what is the average acceleration of this bottle from 6:00 am to 6:40 am

(print clearty)C A bulletin in a canteen almost this location is released at half-dozen:00 AM: Bold that the bottle travels along with the river'$ current, approximately how far due south will the bottle be at 6.40 AM?What Is the average acceleration of this canteen (rom 6:00 AM to vi.40 AM?

(print clearty) C A message in a bottle near this location is released at 6:00 AM: Assuming that the bottle travels along with the river'$ current, approximately how far due south will the bottle exist at 6.40 AM? What Is the boilerplate acceleration of this bottle (rom 6:00 AM to vi.twoscore AM?

What are (a) the average velocity and (b) the average acceleration of the tip of the 2.4 -cm-long hour hand of a clock in the interval from noon to 6 PM? Use unit vector notation, with the $x$ -axis pointing toward 3 and the $y$ -centrality toward apex.

In the even problem. You're different Velocities. Oh, an airplane are given at 2 different times. So do we present these Ruskies stuff on the drop? The directions in the terms off. No southeast and vest And the direct shoes are sure like this Not and so eased. Invest No, the velocities. The initial velocity is given as 1 92 kilometer. Per Are do y'all non? Yeah, it is like this was this Carol is representing ane ninety No kilometer, just, uh, from Oh, do a no. After three hours, the new velocity is do for particular meter. Per are in Northwest direction Means from n to vest at an angle of 45 degree. Say this. So these are that who velocities Is this from O. B? And it is proof or a kilometer? Well, uh, this is causeless every bit the one and this It says y'all, Toby, they do. This is the starting time part off the question. No. For the second part, we accept to discover the alter in the velocity that the alter in velocity will be given every bit the difference in final velocity. The initial velocity. So to find this change in velocity, we volition consummate a parallelogram with the help off these two vectors taking these two raptors esta and just in size off the battlefield. And so here we complete this paragraph one side, this and an stop of this. This is the pattern camp which nosotros complete it. So the Dagnall off this battle of around starting from the tip off, even the tip off the to we requite united states of america the change in velocity means that difference off 5 two and V even this we give us the value off modify in velocity. So the angle between these reactors is 45 degree. As for due south, the magnitude of this departure is concerned. You merely apply trying the law, the tradition which is equally applicable on subtraction also, And according to it, the folder volition become even elsewhere. Terminal videos where minus movement, even veto costs. Tita, the angle between the vectors and here it is. 1 92 sideslip plus 2 40 Slip minus two into one 92 2 40 into co sign off. 45 degree and so unique square off these vectors. So first of all, the sled off 1 92 gives us her is 6000 864 plus the square off who xl gives us 57,000 600 minus. Now the product off these iv terms most ofall toll xl caste will be one of ane route to it was 45 caste then into 2 40 into one 92 and indeed to it becomes half-dozen. 65,000 one 66 0.96 overall iffy ed and subject the stones 36,000 864 less 57,000 and 600 minus 65,000 166 0.296 We get 29,000 297.30 iv The low meter are finally. If nosotros make the square root this term, we will get the slab Hoot Oh, 29,000 to 97.iv volition requite us 171 wind 16 The long meter for our Which is the Magne dude off changing velocity? No, we demand to find yes and then likewise to suppose yous find it's angle with this line most of all, the draw horizontal baseline on this starting from here this the angle above this line volition exist 45 degree and this portal angle. If you want to find out, let us say it. L far then that value the formula for this Daniel probably go the central we are finding with the vector veto. So the course that will be the one sign Tita on even minus veto This volition exist Nieto minus V one, cause Tina, we apply this formula. And so and then l far is equal to fifty-fifty signed Tita divided by 5 Tu minus We've been Toll Eater Come across U minus fifty-fifty osteo. You know, we've won Waas i 92 into sign 45 degree the 2 to 40 minus i 92 Because 45 degree means in the numerator I will accept signed 45 into 1 92 which becomes 1 35 Boeing 76 in the denominator this is this will be seen a sign 45 cost 45 will be having aforementioned values toe 1 35 point 76 So I actually yet through twoscore minus 1 35 176 We give me 104 going to four. And after solving information technology ane 35 0.76 divided past Ponzi earlier going to four. This is i 35.76 divided by 104 0.24 gives united states of america 1.302 And then l for will go x inward 1.302 which is equal toe 50 do 0.47 caste this complete bending. And then if I want to find out this single only if we knew 45 degree less. So the random Peter, if I see will be l to 14 73 minus 45 caste which comes out of the 7 point for 7 degree from the direction is this is and then all belong So off vest, this is the final loss. This is the change in velocity was marinated You're is 1 71.16 kilometre para and direction ist 7.47 degrees south or west. No, the dispatch. If I want to discover out, it volition become Delta Five by delta T and Delta T is three hours certain become one 71.16 divided by three kilometre for our and are so I get acceleration southward i 71 mind 16 divided by three and it is 57.v kilometer are square and the management with women Aforementioned is vii.47 Devery due south off this.

