5

A rectangular box for new product is designed in such Way that the three dimensions always have particular relationship defined by the variable x The volume of the ...

Question

A rectangular box for new product is designed in such Way that the three dimensions always have particular relationship defined by the variable x The volume of the box can be written as 6x + 31x2 53r-30 _ and the height is always * + 2_ [hat are the width and length of the box?

A rectangular box for new product is designed in such Way that the three dimensions always have particular relationship defined by the variable x The volume of the box can be written as 6x + 31x2 53r-30 _ and the height is always * + 2_ [hat are the width and length of the box?



Answers

Use the given volume of a box and its length and width to express the height of the box algebraically.

Volume is $12 x^{3}+20 x^{2}-21 x-36,$ length is $2 x+3,$ width is $3 x-4.$

So in this young question we have like regular box, the length of the box is twice the width. So to the blue. And where the blue is the with late the height of the boxes Half of the week. So s. equals two. Right? We have to find the surface area and volume of the box. So the surface area of the box can be found out by the formula As his equals two times self. L. Multiplied by W plus W. Multiplied by edge plus L. Multiplied by edge. Right here. At least the land W started and her register hide off the box. So we have to substitute the values. So at least ow multiplied by W. Plus I'm learning to wi fi. Two plus the water blow into H. Is W way too late. So when we simplify this, we get to W. Square plus The Blue Square by two plus W. Square, which is equal school three plus one murder. That is seven W. Is square. So this is the surface idea of the rectangular box. To find the volume of the box, we have hell into the learning to edge. That is the product of land, weight and height. Like So this is equals two, two. W. multiplied by the blue, multiplied by the height is W. I do. So when we simplify this, we get the volume as look you. Right? So this is the surface area and the volume of the rectangular boxes. Mhm.

This question. We have rectangular box, the weight of the boxes w Right. The next statement is that the rate of the boxes, 1/3 of the land or in a positive words, we can say that the land of the boxes three times of the week. Right similarly, the height of the boxes one third of the way it it means that edges equals two W A three. Now, the approach to solve this question is that we know surface area of the boxes given by two, multiplied by LW plus wh plus Elledge. And the volume of the box is given by L wh where L is the length of the box. The blue is wit and edges height off the box. So with the help of these formulas, We can find the surface area and volume surface area as equals two. Taylor blew into the blue plus W. Into the white A plus the blue by train to trade. So when we simplify this, we get www square less W square uh for battery, lovely square. So this is a close to three and 239 plus 4, 13 Into the 26 x three. The blue square and the surface area is 26 x three W. Square. Similarly to find the volume. We have the formula LW edge. So land is www. The whitest, the blue and the height is obligatory. So when we simplify this, we get the volume is W cube. Hence the volume of the boxes that look you up. And the surface area is given by this expression. It's like

So this optimization problem we have here a three x 2 rectangle cutting out equal parts squares, X by X. And so that when we lift up those squares Right to make a open rectangle or open box rather get 3 -2 x. Too nice to X. And then X. Right. So let's go ahead and multiply those out here. We're trying to maximize that volume. Do you have 3 -2 x times 2 -2 x time sex. And when we simplify that out here Got six minus four x and six x plus or X squared, is that pay X. Simplifying that here? We've got six is 10 x Plus four x squared setbacks. So we have six x 10 X squared us for execute. Okay, taking the whole thing here, driving with respect to X. That's going to be equal to number here. So dr all of that area got six. It's 20 X Plus 12 x squared equals zero. So from here, when we solve this, this gives us two possible answers. Access approximately equal to .39. 2 more approximately 1.2 74. Okay, testing both of these answers here, plug it into trying to solve for the volume. So here for this 1st 1 We get, the volume is equal to 1.0 56 feet Q. And for the next one get a negative 0.3 and six. So we're going to reject this answer here and our volume. There's 1.056 ft cubed.

