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613; = 0 - 0/v 008 Y 000/ adyoJ u ( V (x/r sayjeaj wa1sks a41 Jayye Adojjua Ul a8uey? [eJ01 a41 S! Jeym cwnuqilinba [ Ieujay} Ts8 :sue) 0} Wasks aOYM 341 Buuq 01 pa...

Question

613; = 0 - 0/v 008 Y 000/ adyoJ u ( V (x/r sayjeaj wa1sks a41 Jayye Adojjua Ul a8uey? [eJ01 a41 S! Jeym cwnuqilinba [ Ieujay} Ts8 :sue) 0} Wasks aOYM 341 Buuq 01 papaau 33!J0 ssew ay} JO} anos (8 9E7 :sue) "J.oos 264 991) 2 67-981* orH) 26x +02 = 7x OSt0 = 13315)) EeE = J1 Jo Jeay- pyppads 34} Sey aajo) aunssv "aunjejadua} Jwes a41 01 Juo? 'JaieM aj1 a41 JpS a41 0} pasn S! BYOOT 0 J0 ssew YHM J.OZZ J0 auniejadua} swax! 93J4} Ie Iqun uoods [aals V Aaxaiduo) Iaw 01 pamolle pue dn) a

613; = 0 - 0/v 008 Y 000/ adyoJ u ( V (x/r sayjeaj wa1sks a41 Jayye Adojjua Ul a8uey? [eJ01 a41 S! Jeym cwnuqilinba [ Ieujay} Ts8 :sue) 0} Wasks aOYM 341 Buuq 01 papaau 33!J0 ssew ay} JO} anos (8 9E7 :sue) "J.oos 264 991) 2 67-981* orH) 26x +02 = 7x OSt0 = 13315)) EeE = J1 Jo Jeay- pyppads 34} Sey aajo) aunssv "aunjejadua} Jwes a41 01 Juo? 'JaieM aj1 a41 JpS a41 0} pasn S! BYOOT 0 J0 ssew YHM J.OZZ J0 auniejadua} swax! 93J4} Ie Iqun uoods [aals V Aaxaiduo) Iaw 01 pamolle pue dn) a41 0} pappe S! JoO 0T_ Iepiul ue 41M aunjeuadua} Je 334403104J0 7u 008 4HIM pally S! Jaujenuox weoyojnis zoze V Je 31 "3.06 = aaubeq ILIO @DO