In the even trouble. You're different Velocities. Oh, an airplane are given at two different times. So practise nosotros present these Ruskies stuff on the drib? The directions in the terms off. No southeast and vest And the direct shoes are sure like this Not then eased. Invest No, the velocities. The initial velocity is given as ane 92 kilometer. Per Are do you not? Yeah, information technology is like this was this Carol is representing i 90 No kilometer, but, uh, from Oh, do a no. Subsequently three hours, the new velocity is do for particular meter. Per are in Northwest direction Means from north to vest at an angle of 45 caste. Say this. And so these are that who velocities Is this from O. B? And it is proof or a kilometer? Well, uh, this is assumed as the one and this It says you, Toby, they do. This is the beginning part off the question. No. For the 2d part, nosotros have to find the change in the velocity that the modify in velocity will exist given as the divergence in final velocity. The initial velocity. So to find this modify in velocity, nosotros will complete a parallelogram with the help off these two vectors taking these two raptors esta and just in size off the battlefield. And then here we complete this paragraph one side, this and an end of this. This is the pattern camp which we complete information technology. And then the Dagnall off this battle of around starting from the tip off, fifty-fifty the tip off the to nosotros requite the states the change in velocity means that difference off V two and V even this we give us the value off alter in velocity. So the angle between these reactors is 45 caste. As for s, the magnitude of this difference is concerned. You simply apply trying the law, the tradition which is equally applicative on subtraction also, And according to it, the folder will become even elsewhere. Concluding videos where minus move, even veto costs. Tita, the angle between the vectors and here it is. 1 92 slip plus two 40 Slip minus two into one 92 2 40 into co sign off. 45 degree so unique square off these vectors. So first of all, the sled off 1 92 gives usa her is 6000 864 plus the square off who 40 gives us 57,000 600 minus. Now the product off these four terms near ofall cost twoscore degree volition be one of one road to it was 45 degree then into ii 40 into one 92 and indeed to information technology becomes six. 65,000 1 66 0.96 overall iffy ed and field of study the stones 36,000 864 less 57,000 and 600 minus 65,000 166 0.296 Nosotros become 29,000 297.30 four The depression meter are finally. If we make the foursquare root this term, nosotros will get the slab Hoot Oh, 29,000 to 97.4 will requite us 171 wind 16 The long meter for our Which is the Magne dude off changing velocity? No, we need to find yes and so also to suppose you discover it'southward angle with this line most of all, the draw horizontal baseline on this starting from here this the angle above this line volition be 45 caste and this portal angle. If yous want to discover out, permit us say it. 50 far then that value the formula for this Daniel probably go the cardinal we are finding with the vector veto. So the form that will be the i sign Tita on even minus veto This will be Nieto minus 5 one, cause Tina, we apply this formula. So then l far is equal to even signed Tita divided by V Tu minus Nosotros've been Cost Eater Meet U minus even osteo. You know, we've won Waas 1 92 into sign 45 caste the 2 to twoscore minus i 92 Considering 45 degree ways in the numerator I will have signed 45 into 1 92 which becomes 1 35 Boeing 76 in the denominator this is this will be seen a sign 45 toll 45 will be having same values toe 1 35 bespeak 76 So I really all the same through 40 minus 1 35 176 We give me 104 going to four. And after solving information technology 1 35 0.76 divided by Ponzi earlier going to four. This is 1 35.76 divided by 104 0.24 gives the states one.302 So 50 for volition become ten inwards i.302 which is equal toe 50 do 0.47 degree this complete angle. And then if I desire to find out this single only if we knew 45 degree less. So the random Peter, if I meet will be l to xiv 73 minus 45 degree which comes out of the seven point for seven degree from the direction is this is and so all vest And so off vest, this is the terminal loss. This is the change in velocity was marinated You're is i 71.sixteen kilometre para and direction ist 7.47 degrees south or west. No, the dispatch. If I want to find out, it volition get Delta V by delta T and Delta T is three hours certain become 1 71.xvi divided by three kilometre for our and are so I get acceleration s ane 71 listen 16 divided by three and it is 57.5 kilometer are square and the direction with women Same is seven.47 Devery south off this.