So for this question, we're giving the volume off the off the box and the length and the weeds. Well, we're supposed to find the eyes of the books, and we're giving the volume as, um 10 X cube plus teddy eggs squared minus Kate eggs minus 24. We're giving that the lens is to and the weeds is X plus three. So basically, we're finding the IEDs. So, um, we're going to consider information we're giving. We know that the volume off a box, um, is the product is a product of length, width and height, and the formula we have is the volume is men's times, breath, times, heights or lent times we time height. But yeah, we have on the formula we're giving from the top is 10 x cube close. That's the X squid minus eight eggs minus 24 equal to we can see that it's learned times read times we times height, or we can say that the bread is the same thing as that weeds. But to make it easy to understand, I'm just gonna pull the weeds there. So this is going to be called to land times, breath time, sweets, But instead of doing that, we're going to do to which is the lens times, the wits. We know that wit is Extras three. So we're gonna put extras three there Times Heights. That height is unknown. Working for it. So that's it They were going to solve for age. So starting off, we're going. Thio, find this side. This is going to be called to two X lost six close brackets age. Right. So from there, we can divide on both sides by two explores six. So we have aged to the left and then this entire system, um, question is going to be divided by two extra six so we can find X. We can find a trader waas that c x quit minus eight x minus 24 divided by to expose six. I'm from there. From there, we'll divide the volume by the product now the volume by the product of wheat and lanes by using the long division formula so we can find the heights. So by using the long division forming that we're gonna have on this, um, I'm sorry about that. We're gonna have this and then we're going to divide it by two x plus six. They were gonna have 10 X cube. Who was? That's the X good minus eight X minus 24. So when we do this, we're going to have minus. So when we divide two x on with the 10 X was cube, we're going to have, um you're gonna have five eggs. Squid, and then, um, we're gonna have full minus four. So the remaining off the division is going to be minus train x que waas dead sea X squid, close brackets. And they would divide by minus eighth eggs, the one that was left there minus 24. So when we do this, we're going to have my nose minus eight x minus 24. Valid by zero. So therefore, the questions off five X squared minus four. The questions is five x squared minus for it's the questions and that's going to be the IEDs. The height of the box is going to be five. X quit man useful Ambassador


