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KJidLuula67%DtAD9 IQuestion (1point) Porablr Lantrt cmoina Awlloanadincect mourcCiuCindioca bordkroana PaaleEal mlsEnt eusytotrara Dont bu {o tithn uenaider [0 Tent Inthcccd Th "here Haueu pentne Jnoeaceame nabalru Dalntn Jc0 Tncaal 704049 ZAlurodtIst attemptPcriodic TableSte HintDeterminathevan ote7420 CIa)

KJid Luula 67% DtAD9 I Question (1point) Porablr Lantrt cmoina Awlloanadincect mourcCiuCindioca bordkroana PaaleEal mlsEnt eusytotrara Dont bu {o tithn uenaider [0 Tent Inthcccd Th "here Haueu pentne Jnoeaceame nabalru Dalntn Jc0 Tncaal 704049 ZAlurodt Ist attempt Pcriodic Table Ste Hint Determinathevan ote 7420 C Ia)



Answers

Divide. Then check by multiplying.
$$56,883 \div 67$$

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.

Hello. So the question is uh I think that will be X double dough plus six X. Store plus 34 X. Is equal to 68 which is a differential equation. And the initial conditions are given we need to solve this differential equation. Okay so let us right disease this second order differential equation. First. So that would be X double dot plus six extra plus 34 is equal to 68. And the initial condition that are given to us X zero is equal to five X. 50.0 is equal to seven Doors. zero is equal to seven. So let us solve this part. This is a simple way to solve the differential equation. So initially we will evaluate the complementary function. So that complementary function can be easily evaluated by this taking the only this part. Okay plus six X dot plus 30 for taking this equal to zero. I'm just initially evaluating the first part of the ocean. That is the complementary function. Okay, we know that. We can write it S. T. Two eggs over the T square plus six day over day T. In two x plus 34 is equal to zero. Let D. Is equal to day over day T. So the square over DT square will be the square. So that will be the square X Plus six b. x Plus 34. So this will be x. X. So let me correct it. So this will be X. So 34 X. Is equal to zero. So equation will be the square plus 60 plus 34. This is a kind of a quadratic equation. We can easily solve the quadratic equation. So the solution will be these equal to minus six plus minus square would six square -4 a. c. where a is one And she is 34 divided by oh to a two into one. So they will be equal to minus six plus minus like me. So all these calculate, let me solve this part using the calculator. So if we solve it we get value Statistics -4 in 234 squared. So that will be minus. So that will be 10. That will be missionary number because four into 34 is greater than the six square. So that will be plus minus 10 off ι divided by two. So from here the value of the will be equal to -3-plus -5. So that's a complimentary function. Only the complementary function of the equation is E. Is just a grandstand. E. to the power -3 D. And of course five of D Plus B. It would take that -3. So we can easily write this function sign of five of the just remember how we can write this function. So this is a complementary function. Now it is Time to evaluate the particular integral. So particular integral will be equal to but it's on the right hand side. So that will be 68, divide this by the square plus 60 plus 34. Okay so now it is a time to solve this. So we can write it as 68 into it. To the power of zero T. There is a formula if that zero into T. If the power of that exponentially zero. We substitute that zero into the denominator and check what we will get. So that particular integral will be 68. Substitute that value of zero and the denominator devalues. So that will be zero plus zero. This is this is a normal way to solve this differential equation particularly in developed this differential equation. So that will be 68/34. So particular integral will be equal to do so our total solution or we can say x will be equal to let us right initially the complementary function A. We can take a course. It would be five G. It was five D. Nice be signed five D. Exponential minus treaty plus two. And uh the initial conditions have already given to us X zero is five extra zero is seven. So X. At at T is equal to zero is five. Extort at the is equal to seven is equal to zero is equal to sin. So initially substitute taxes equal to zero what we will get. We basically want to evaluate the value of A. And B. So when we take at T. Is equal to you so that will be five. He is equal to zero. Co zero is one exponential minus zero exponential to the power zero is one. Sign 00. And so we will get A plus two. So from here the value of A will be equal to five minus two which is equal to three. and 2nd point is the differentiation of acts with respect to time and after that substitute the value of it is equal to zero. We get it's value is equal to seven. Okay so let us differentiated ones. So we get ex dot is equal to using the product too. So that will be -A. into five signs five D plus five B. Course five P exponential minus treaty as it is. And then differentiate exponential minus treaty keeping the for strong constant. So that will be plus A. goes five d plus B. Sign five D. And the differentiation of this exponential thomas minus three exponential minus treaty. And the differentiation of this too is equal to zero because it is just a constraint. Now substitute the value of T. Is equal to zero and extruded, T is equal to zero is equal to seven. So seven is equal to Sign 000 plus five. Be exponential to the double zero is one And second time we get -3 b. Tom is inconclusive. So And the value of a. We know that three so five B minus three in 23 is equal to seven. So five B is equal to seven plus 9 30 16. So from here the value of B will be equal to 16 over what? So let us substitute the value of constant in order to hide the complaint solution. So X. Will be equal to A what is a three Exponential -3 T. And uh course three T. I think that he contained tom co sign So it was five D. I think I did something wrong. No they described so that will because five in place of three so cause five T plus 16 Over five exponential- Treaty sign 5 50 plus two which is the required solution of the situation. Hope this clears your doubt and thank you.

