
5 answers
Question 51ptsAmotion diagram for some moving object is shown here: Each frame (dot) of the motion diagram represents 1 s. Over which of the labeled regions are the object's velocity and acceleration in opposite directions? (If there is more than one region; fou must select all of them:)[=11$t =0Region 1Region 2Region 3Region 1Region 2Region 3None of the regions
Question 5 1pts Amotion diagram for some moving object is shown here: Each frame (dot) of the motion diagram represents 1 s. Over which of the labeled regions are the object's velocity and acceleration in opposite directions? (If there is more than one region; fou must select all of them:) [=11...
5 answers
Consider the initial value problem for function y given by;6y + 8y = 3&6t _ 2)_y(0) = 0(a) Find the Laplace Transform of the source function, F(s) = L[3 &6 - 2)] .F(s) 3e^(-2s)(b) Find the Laplace Transform of the solution, Y(s) c[yc)] :Y(s) (3e^(-2s))(s^2-6s+8)(c) Find the solution y(t) of the initial value problem above.y(t)Recall: If needed, the step function at € is denoted as u(t = c)
Consider the initial value problem for function y given by; 6y + 8y = 3&6t _ 2)_ y(0) = 0 (a) Find the Laplace Transform of the source function, F(s) = L[3 &6 - 2)] . F(s) 3e^(-2s) (b) Find the Laplace Transform of the solution, Y(s) c[yc)] : Y(s) (3e^(-2s))(s^2-6s+8) (c) Find the solution y...
5 answers
Determine the following indefinite integral Check your work by differentiation f(sec?x+8)dx J (sec 2x+8) dx =
Determine the following indefinite integral Check your work by differentiation f(sec?x+8)dx J (sec 2x+8) dx =...
4 answers
Solve the system of equations_x+y+z = 2 x-Y+3z = 14 3x+y+z = 60A {(2, - 3,3)} 0 B. {(3,2, - 3)} 0 C. {( - 3,2, 3)} 0 D. {(3, - 3,2)}
Solve the system of equations_ x+y+z = 2 x-Y+3z = 14 3x+y+z = 6 0A {(2, - 3,3)} 0 B. {(3,2, - 3)} 0 C. {( - 3,2, 3)} 0 D. {(3, - 3,2)}...
5 answers
Propose an efficient synthesis to the following product Please include your arrow pushing mechanism and any reagents you use_
Propose an efficient synthesis to the following product Please include your arrow pushing mechanism and any reagents you use_...
5 answers
Consider the structure of D-arabinose. Identify the enantiomer and name the enantiomer: CHOHOOHOHCHzOHWhich structure is the enantiomer of D-arabinose?OACHOCHOOHHOOHOhOHOHCH?OHCHzOHCHOCHOOhOHHO-OHHOHOCHzOHCHzOHOFCHOCHOOHHOHOOHOhHOCHzOHCHzOHWhat is the name of the enantiomer?name:
Consider the structure of D-arabinose. Identify the enantiomer and name the enantiomer: CHO HO OH OH CHzOH Which structure is the enantiomer of D-arabinose? OA CHO CHO OH HO OH Oh OH OH CH?OH CHzOH CHO CHO Oh OH HO- OH HO HO CHzOH CHzOH OF CHO CHO OH HO HO OH Oh HO CHzOH CHzOH What is the name of th...
5 answers
Cricket ?3.39 PM7186~X 4-3 Nota You have ilready done ths problem) X + Asmplo"s (lf any) AIL Enlctecots (I617} ) Th inlcnals whcre Ix)is IncTeasing and where il is Decreasing: AII Relativc Extrcma (Ii any ) Tc inxnals whcre Ix) is Concaie Up und where i is Concave Dovn AlI lalktion points (If an And also Sketch Mx)
cricket ? 3.39 PM 7186 ~X 4-3 Nota You have ilready done ths problem) X + Asmplo"s (lf any) AIL Enlctecots (I617} ) Th inlcnals whcre Ix)is IncTeasing and where il is Decreasing: AII Relativc Extrcma (Ii any ) Tc inxnals whcre Ix) is Concaie Up und where i is Concave Dovn AlI lalktion points (...