Answers

7x2 + 15x + 03 = 0

In this problem to victor's are given you victories minus three icap plus five Jacob. And we victories. I kept minus two shaka. We have to find magnitude of various combinations of these vectors. So before starting to solve the models values. First of all we should recall that if we know any vector let us say A I cap bless plus me, Jessica. This is any vector are better. All right. So how do we find models of our victor? So we simply put a square root and we inquire the coefficient of Icap and Jacob. So this will be a squared plus B squared. So this will be very useful formula for this entire problem. Just remember this formula how we are going to deal with the models of any victor. So coming back to the problem in first part we have to find models of Ivan models of you victor. So what is the eu victor? You victories minus three Icap plus five Jacob. So here what is the value of A. As we can see that? This will be A and this is B. So we can solve this marvelous as esquire wrote off a square that is minus three square plus five square. So this will be square root of nine plus five squared is 25. So this will be a square root of 34. In decimal it will be 5.83 Therefore models of you is equals to 5.83 So this is the answer for first part. All right now moving to the second part and second problem we have to find models of we victor. So what was the v victor victor was I kept minus two Jacob so I kept minus two Jacob. So how do we show this? This will be square root of coefficient of icap is one here so this will be one square plus minus two. Holy square So this will be square root of one plus pool. That is square root up five. So in decimal format this will be 2.236 Therefore models of v victor is two point 236 So this is the answer for second. Now going to the third part we have to find the value of models of do you? So how do we find the value of to you? So we can do two things. Either we can keep this, we can we can take this term tooth or the constant term outside of these models because whenever a vector is multiplied by a constant any vector let us say our victor is multiplied by a constant, then this will be equal to we can take the constant term outside the modelers. So C times are victor models of our victim so we can use this property of victor to solve this problem. Or the What could be the second method? Second method could be either we will multiply the victors or you vector by two. Each term of you vector that is Icap coefficient will multiplied by two and Jacob coefficient will be multiplied by two. And then we will proceed with the similar in a similar fashion that we have building first or second part. So better to do in a new fashion so we can keep to outside the model is so this will be two times more of you victor and more of you vector. We have already calculated in first part it was 5.83 Therefore its value will be two and two. Five point 83 So this comes out to be six 11.16 Therefore more of to you. It's equals to 11.66 So this is the answer for third party. No moving to the fourth part, we have to find models of half of the victor, so again half is a constant, so we can keep it outside. The model is bracket, so it will be half of models of v victor. So models of the victor, we have calculated in second part, this was 2.236 So this will be half in two, two point 236 So it comes out to be 1.118 Therefore, models of half of the victor is equals to 1.118 So this is the answer for fourth part No and fifth part, we have to calculate models of U plus v better. So here we cannot directly add the models of You better. Plus models of the victor because that is a different thing. So first we will solve these vectors. So what was the you victor? You vector was minus three. Icap plus five Jacob. What is the vector vector was my cab minus two Jacob. So if you saw this it will be so we can collect the coefficient of icap. Here, the coefficient is minus three. Here is one, so minus three plus one will be minus two. So this is minus two I cab and Jacob coefficient here it is plus five. Here it is minus two. Therefore it will be plus three Jacob. No we have. Now we can proceed with as we have done in previous parts. So what will be the battle you of this model is the square root of minus two. Holy square bless five square that is square root of four plus four plus 20. Alright, so here it is not five. Just three actually plus three squared. So this is nine, that is square root of 13. The square root of 13 has the value 3.605 Therefore models of you pless p victor is equals to 3.605 As you can see here one thing that you can observe from this result that what was the models of you vector models of you? Hector was 5.83 And what was the models of director? 2.236 So if we add these to five, if we in fact if we remove the decimal part, the value of U plus V is going to be more than five plus +27 More than seven. But here the value of U plus V is three point something. So we cannot solve. So we cannot directly add the magnitude of vector and we vector to solve more of you. Plus B. So more of you. Plus V is different from most of you. Plus modern, be more of you. Plus B is not equals two more of you. Plus more to be both of these are different things. All right, so let us move to the next problem in which we have to calculate more of u minus v. So we can put the value of your vector again. Just we have done in previous part minus three. Icap plus five Jacob minus what is Director Ica minus two Jacob. So if you put these values it will be minus three icap plus five Jacob. And we have to multiply negative sign with all these drums inside the bracket so it will be minus icap plus to Jacob. Now we can collect the coefficients of Icap and Jacob. So I kept coefficient will be minus three icap minus icon that will be minus four I kept and five Jacob plus to Jacob that is seven Jacob. So how do we solve this? This will be square root of minus four. Holy square plus seven. Holy square so this will be a square root of 16 plus 49. So this will be square root off 65. So the square root of 65 has the value 8.62 Therefore more of U minus V is equals to eight point G 262 So this will be the answer for sixth part. No let us move to the last part. I did seventh part in which we have to find the value of more of U minus Mahdavi. As we can see here that instead of more of U minus we we have to calculate more of separate directors so we can directly put the values of more of you and model we hear more of you, We have calculated in first part it was 5.83 and Model Vivas 2.236 Therefore its value is going to be 3.594 Therefore more of u minus motor V as equals to 3.594 So this will be the answer for the last part of the problem. Are they are done with the all the parts of this problem?