Here we have some other scenario. A auto travels three quarters of the way around a circle with radius twenty m. As yous can see, I've drawn it over here. It does this in a time delta T of 8.5 seconds at a constant speed. Permit's detect that abiding speed earlier we movement on. Then if information technology traveled 3 quarters of the style around the circle, that's going to be 3 quarters of the circumference 2 pi R. Only we know that radius to be 20 k. So we can detect that total distance past plugging information technology in 0.75 times two loftier times 20 we go that to be 94 0.25 m. And then to find the speed s we're going to divide that altitude 94.25 m past the total time. eight.v seconds to find the speed, we get that to be 11.9 one thousand per second. That constant speed with which the automobile travels around this check. So now we ask yourself what is the boilerplate velocity for this trip and to practise that? We're going to demand the deportation. That'south going to be the distance between the initial in the last. Lucky for the states, we know this distance to exist our 20 1000 in this altitude, There'southward also R. twenty g. The 10 and Y components sort of find the length of this vector, the magnitude of this vector, the magnitude of the displacement. We're going to exercise the square root of 20 squared plus 20 square using the Pythagorean theorem to discover that length, and nosotros notice that length how to exist 28.28 m. For Now to find the boilerplate velocity, nosotros have to split that distance 28.28 thousand by the amount of time 8.5 seconds. And nosotros get that velocity, that boilerplate velocity to be three 0.33 1000 per second. Okay, you know, ask yourself what is the motorcar's average acceleration during this fourth dimension and you might recollect zero because the speed is constant. We accept to recollect that velocity and acceleration are both vector quantities, so we have to take changes in direction into consideration likewise. And so let's break downwards these velocity components that I've fatigued off to the side into their Ten and Y components. Let's beginning with the final, the X component of this one is going to be zero because information technology's directed directly downwards. For that reason, the Y value is going to be negative xi.9 Why did I choose that value? Because that is a constant speed with which the car travels around and that X component zero, let's do the same for the initial. That Ten value is going to be negative 11.9 considering information technology's directed to the left and that Y value is going to be zero. There's no vertical move right there. And so at present let'due south find the change. Let's start by finding the changing Ten. 10 goes from eleven.9 to 0. Terminal nothing minus initial 11.9 gets a positive xi.ix k per second. They increased past that corporeality. At present let'due south find the change and why the modify in Y is going to exist the final negative 11.nine 1000 per second minus the initial, which is zero. So we find that change to be xi 109 meters per second. At present, let's encounter if we tin observe the magnitude of this acceleration. We're going to exercise that in one case again using the pythagorean theorem where we practice the square root of eleven.nine squared that irresolute X plus 11.9 squared the magnitude of the changing why? Because squaring does not care if information technology's positive or negative, plugging information technology in the square root of eleven.nine squared plus xi.9 squared. We find that magnitude to be 15.6 8 1000 per second, keeping our units consistent to finish it off and finding that boilerplate acceleration, all nosotros have to do is split that change in velocity 15.68 k per second by the corporeality of time, which is eight.5 seconds. And we go a value. Uh huh. one.85 meters per 2d squared. Yous might inquire yourself how does a car moving at a abiding speed? Have a non zero average dispatch. And that kind of goes back to what I mentioned before that velocity and acceleration or vector quantities. So if your velocity is changing, there must exist an dispatch. That's the definition of acceleration. But we have to call up that a change in direction is also a modify in velocity. You can imagine this like whenever you're in a auto, if you brand a right turn or left plow, you feel a force that pushes you in this new management, even if y'all become about it in a abiding speed. Then that is how a car moving at this abiding speaking, take a not zero average acceleration because it is changing in direction even if it's not changing in speed. Cheers.

