solve-the-given-problems-by-finding-the-appropriate-derivatives-in-the-design-of-a-rectangular-con-3

Question

Solve the given problems by finding the appropriate derivatives.
In the design of a rectangular container the area $A$ (in $\mathrm{cm}^{2}$ ) of the base is expressed as $A=6 x^{2}-11 x-10,$ and the height $h$ (in cm) is $h=4 x+3 .$ Use the product rule to find the derivative of the volume $V$ with respect to $x$ for $x=5.00 \mathrm{cm}$.

Gregory Higby · Accepted Answer

And it seems like a very weird way of asking this question because you can do it a lot faster. I think you can do it a lot faster by doing something else minus 11 x minus 10. Um Well I guess I guess what we&#x27;re doing is we&#x27;re finding the volume and the area. Uh Yeah, yeah, I&#x27;m not sure of the problem. And the height is this four x minus three. Four X plus three, sorry. So the volume is multiplying those two pieces together. So yeah, we&#x27;re going to use the product rule because right here is your product to find D. V D X. Which you take the derivative of the left side, which would be 12 x minus 11. Leave the right side alone. And then plus now take the derivative of the right side, which is for leaving the right side alone. And now what we&#x27;re asked to do, so I don&#x27;t know if you want to circle that, but that&#x27;s the correct derivative, is they&#x27;re asking you to figure out the answer when ax equals five. And uh some students might just go to a calculator. Um because I don&#x27;t know how good you&#x27;d be at at knowing 12 times five is 60 um minus 11, so I&#x27;ll be 49 then four times five is 23 plus for Yeah, you might want a calculator to get all these answers, and that&#x27;s what I&#x27;m doing. Uh six times 25 because that&#x27;s what five squared is 11 times five is 55 minus 10, it is 85. So then from here, I definitely want to calculate because I don&#x27;t feel like doing 49 times 23 in my head or uh four times 85. But the correct answer should be 14 67 as far as units go. Um It looks like that since centimetres and I don&#x27;t know, it doesn&#x27;t give us really an X. What does X. Stand for? I don&#x27;t know. It&#x27;s usually a time unit. I don&#x27;t know at the time as though when I&#x27;m rereading the problem. All right, so I&#x27;m just going to have 14 67 and down.

Sherrie Fenner · Answer

I hate We&#x27;re looking at the volume of a creek. So you know that volume ISS blame times. What kinds? Height. And I have the volume h you must by H where a six h. We know the height equals h. The length equals H plus two. We don&#x27;t know the way that question or so I want to get W by itself Submit by l H. Carol eight. So I have double you equals buying over main, divided by high So well, you h you bust five h whatever plus six eight Divide by al Times H h times h plus Yeah, so I h cubed plus five h We&#x27;re plus six h over h squared plus two h seven. Now I am going to do each my hair plus two h The live in two Yeah, plus by inch where but a So I want h year each lines inches each. You&#x27;d h times to h two inch. Where&#x27;d when I subtract those? I get three h Square six h. They have multiplied by the pretty refunds. Each player is three h player attempts late six h major C zero. So my wit equals H plus the reading