So we're giving information for two different sets of data. And so let's call one set of data set one and information for the other set of data will be called set to. So range is defined as the maximum value in the data set of mine is the minimum value in the data set for So for the first day to set the maximum value Is 6.10 minutes. And for the other data for this dataset. Also The minimum time is 0.38 minutes for the other day to set the maximum value Is equivalent to 10.49 minutes. We'll have a minimum value Is given by 3.82 minutes. So you can find that the range first at one is Is equivalent to 5.72 minutes while the range were sent to is equivalent to 6.67 minutes. And really the only conclusion you can really draw from the range of the data is that there's really a greater for the second set of data there is essentially a greater difference between the maximum and minimum values. Branch isn't often the most particularly useful set of data since basically it's only also it's if you're only given the range and you're not given the maximum and minimum values range isn't particularly useful. Us US parameter basically to interpret. So mean is defined as the sum of everything in the data set divided by the number of elements in the data set. So for set one, if you plug everything into the one very little stats function, you can find that the mean is approximately, so you find that the mean for set one is equivalent to 3.88 minutes. While the mean first step to similarly using one variable Stassi in or plugging in Basically directly into the formula is equivalent to 7.02 minutes. So you can see here that there is essentially a significant difference, significant difference between the waiting times of basically these two sets of data, to be conclusively sure though that there is a significant difference between the two sets of data. Technically you would have to run a two sample T test, but just by eyeballing it, there seems to be a significant difference in the waiting time based on the mean of the of the two different sets of data. However, it's also important to remember that essentially mean can be easily skewed to the right or skewed to the left by different sets of outliers. So we have to be careful, especially with mean and often the median is a better way of approximating. So in this case were also asked for the sample standard deviation and in this case we're using specifically the sample standard deviation rather than the population standard deviation, Since we're only given basically a subset of the basically the total number of customers that enter basically this location. So the sample standard deviation for the first set of data is equivalent to Equals 1.55 minutes. While the sample standard deviation for the second step of data is equivalent to 2.24 minutes. So the sample standard deviation gives us a very good idea of basically the variability of data and since basically set to has a larger sample standard deviation, essentially this implies that there's typically greater variation in data for basically the second step second, basically the second set of data. And we're also asked to find the coefficient of basically the coefficient of variability mhm which is typically defined as this population standard deviation over the population means. But in this case, since we're treating a sample, we have the sample values. So the coefficient will just call in this case we can call it new or something like that is equivalent to the sample standard deviation divided by the mean of the sample. Okay, so for the first step of data were given that essentially The sample standard deviation is 1.55 minutes Divided by the mean, which is three eight minutes. So that gives us a final value for the coefficient of variation Of about 0.4. Well, for the other South data are mean is given us seven points 02 Minutes. While our sample standard deviation is 2.24 minutes. So this is basically has um you of about 2.24 by the seven point there are two, about 0.32. So the importance of essentially the coefficient of variation is basically adjusts the mean, basically the sample standard deviations for the different means. So although it appeared initially that essentially we had greater greater variation and sent to based on just eyeballing the sample standard deviation in actuality, we have a lower coefficient of variation for sent to. So the lower coefficient of variation means for that specific mean, for set two, basically you have lesser variation around the mean, while for basically it's actually greater for someone. So also it's important to be careful not to be misled by essentially the sample standard deviation, basically just by the value of the standard deviation itself unless basically the only case where basically you can directly interpret the sample standard deviation is if you have two different samples with the same mean. So in that case, basically the coefficient forum that isn't really, you don't have to use the coefficient formula since you can directly interpret it from the sample standard deviation right? And the last piece of information were being asked is basically the scariness of the two different sets of data. So for these sets types of data, probably the best way the best way to check for squareness is to use basically dot plots since basically Top Plus can give a good indication, like you have a good indication of the shape of the data. So essentially we can draw dot plots for a set one and set to So the dot plot for set one, the range of values is typically from From the lowest is about zero to the highest, which is about six. So so 123, four and 5. And we're just going to approximate. So 4.21 5.55, 5.13 4.77, 2.34, 3.54, 3.20 4.5 6.1, And 3.79. So, you remember in this case that the average is essentially about 3.88. Yeah, So we can just nearly draw a line here for 3.8. So we can see that approximately the number of values on both sides is relatively equal. So basically this shape of the distribution is nearly symmetric in this case. So there's not really a significance here, nous. And so we're going to do the exact same process for the other set of data in this case for the other set of data being everywhere ranging from Essentially 3.82 To about 11. Maximum of 10.5 or 11. So we can still label or box plot dot plot here. Yeah, Just approximation will be fine in this case. So we have 10.5. About 6.68 5.64 4.08, 6.17 9.91 5.47 9.66 5.90 8.02, 3.82 And 8.35. So we're essentially given that the average in this case is about 7.02. So once again, we can draw a line for 7.02 here approx. So we're we can see that this basically is left. Uh This is less symmetrically distributed, it seems since, but it's still pretty close to the metric, although this has more of a skewed to the right distribution. But it's basically cement it's nearly symmetric basically to about skewed to the right, since the mean seems a little bit higher than it should be compared to the other values. It seems like the mean is being pulled towards a higher value by basically the higher values of the 8910 11 Region.