Similar Solved Questions

5 answers
V Ee 1 1 } 1 I [ eee W L 8 E 2 # 8 8 # H 8 0 1 0 U H 8 K 2 5 1 8 2 ] 0 } L 8 5 1
V Ee 1 1 } 1 I [ eee W L 8 E 2 # 8 8 # H 8 0 1 0 U H 8 K 2 5 1 8 2 ] 0 } L 8 5 1...
3 answers
In a simple random sample of size 51, taken from population; 22 of the individuals met specified criteriaWhat is the margin of error for 90% confidence interval for the population proportion?Round your responseeast decimal places_NumberWhat is the margin of error for 95% confidence interval for p?Round your response to at least decimal places_Number
In a simple random sample of size 51, taken from population; 22 of the individuals met specified criteria What is the margin of error for 90% confidence interval for the population proportion? Round your response east decimal places_ Number What is the margin of error for 95% confidence interval for...
5 answers
Platyhelminthes (flatworms) have a bilateral symmetry and therefore are coelomates True FalseQuestion 7 (1 point) Which is a major feature of Ecdysozans?Molted cuticleEndoskeleton of chitinEndoskeletonTrochophore IarvaQuestion 8 (1 point) Cniderians were the first animals to evolvemovement and therefore have muscles True FalseA
Platyhelminthes (flatworms) have a bilateral symmetry and therefore are coelomates True False Question 7 (1 point) Which is a major feature of Ecdysozans? Molted cuticle Endoskeleton of chitin Endoskeleton Trochophore Iarva Question 8 (1 point) Cniderians were the first animals to evolvemovement and...
5 answers
Which of the following is the inverse of fx)=4*?f-I(x) = V4f '(r) = %f-1(r) = 10g4*f '(r) = log,4Save
Which of the following is the inverse of fx)=4*? f-I(x) = V4 f '(r) = % f-1(r) = 10g4* f '(r) = log,4 Save...
5 answers
Q10. For the circuit containing combination of capacitors shown below, find the charge (Q) and potential difference (V) for each capacitor The potential difference across the battery is 11 V. Please show all your work. Draw diagrams to illustrate how you systematically simplify the circuit to calculate the needed quantities step by step.4 pF Cz 12 pF11 V2 pF
Q10. For the circuit containing combination of capacitors shown below, find the charge (Q) and potential difference (V) for each capacitor The potential difference across the battery is 11 V. Please show all your work. Draw diagrams to illustrate how you systematically simplify the circuit to calcul...
5 answers
Methyl glycosides of 2 -deoxy sugars have been prepared by the acid-catalyzed addition of methanol to unsaturated carbohydrates known as glycals.
Methyl glycosides of 2 -deoxy sugars have been prepared by the acid-catalyzed addition of methanol to unsaturated carbohydrates known as glycals....
5 answers
COLOR THEMEZOOM1. The coordinate grid shows points P, Q, R,and S.All the points are integers coordinates for theseWhat is the value of the X-coordinate of point P?
COLOR THEME ZOOM 1. The coordinate grid shows points P, Q, R,and S.All the points are integers coordinates for these What is the value of the X-coordinate of point P?...
4 answers
Use lhe slmplex melhod (0 maxlmlzeP= 7I1 + 1312sublecl (o52 3 412 4 112I[II 2 0I2 > 0Af,
Use lhe slmplex melhod (0 maxlmlze P= 7I1 + 1312 sublecl (o 52 3 412 4 112 I[ II 2 0 I2 > 0 Af,...
5 answers
1. given the equation for the graph y=sin(x), shift pi/12 to the left, reflected across the x-axis, translated 5 units downward, then stretched by a factor of 4. A) y=-4 sin (x + pi/12)-20B)y=-4 sin (x - pi/12)-20C)y=-4 sin (x+ pi/12) -5 D)y=-4 sin (x-pi/12)+202. write the polar form: (square root 3 + i) ^5A) (10, 150 degrees)B) (2, 30 degrees)C) (10, 30 degrees)D) (32, 150 degrees)
1. given the equation for the graph y=sin(x), shift pi/12 to the left, reflected across the x-axis, translated 5 units downward, then stretched by a factor of 4. A) y=-4 sin (x + pi/12)-20B)y=-4 sin (x - pi/12)-20C)y=-4 sin (x+ pi/12) -5 D)y=-4 sin (x-pi/12)+202. write the polar form: (square root 3...
5 answers
Deline pholoelecuic effectDiscuss the "Detimental Findings of photoekccuic effec Fxplain Fin-lein phatuelectric equation X-rys W length 15,0 pI jre scmliend Irom urget_ Calculuute (} the wavelength of the X rays scalletd through 55" . (ii) the miximum Wnvelength present In the scullered X-rys and (iii) the miLximum Kinetic energy Of the recoil elecuans.
Deline pholoelecuic effectDiscuss the "Detimental Findings of photoekccuic effec Fxplain Fin-lein phatuelectric equation X-rys W length 15,0 pI jre scmliend Irom urget_ Calculuute (} the wavelength of the X rays scalletd through 55" . (ii) the miximum Wnvelength present In the scullered X-...
1 answers
In Exercises $23-28,$ use areas to evaluate the integral. $$\int_{a}^{b} 3 t d t, \quad 0 < a < b$$
In Exercises $23-28,$ use areas to evaluate the integral. $$\int_{a}^{b} 3 t d t, \quad 0 < a < b$$...
5 answers
Yca/dzlle/content/278291/viewContent/372/348 Niew4-9b Plot the steady state ozone profile using your data (height against ozone concentration in molecules cm Interpolate the points t0 make smooth graph:[ L L1OE +000E+13 Ozone concentration Umolecules cm )4.0E+134-9c . Compare the grpl abore with your leclure notes. Give Teisons (other than catalylic ozone destruction) why the steady stale [O,] is likely overestimate near the tropopause2WeHackinos
yca/dzlle/content/278291/viewContent/372/348 Niew 4-9b Plot the steady state ozone profile using your data (height against ozone concentration in molecules cm Interpolate the points t0 make smooth graph: [ L L1 OE +00 0E+13 Ozone concentration Umolecules cm ) 4.0E+13 4-9c . Compare the grpl abore w...
5 answers
A cart starting from rest rolls down a frictionless 1.0m high hill. It travels adistance 2.0 m along the rough bottomsurface until it comes to rest. What is thecoefficient of kinetic friction alongthe bottom surface?
A cart starting from rest rolls down a frictionless 1.0 m high hill. It travels a distance 2.0 m along the rough bottom surface until it comes to rest. What is the coefficient of kinetic friction along the bottom surface?...
5 answers
1MRY inhibitor2NZT inhibitor3GRS inhibitor2VIX inhibitor4ALD inhibitorHN1ZOY inhibitorOH OHYour enzyme is inhibited by one ofthe compounds depicted above The inhibitor for your specific protein is indicated via the PDB protein code shown:On the basis of the enzyme's structure,its substrate and mechanism of action_ predict what type of enzyme inhibitioncompetitivenon competitive} may occur and
1MRY inhibitor 2NZT inhibitor 3GRS inhibitor 2VIX inhibitor 4ALD inhibitor HN 1ZOY inhibitor OH OH Your enzyme is inhibited by one ofthe compounds depicted above The inhibitor for your specific protein is indicated via the PDB protein code shown: On the basis of the enzyme's structure,its subst...
1 answers
Knowing that $\alpha=40^{\circ},$ determine the resultant of the three forces shown.
Knowing that $\alpha=40^{\circ},$ determine the resultant of the three forces shown....
5 answers
QuestionSketch each graph = using transformations of parent function (without table of values)42 Yi =M-3Question 2For Exercises 41 through 48, determine the following (answer in interval notation as appropriate): (a) domain and range of the function;; (d) interval(s) where the function is incrensing. decreasiug_ 0r' coustant:
Question Sketch each graph = using transformations of parent function (without table of values) 42 Yi =M-3 Question 2 For Exercises 41 through 48, determine the following (answer in interval notation as appropriate): (a) domain and range of the function;; (d) interval(s) where the function is incren...
3 answers
(20 points) Find the Fourier series of f On [~L, L] and determine its Sum for -L < L, where Fn(r) 2 (, COS( "T7) b, sin( ") f() =2 3r2,
(20 points) Find the Fourier series of f On [~L, L] and determine its Sum for -L < L, where Fn(r) 2 (, COS( "T7) b, sin( ") f() =2 3r2,...

-- 0.020717--