Dorcas Attuabea Addo · Answer

we have a keep with side lane are inscribed in a sphere So you realize that you have your sphere here. So this is your fear and you have a key. So this is a key inscribed in mids. So this is the Q which is inscribed in this fear. There&#x27;s a rice oclock boom and it is described words in a Celinda. So this is our selling that and we have seen that the cycling that&#x27;s the slides heights off the Coombe, the slain ties of the cool. Yeah, it&#x27;s equal to it&#x27;s Dyment. Sir, What is the volume off the ceiling? The so for A. Okay, so for a we want to find a volume off the Celinda. Hey, but if you take let&#x27;s look at this figure. Yes, If I take the figure the base off the key selects with babies of the queue The base of the key, which is a c have you A You&#x27;ll be your c a d said as they basically keep baby C K. Lacey, This is babies. I&#x27;m talking our worlds. This is a be see okay for these beings you realized that so they have big You see this is so so we want to look at they reviews, realizes he is going to be over soon. From my dagger, this is was what was too. That is the beast off the key we have. So that&#x27;s going to find with these bees, I can find a finally, really, it&#x27;s a let&#x27;s find a radios off this fear. So I want to find the reviews off this fear in a sense. Of what? What are there&#x27;s off my arm, which is the length of this sites. That is the length periods of this fear is going to be the leg off the sides off towards the queue so that I have from here to day my new see squeak is things to me from these I got me woods are we went to school. Bless soon sleep, which is shoe Have a virtue. Sweet. So that&#x27;s my you see, if I think the Spurs and both sides have skirts off to our work suit just equally. Both are far. If you&#x27;re Asian allies, roots up. What&#x27;s soon? So that is the radius off this fear I&#x27;m looking at. Then let&#x27;s records the triangle. Yes, I think my triangle here would she each wait? See your GP? This is she eight. So with this small triangle, this more triangle we are talking about that is who your G In age today, Michael CDA beds lives because that&#x27;s triangle likes People will see that triangle triangle G h You realized as I have. So that was my who let me do it&#x27;s have the triangle That&#x27;s what&#x27;s night grew they 90 and age You realize that I have words this sake to be what I am which is a reveals then this side these greens in the woods spirits of to, uh, with this, I think then friends I can&#x27;t find the leg off Koji Sone to find the length here these late hours to find I also find this leg okay, which is the radius off days Fear that&#x27;s will. So with these do I have realized that you guys that have Bujji Cooper Gates guruji square is going to be words uh, the readers of this fear which we already so full is my are two of us square itself soon squared less I got sued screen and this is going to give me words ask way too good to bless, uh, full wishes, things that people three. As so if I find who g that&#x27;s is the lane off Koji, which is also the radius of this fear is going to be skirts off three over to, um, safe year. No way. The years is there really use off this fear of this fear. A is equal. So spirits of three blood soon words are Then if we say the figure, so you realize that in. So let&#x27;s look at the figures. We have a key. So with this figure with a triangle I jinky and you, it&#x27;s fear it needs. I would also also find the radius are smoke. So with the radios, like frank words the diameter off the cylinder. So I want to find a diameter off my Celinda here. So let&#x27;s look at its this figure. So it&#x27;s been CDA. Let&#x27;s go sit down and figure they say, have a triangle this next strangled. I que humane TCI. I want to. So for the time insanity the day that I want to Fine. And I have Woods, the Saco he needs. So a A let&#x27;s list tickets taking you feel curious Circle. Okay, Good Oh, So, Lucy, this is a Sekou. If they go described he needs this is saying of the Saco, which is all Let&#x27;s see a is and they Yeah, so that&#x27;s that&#x27;s the angle here, you stated. See? I mean, they have forgets This is cool. The sense of your looking. That&#x27;s so this is going to be this does a screenings off the table. But to our this fear just so full the angle here Eassey is 60 degrees here I said no. In this figure, we can&#x27;t say from here taking the triangle c five c triangle who and she you realize that cunt, etc. So I have that day 82 people. So we&#x27;re L g, which is one over skirts of the me vehicles gay over de over soon. So this implies that security is going to be two spirits of theory A. That we know what a is redeye&#x27;s it&#x27;s a sues for doing is what&#x27;s very rich. The readable birds who was it is equally in court. My be here is going to be the same day. So this Carso&#x27;s that&#x27;s with three sites. We do these graves and give you read. Uh so this B is the diameter off words they