And there is some problem with their statement. Yesterday I did a motion same as this. This is a differential equation. So first I'm very big extort Plus and second told Me six extort Plus 34 eggs Is equal to 68. and the initial conditions are at zero is equal to five X. Door ZO. Is equal to seven. So we need to solve this differential equation. So this differential equation is like do you two over D. D. Two X plus six. Dx over D. T. Plus 34 X is equal to 68. Let us take the over dp. We can solve the situation in a way such that we break the first part into uh first initially shoulder part left hand side of the equation. And their solution gives us the complementary function and the second part gives us a particular integral. So let us take the over the T. Is equal to date. So when we substitute this value we get the square plus 60 Plus 34 is equal to zero. This is a kind of differential equation. This will gives us the complementary function. Okay, so when we saw what we get D simple quadratic equation minus six plus minus square six square minus four into a C. One and C is 34 divided by the way which gives us too. So they will be equal to minus C plus minus this. This very uh that discriminate basically equal to negative negative gives us the negative values. So which will be 10. Can I use the imaginary nobody. I live by two. So from here they will be equal to -3-plus -5 items. So this gives us the complementary function and complementary function is equal to. And we get the two solution. Since since it is a quadratic equation so -3 is common to both of this. The way of fighting the solution is into -30 is common to both of the system. So I'm taking it to the -30. Common and inside A course five basically the solutions are military in nature plus B. Sign five. Okay so one it is time to evaluate the particular integral particular integral is evaluated by using the items item. So there will be 68 divided by that day. Square down day square plus 60. I think that is 60 plus 34. We can write it in the home 60 82. The power zero t Divided by the square plus 60 plus 34. This home of solution in the form of solution. This zero of that exponential power will be substituted in the denominator. So we get particular into equal is equal to 68 divided by zero plus zero square 06 in 200 plus plus 34. So that will be equal to. So the solution will be equal to complete solution will be equal to complementary function plus particular in google. So why will be equal to eat the power minus treaty. E. Cause five D. Close B. Sign five deep plus. Okay so this is the value of Y. Given that. So. No this is not why but X. So so why not? Why? But X. Thanks. Okay so they We know that initial conditions are like zero is equal to five and extolled zero is 7th 19. Yes so exactly is five and X. Door geo is equal to seven. So let us substitute the value of zero. And uh we come to say that what we will get. So at X. Zero is at T. Is equal to zero Xs five. So that is equal to it. To the power zero is one Cozy always one sign 00 Plus two. So from here it will be equal to the second. We need to evaluate that DX over duty. Extort is equal to the eggs of a deity which is the by deity of that X. X. Is equal to into the power. Let us to the first differentiation of to the power. That's right. It Shelly A Coast five D. Let's be signed five D. Plus two. Okay. Oh it is a time to differentiate it So that will be -3 to the Power- Treaty. Into a Coast five T plus B signs five G. Now differentiate the second um post um as it is plus E. To the power minus treaty. Cause five days -5 A. sign five d. Plus five. The cause five T. And the differentiation of bones can come to is equal to zero. Now substitute the value of T. Is equal to zero extra 07. That is equal to That is -3 A. And B is equal to zero proficient or B zero. Then geo is signed to museo coast thomas plus five weeks. We know that is equal to three so five B. Is equal to seven Plus three and 2. So be will be 165. Hi now the complete solution becomes X. Is equal to the to the power minus treaty. E. three course 5 d Plus 1655. Sign five D plus just a required solution of this differential equation. All the squares you're doubting. Thank you.

The question that is given to us is a quadratic equation. That is seven x square was 15 X. Last three equals zero. What do you need to do? We need to find the value of X. So we'll use the quadratic equation. That is minus B plus minus Root to a B sq -4 AC. Do you hear me do it? This will be equal to minus B minus 15 plus minus rude to her. 15 squared -4-7 in 23. This is required to do this really well. Right two and 2 seven. So we get the value minus 15 plus minus room door 2 25 minus 7- three. There it is 21 and 24. That is four into 21 is 84 divided by 14. Now the value that comes out is -15 plus minus root over 1 41. That is to 25 minutes, 84 gives 1 41 and route over 1 41 equals 11 point 87 the world by 14. So we'll get to values since it is a courtyard in question 15 plus 11.87 12 by 14 and -15 -11.87. They were by 14. Upon calculating this value figured the final values as -0.22 And -1.92. These are all these are our final values


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