So here we are given this expression and we need to solve this. So first we take the 60 ft to the right and that will give us a question. 7 -5 x rays to -5 x three is equal to -2 x 64, That will be -1 x 32. And we can express the study to ask two ways to fight. So this will give us seven minus five x rays to minus five by three as minus tourists to minus five because one by tourists to fight, we can write it as tourists to minus five And we can just cube both the sites and we get 7 -5 bucks raised to minus fight is equal to -2° to -5 whole cube. So this will give us 7 -5 x rays too, -5 is equal to- tourists to -15. So from here we can take the negative sign off here because when we reciprocate we can write seven minus five x rays to minus five as one by seven minus five x rays to fight And that will be equal to -1 by tourists to 15. So from here We can definitely equate 7 -5 x rays to fight with tourists too, -2 is 2 15. We can take the 5th root on both the side. So Taking the 5th root here and the 5th root on the right hand side, We get 7 -5 x. Because we know x rays to em whole race to end as x rays to obtain them. So five and 1 x five that will cut and will get 7 -5 x As -2 is 2, 3. So this will give us 7 -5 x as -8. And we can just take minus it to the left side and minus five X to the right. We'll get 15 as five X. And solving this gives us the value effects as through.

All right, so we're tryingto divide 56,883 by 67. So let's set it up so that we can do our long division. All right, So 67 cannot go into five. It cannot go into 56. However, it can go into 568. We just have to figure out how many times. So I'm gonna use the 1st 2 digits. Um, this number right here to train guests. How many times can six go into 56? Well, six terms. Seven. I would give me 42 six times a would give me 48. Six times nine would give me 54. So I'm thinking that maybe it can go in nine times, so I'm gonna check so 67 times nine. 63. And that would be 60. So this is not gonna work. It's just a little bit too big. So I'm gonna try 67 times eight and see if that would work out a little bit better. This would be 56. Carry the 5 48 49 50 51 52 23. All right, so this looks like a good one. We don't want to go over. Um, we want to be just as close as we can get, but below. So it's gonna go in eight times and that's going to give me 536 And now we subtract so to and three So 32. Then I moved on. I bring down my eight, and I'm going to see how many times 67 can go into 328. So I'm going to use this same method of looking at those 1st 2 digits and seeing how many times six can go into those first huge is it? So, um, let's try six times four, which is 24 six times five, which is 30. So this one's pretty close. However, I know it's gonna go over because that's seven. So if I did 67 times five, I'd get 35 then I'd have 3 35 So because I know that five times seven is 35 I'm gonna carry over a little too much so I can do 67 times four. So four times seven that's 28. That's 24 plus two is 26 so 67 times, for it can go in four times. I am subtracting again, right? And getting 60 and then I bring my three down. So I have 603 Well, I already did this math ones, even though the first time I did it was wrong. I do need it now because 67 times nine is gonna be 603 which is the exact number that I need to make it. So I do not have anything remaining. So your answer should be 8 49 and it wants you to go back and check just to make sure that you are correct. So I'm gonna go 8 49 times 67. So seven times 9 63 seven times 4 28 30 Oh, are 56 59 six tons. Nine is 54. That's 24 29 6 times eight is 48 plus two is 50 at these altogether. And I get 5683 which iss this number right here. So that I know that I am correct.


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