selling them did any? Some of this sitting now wants to find a height because we know they die. I can&#x27;t find my heights because it once so full the volume. So that&#x27;s for my height age. So we have finding a hides the cylinder and for the heights off the ceiling There we see the triangle so they seem to think they play on who he i e you realize they have time 60 from here This is a time 60 were looking So I have time 60 then succeed to be equal to the heights of the Selena Each over the onwards shoe, which is Woods Square roots off three to be age you guided by would be one words so so that if I simplify realized that my agents people too Scrivens of doing work. Sue, let&#x27;s do what is Do you know what he is? This was very so health scares off very own soon Biswas Me, uh, with just words. My height. So my heights off the silly, nice three little girls to woods. Um I didn&#x27;t find my vote you so from he since we knew the heights. We could express the volume. So will you. Off the ceiling there green. It&#x27;s the cords I for So first think it&#x27;s a game. So v is guy very awful. Be straight h his bulls. And by full it is D is three r squared and ages was three squares off the Weeble But do, uh so that&#x27;s increased. Simplify. You&#x27;re like they have by over full nice weight are sweet dives mean schools off the that Sioux, Uh, this was physically gets was swing, see? So they square So three, uh, Cade&#x27;s by, uh, key. So this is full the a pads way. We are finding words the volume itself. So this is our volume off the selling then would want so find for the bus. So for B the seas certifying the volume. So for b once and find the volume of the king. So, William Oh, a king If you take the diagram again for volume off the keep let&#x27;s look as the cross section of you along the dye ankle now. So once it&#x27;s a very they think, of course, because section section you I long a long Did I gonna be e if you do died serialize is this is the figure we have. So let&#x27;s look as a key. I have See if this is as saints that who have cheese and this is he. So this is only only people their core section of you, along with our d so business key it is. This far away exists. Lacey, This is was our X words answer So that IAEA realized that the coordinates of in here is going to get over squares off soon, then with my E. But if I think that so off the so off the Q. You realize that it&#x27;s up off the Q. This is our cue. This is a key we have. This is the This is Woods Me If you just think it&#x27;s so you realize that this I good night here. This was scruples off soon he So this is the woods it so dopo for. It&#x27;s the view of the words of the queue. Have you been keen? So now if this figure now, listen, that&#x27;s this figure lazy. This is figure. So this is figure. I they say this is figure to us. Well, so you realize that figure out one represents was they came. How long did I cannot be? So that&#x27;s the length length off the dye. Gonna Dini off the Q is great TV D A Swayed is with plus e screen wishes was to eggs Quaid. So that&#x27;s my name. Me a loon is great to give me square so soon is it wishes squares to a. That is the what you have here. So help square roots Sewell was in. So when this I can find this information, let&#x27;s try to find finally in question on the line. So let&#x27;s find a cuisine increasing off the line of the A B Bay using you know, it&#x27;s aims Way, he says. 16. Why exits testing? If I do so you realize, as always, up X over my eggs. That station black your way over your way in the 16 to be equal towards one. What is this ant eggs in that section? It says one. So how takes plus in our wine cut section is three. So who are we to be put? So one invites for this equation off the line, then I have woods, so this is a pushing off the line, but we come foods spoons Record means that is the over school. So too e in the in the above equation off the line. So about squishing. That&#x27;s the question of the lane. Yeah, sucking about So with, that&#x27;s what do I have? Some weeks have a over square. Which of two class words gay over to me People&#x27;s one. Simplify this in place that have e inside graphics one over spirits off food plus one, which is cool. So the way. So if you simplify legs simply by if you simplify, you know what Happy bracket three Bless Screw itself to like the mean square so soon Waas This is the length so I really see the length length off this side is side of the okay. He is going to be three soon over Leela&#x27;s Samsung Bullets too. So, volume off the Q we know bully bullying off key. Building off the key he was would take you visibility And if I knew what is and find So I know what my eats in a listing volume so moving is going to be in court. So we came the spirits off soon all over the re glad square. So too, Hugh using glass. 54 sames Sue, Who&#x27;s soon keep this is the volume is, therefore gives us the volume off the keep we are trying to So which is 54 would suit over doing plus square root of +20