Okay. Our questions says the motorcar is moving with the speed of 18 meters per 2d due southward at one moment and 27.five meters per second due east viii seconds afterward. Over this time interval, determine the magnitude and direction of a information technology's average velocity be its average acceleration and see what is its average speed. Hint. Tin you make up one's mind all of these from the data given? Okay. So, um, I write down here what we were given in the problem, which was that nosotros were given that one of the velocities which I call actually I should switch these around because it tells me that initially information technology's going minus eighteen meters per 2nd south, right, So we'll telephone call that the one. The one is eighteen minus 18 meters per 2nd. Southward south is the minus J lid directions that two minus 18 meters per second. Jay had direction so Five ii velocity. The 2nd velocity is 27.5 meters per 2nd due eastward, which I phone call the positive I have direction And so 27.5 meters per second. The I had direction and and then tea is 8.0 seconds. So maybe I should merely go ahead and depict out here. Sigrid were using. So typically, this would be northeast southwest. Just we're calling this farewell in this, Jay. Good. Now information technology asks us to a outset determine whether or not it's even possible to find the average velocity than be the boilerplate acceleration. So meet, it wants united states of america to find the boilerplate speed. Okay, but and then it says hint, Tin can these be done? Well, eh? The average velocity is deportation, divided by a last elapsed time. And since the displacement is not known, the average velocity cannot be determined, so a cannot exist determined. And then you can get ahead and write that for, eh? This great out whatever faster tin can exist determined. Okay, Now part be going to the average loss average dispatch while nosotros do. I know that this can be determined because the average dispatch would but call this a average hither, eh? A Sunday for average is equal to D change in velocity spectres divided by changing times and delta V Delta t. Okay, well, this is equal to Ah 27.5 minus minus xviii in ah, 0.0. And that's in D J. had direction. This is in the eye. Had management. Okay. And so all of this is divided by 8.0 which is the change in fourth dimension. That was elapsed. Minutes, seconds. Miss his meters per second. Okay, If y'all carry this out, you'll observe that 27.5 divided by eight is 3.44 class 3.four flooring in the eye had direction plus minus minus xviii which is plus eighteen divided by a 2.25 And that isn't the J had direction. The unit's here or meters per second squared since this is acceleration. Okay, that'due south the average. At present information technology also wants us to not just determine the average and wants u.s. to determine the magnitude and direction of this boilerplate value. Well, the magnitude of a boilerplate ace of a country right that says more eligible today is equal to the foursquare root of the square of the values that brand information technology upwardly. And so 3.44 squared plus 2.25 cool squared. Okay, y'all carry this out, you go 4.11 Who 0.11 and that's in meters per second squared since acceleration Okay, There's the magnitude. And now we also want to find the direction. Well, in society to exist able to detect this direction breaking news. Our trig identities for changing data is equal to the opposite over the side by side Don't sell me. Draw out the triangle that I'm talking about here. So this is a right 90. Today we but determine that. And this is Ace. Um, the Simply run across, this would be the J chapeau directions. This is a some J. And this is Thie. My hat direction. So this would be a skilful bye. Okay, And so contrary over side by side for this angle. Here, this is the angle nosotros desire to determine. This is data. Well, that's going to be ii.25 divided by 3.44 All right. And nosotros want to solve for theta. Then we solve. For theta, it is equal to the inverse tangent of 2.25 divided by 3.44 three points. Flooring 23 And if you carry that out, you lot'll find that the inverse tangent of 2.25 divided by iii.3 for iv is 33.ii degrees. Okay, well, and that is two in the jihad direction relative to the I had management. Well, Jay had, if you lot call up, was ah North represents north and south, And so it'southward in the positive J had direction. So information technology'due south in a positive n direction. And that's relative to the I had direction, which is east. So this is north of east. So this right north for in Oran for north and e for east so north of East box set in their direction. Okay. Then the very last thing we were asked to determine was the average speed, right? So C is the average speed. So nosotros will go ahead and, uh, get a new page here just for Parsi since we ran out of room on the other page. But withal, if you think, the hint was can you determine all of these to the first affair we demand to ask ourselves is can't even decide this. And the answer is no. Since the boilerplate speed is altitude travel divided by fourth dimension, the last and the distance traveled is non known. Nosotros unfortunately cannot determine this. Then even though we're not starting a new folio, there'southward null we can do here so we tin can write out. I cannot determined as our solution for Parsi. That's information technology

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four.2.27Determine whether the functions Y1 and Yz are linearly dependent on the interval (0,1)Yh =i-2 sin ?t, Yz 12cos ZtSelect the correct choice below and, ifnecessary; fill in the answer box within your choice_Since Y1 Dyz on (0,1), the functions are linearly dependent on (0,1) (Simplify your respond) Since Y1 Jyz on (0,1), the functions are linearly independent on (0,1) (Simplify your answer) Since Y1 not abiding multiple of Yz on (0,i), the functions are linearly independent on (0,1).Since Y1

4.two.27 Determine whether the functions Y1 and Yz are linearly dependent on the interval (0,1) Yh =1-two sin ?t, Yz 12cos Zt Select the correct choice beneath and, ifnecessary; make full in the answer box within your choice_ Since Y1 Dyz on (0,one), the functions are linearly dependent on (0,1) (Simplify your a...

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5 linear relationships for 5 businesses are described here in words, equations, tables, and graphs. Determine which equation, table, and graph lucifer each clarification, and so tell whether or not the human relationship is a direct variation. Record your answers in a tabular array similar this i.

Five linear relationships for five businesses are described here in words, equations, tables, and graphs. Determine which equation, table, and graph friction match each description, and then tell whether or not the human relationship is a directly variation. Record your answers in a table like this one....

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