5 answers
The graph of f (z) is shownList the critical values of f (x)
The graph of f (z) is shown List the critical values of f (x)...
5 answers
Find the derivative of the function at Po in the direction of u.flx, Y, 2) =~4xy3z? , Pol-4,-64,16),u = -2i +j - 2kA) 234.881,024B) 83,886,080C) 67,108,864218,103,808 D)
Find the derivative of the function at Po in the direction of u. flx, Y, 2) =~4xy3z? , Pol-4,-64,16),u = -2i +j - 2k A) 234.881,024 B) 83,886,080 C) 67,108,864 218,103,808 D)...
5 answers
Refer , the Venn dlagrm the right for events probabIily: Aand In an equa ly likoly sarnplo spnco Find Ine Irdicalod PUAnB))PIAnB)) = (Type docimn |
Refer , the Venn dlagrm the right for events probabIily: Aand In an equa ly likoly sarnplo spnco Find Ine Irdicalod PUAnB)) PIAnB)) = (Type docimn |...
5 answers
PROBLEM # 1 (9 points) The equation for a wave on a string is given below D(x,t) 0.021m sin [2i{(2.0)x + (30)t - 1/2}] where x is in m and t is in seconds The linear density of a string is 1.4 x 10-4kg/mFind the wave speed, tension; wavelength; angular frequency.
PROBLEM # 1 (9 points) The equation for a wave on a string is given below D(x,t) 0.021m sin [2i{(2.0)x + (30)t - 1/2}] where x is in m and t is in seconds The linear density of a string is 1.4 x 10-4kg/m Find the wave speed, tension; wavelength; angular frequency....
1 answers
Use the change-of-base formula to find each logarithm to four decimal places. See Example $9 .$ $$ \log _{7} 3 $$
Use the change-of-base formula to find each logarithm to four decimal places. See Example $9 .$ $$ \log _{7} 3 $$...
5 answers
Suppose that we have measured three data points (1/3,0), (3/2,1) and (-2,1). our model for these data asserts that the points should lie on a line. If y-mxtc is the line which best fit the given data points, what are the values of m and c?Select one:a,m=1,c-2b.m=1,c=-3/2m-2 c-1d. None of these
Suppose that we have measured three data points (1/3,0), (3/2,1) and (-2,1). our model for these data asserts that the points should lie on a line. If y-mxtc is the line which best fit the given data points, what are the values of m and c? Select one: a,m=1,c-2 b.m=1,c=-3/2 m-2 c-1 d. None of these...
5 answers
Find the area of the region bounded by the graphs of the given equations. y =5x+6 y=xThe area is (Type an integer or simplified fraction )
Find the area of the region bounded by the graphs of the given equations. y =5x+6 y=x The area is (Type an integer or simplified fraction )...
5 answers
Sentcho Type &Jnment 3 20.docxANAtaiSo.(glAROlql Gh, Qi2NO eZNO,g)JNO_lsl H;Cx2V0oNOlal[ntpo: ctlca of nluetad0 Iron cceethcerutmll rouatlun lar tF TCICLIcn5oxyccn ImolvJefrd hrouck Hcttct'cch(Nac tn:
Sentcho Type & Jnment 3 20.docx ANAtai So.(gl AROlql Gh, Qi 2NO e ZNO,g) JNO_lsl H;Cx 2V0o NOlal [ntpo: ctlca of nluetad0 Iron cceethcerutmll rouatlun lar tF TCICLIcn5 oxyccn Imolv Jefrd hrouck Hcttct 'cch (Nac tn:...
5 answers
1 f2sin x %/1+5cosx dx2 J(tan 2x+ cot 2x)? dx X 2cos 3_ ( 4 dx Sin 4
1 f2sin x %/1+5cosx dx 2 J(tan 2x+ cot 2x)? dx X 2cos 3_ ( 4 dx Sin 4...

-- 0.019280--