Robert Daugherty · Answer

section 8.4 Problem number four We have a function f of U and V is you squared plus five u V plus a V squared and were asked to find the partial derivatives. So the derivative with respect to you So this says, treat you as if it were a variable. Everything else is a constant said the derivative of you squared. It&#x27;s going to be to you. And then in the next term, five V is a constant, and that is a derivative to you. Plus five V. Now find the derivative with respect to V and this exercise, your V is the variable. Everything else is a constant, so when you take a driven out of here, you get five you plus two V.

Dorcas Attuabea Addo · Answer

we have a keep with side lane are inscribed in a sphere So you realize that you have your sphere here. So this is your fear and you have a key. So this is a key inscribed in mids. So this is the Q which is inscribed in this fear. There&#x27;s a rice oclock boom and it is described words in a Celinda. So this is our selling that and we have seen that the cycling that&#x27;s the slides heights off the Coombe, the slain ties of the cool. Yeah, it&#x27;s equal to it&#x27;s Dyment. Sir, What is the volume off the ceiling? The so for A. Okay, so for a we want to find a volume off the Celinda. Hey, but if you take let&#x27;s look at this figure. Yes, If I take the figure the base off the key selects with babies of the queue The base of the key, which is a c have you A You&#x27;ll be your c a d said as they basically keep baby C K. Lacey, This is babies. I&#x27;m talking our worlds. This is a be see okay for these beings you realized that so they have big You see this is so so we want to look at they reviews, realizes he is going to be over soon. From my dagger, this is was what was too. That is the beast off the key we have. So that&#x27;s going to find with these bees, I can find a finally, really, it&#x27;s a let&#x27;s find a radios off this fear. So I want to find the reviews off this fear in a sense. Of what? What are there&#x27;s off my arm, which is the length of this sites. That is the length periods of this fear is going to be the leg off the sides off towards the queue so that I have from here to day my new see squeak is things to me from these I got me woods are we went to school. Bless soon sleep, which is shoe Have a virtue. Sweet. So that&#x27;s my you see, if I think the Spurs and both sides have skirts off to our work suit just equally. Both are far. If you&#x27;re Asian allies, roots up. What&#x27;s soon? So that is the radius off this fear I&#x27;m looking at. Then let&#x27;s records the triangle. Yes, I think my triangle here would she each wait? See your GP? This is she eight. So with this small triangle, this more triangle we are talking about that is who your G In age today, Michael CDA beds lives because that&#x27;s triangle likes People will see that triangle triangle G h You realized as I have. So that was my who let me do it&#x27;s have the triangle That&#x27;s what&#x27;s night grew they 90 and age You realize that I have words this sake to be what I am which is a reveals then this side these greens in the woods spirits of to, uh, with this, I think then friends I can&#x27;t find the leg off Koji Sone to find the length here these late hours to find I also find this leg okay, which is the radius off days Fear that&#x27;s will. So with these do I have realized that you guys that have Bujji Cooper Gates guruji square is going to be words uh, the readers of this fear which we already so full is my are two of us square itself soon squared less I got sued screen and this is going to give me words ask way too good to bless, uh, full wishes, things that people three. As so if I find who g that&#x27;s is the lane off Koji, which is also the radius of this fear is going to be skirts off three over to, um, safe year. No way. The years is there really use off this fear of this fear. A is equal. So spirits of three blood soon words are Then if we say the figure, so you realize that in. So let&#x27;s look at the figures. We have a key. So with this figure with a triangle I jinky and you, it&#x27;s fear it needs. I would also also find the radius are smoke. So with the radios, like frank words the diameter off the cylinder. So I want to find a diameter off my Celinda here. So let&#x27;s look at its this figure. So it&#x27;s been CDA. Let&#x27;s go sit down and figure they say, have a triangle this next strangled. I que humane TCI. I want to. So for the time insanity the day that I want to Fine. And I have Woods, the Saco he needs. So a A let&#x27;s list tickets taking you feel curious Circle. Okay, Good Oh, So, Lucy, this is a Sekou. If they go described he needs this is saying of the Saco, which is all Let&#x27;s see a is and they Yeah, so that&#x27;s that&#x27;s the angle here, you stated. See? I mean, they have forgets This is cool. The sense of your looking. That&#x27;s so this is going to be this does a screenings off the table. But to our this fear just so full the angle here Eassey is 60 degrees here I said no. In this figure, we can&#x27;t say from here taking the triangle c five c triangle who and she you realize that cunt, etc. So I have that day 82 people. So we&#x27;re L g, which is one over skirts of the me vehicles gay over de over soon. So this implies that security is going to be two spirits of theory A. That we know what a is redeye&#x27;s it&#x27;s a sues for doing is what&#x27;s very rich. The readable birds who was it is equally in court. My be here is going to be the same day. So this Carso&#x27;s that&#x27;s with three sites. We do these graves and give you read. Uh so this B is the diameter off words they selling them did any? Some of this sitting now wants to find a height because we know they die. I can&#x27;t find my heights because it once so full the volume. So that&#x27;s for my height age. So we have finding a hides the cylinder and for the heights off the ceiling There we see the triangle so they seem to think they play on who he i e you realize they have time 60 from here This is a time 60 were looking So I have time 60 then succeed to be equal to the heights of the Selena Each over the onwards shoe, which is Woods Square roots off three to be age you guided by would be one words so so that if I simplify realized that my agents people too Scrivens of doing work. Sue, let&#x27;s do what is Do you know what he is? This was very so health scares off very own soon Biswas Me, uh, with just words. My height. So my heights off the silly, nice three little girls to woods. Um I didn&#x27;t find my vote you so from he since we knew the heights. We could express the volume. So will you. Off the ceiling there green. It&#x27;s the cords I for So first think it&#x27;s a game. So v is guy very awful. Be straight h his bulls. And by full it is D is three r squared and ages was three squares off the Weeble But do, uh so that&#x27;s increased. Simplify. You&#x27;re like they have by over full nice weight are sweet dives mean schools off the that Sioux, Uh, this was physically gets was swing, see? So they square So three, uh, Cade&#x27;s by, uh, key. So this is full the a pads way. We are finding words the volume itself. So this is our volume off the selling then would want so find for the bus. So for B the seas certifying the volume. So for b once and find the volume of the king. So, William Oh, a king If you take the diagram again for volume off the keep let&#x27;s look as the cross section of you along the dye ankle now. So once it&#x27;s a very they think, of course, because section section you I long a long Did I gonna be e if you do died serialize is this is the figure we have. So let&#x27;s look as a key. I have See if this is as saints that who have cheese and this is he. So this is only only people their core section of you, along with our d so business key it is. This far away exists. Lacey, This is was our X words answer So that IAEA realized that the coordinates of in here is going to get over squares off soon, then with my E. But if I think that so off the so off the Q. You realize that it&#x27;s up off the Q. This is our cue. This is a key we have. This is the This is Woods Me If you just think it&#x27;s so you realize that this I good night here. This was scruples off soon he So this is the woods it so dopo for. It&#x27;s the view of the words of the queue. Have you been keen? So now if this figure now, listen, that&#x27;s this figure lazy. This is figure. So this is figure. I they say this is figure to us. Well, so you realize that figure out one represents was they came. How long did I cannot be? So that&#x27;s the length length off the dye. Gonna Dini off the Q is great TV D A Swayed is with plus e screen wishes was to eggs Quaid. So that&#x27;s my name. Me a loon is great to give me square so soon is it wishes squares to a. That is the what you have here. So help square roots Sewell was in. So when this I can find this information, let&#x27;s try to find finally in question on the line. So let&#x27;s find a cuisine increasing off the line of the A B Bay using you know, it&#x27;s aims Way, he says. 16. Why exits testing? If I do so you realize, as always, up X over my eggs. That station black your way over your way in the 16 to be equal towards one. What is this ant eggs in that section? It says one. So how takes plus in our wine cut section is three. So who are we to be put? So one invites for this equation off the line, then I have woods, so this is a pushing off the line, but we come foods spoons Record means that is the over school. So too e in the in the above equation off the line. So about squishing. That&#x27;s the question of the lane. Yeah, sucking about So with, that&#x27;s what do I have? Some weeks have a over square. Which of two class words gay over to me People&#x27;s one. Simplify this in place that have e inside graphics one over spirits off food plus one, which is cool. So the way. So if you simplify legs simply by if you simplify, you know what Happy bracket three Bless Screw itself to like the mean square so soon Waas This is the length so I really see the length length off this side is side of the okay. He is going to be three soon over Leela&#x27;s Samsung Bullets too. So, volume off the Q we know bully bullying off key. Building off the key he was would take you visibility And if I knew what is and find So I know what my eats in a listing volume so moving is going to be in court. So we came the spirits off soon all over the re glad square. So too, Hugh using glass. 54 sames Sue, Who&#x27;s soon keep this is the volume is, therefore gives us the volume off the keep we are trying to So which is 54 would suit over doing plus square root of +20

Ankit Gupta · Answer

abortion. It is given that V is equal store and time stuff. New Times Edge and we need to solve this for. And so let&#x27;s divide the question by W. H. Then we will get we upon the loop. Edge is equals toe edge upon the edge. This top management we can sell. Then we can ride and is equals to be over that blue edge. That will be the answer.

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Solve the given problems by finding the appropria…

Problem 47 Easy Difficulty

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus