course Mth 174 ²„}Ýë™Û×ç¹ÈöKý~¡È؇¢RŽ¥}½¯éa›Ìassignment #019 019. `query 19 Cal 2 08-05-2008
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09:32:47 Query problem 11.5.8 (3d edition 11.5.12) $1000 at rate r
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09:32:49 what differential equation is satisfied by the amount of money in the account at time t since the original investment?
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09:32:51 What is the solution to the equation?
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09:33:06 Describe your sketches of the solution for interest rates of 5% and 10%.
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09:33:10 Does the doubled interest rate imply twice the increase in principle?
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09:33:32 Query problem 11.5.22 (3d edition 11.5.20) At 1 pm power goes out with house at 68 F. At 10 pm outside temperature is 10 F and inside it's 57 F. {}{}Give the differential equation you would solve to obtain temperature as a function of time.{}{}Solve the equation to find the temperature at 7 am.
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09:33:34 What assumption did you make about outside temperature, and how would your prediction of the 7 am temperature change if you refined your assumption?
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09:33:55 Query problem NOT IN 4th EDITION???!!! 11.6.16 (was 10.6.10) C formed at a rate proportional to presence of A and of B, init quantities a, b the same
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09:33:58 what is your differential equation for x = quantity of C at time t, and what is its solution for x(0) = 0?
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09:34:00 If your previous answer didn't include it, what is the solution in terms of a proportionality constant k?
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09:34:09 Query problem 11.6.25 (3d edition 11.6.20) F = m g R^2 / (R + h)^2.{}{}Find the differential equation for dv/dt and show that the Chain Rule dv/dt = dv/dh * dh/dt gives you v dv/dh = -gR^2/(R+h)^2.{}{}Solve the differential equation, and use your solution to find escape velocity.{}{}Give your solution.
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09:34:21 Query problem 11.6.20 THIS IS THE FORMER PROBLEM, VERY UNFORTUNATELY OMITTED IN THE NEW EDITION. rate of expansion of universe: (R')^2 = 2 G M0 / R + C; case C = 0
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09:34:23 what is your solution to the differential equation R' = `sqrt( 2 G M0 / R ), R(0) = 0?
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09:34:25 How the you determine the nature of the resulting long-term expansion of the universe, and what is your conclusion?
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09:34:40 Query problem 11.5.18 NOTE: THIS PROBLEM HAS BEEN OMITTED FROM THE NEW EDITION OF THE TEXT. VERY UNFORTUNATE. absorption of light in water
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09:34:42 what is your intensity function?
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09:34:44 If your previous answer didn't include it, what is the intensity function in terms of a proportionality constant k?
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09:34:48 if 50% is absorbed in 10 ft, how much is absorbed in 20 ft, and how much in 25 feet?
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09:34:49 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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Dԕˆx»€§“ñÂR‡Ýœ¼¹…»µ¼£Å±Sø assignment #019 019. `query 19 Cal 2 08-05-2008
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12:02:51 Query problem 11.5.8 (3d edition 11.5.12) $1000 at rate r
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12:36:15 what differential equation is satisfied by the amount of money in the account at time t since the original investment?
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RESPONSE --> I first tried to use the P(0) * e^-kt, but I ended up getting a bad answer and it seemed wrong. So my equation was M = P(0) * (1 + r)^t. dP/dt = P(1 + r)^t. (1/p) dP = (1 + r)^t dt. (My first attempt went bad because I took the integrals and on the right side I had (1 / t+1) * (1 + r) ^ (t+1), and this caused problems, but I will show my attempt.) ln[abs(1/P)] = (1 / t+1) * (1 + r) ^ (t+1) + C -> abs(1/P) = e ^ [(1 / t+1) * (1 + r) ^ (t+1)] * e^C -> 1/P = B * e^[(1 / t+1) * (1 + r) ^ (t+1)] where A = e^C and B = +-A. After multiplying then dividing by P I have P = 1 / [B * e^[(1 / t+1) * (1 + r) ^ (t+1)]]
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12:40:55 What is the solution to the equation?
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12:57:30 Describe your sketches of the solution for interest rates of 5% and 10%.
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RESPONSE --> I didn't answer the last question. So i will answer it now. I solved for be to a decimal answer which I do not like, so I just used this B = 1 / (P * e^[(1 / t+1) * (1 + r)^(t + 1)]) When t = 0 and r = .05 and P = 1000, B = 1 / (e^(1.05)(1000)). After thrity years I found the value of the money to be $12968.13.
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13:00:45 Does the doubled interest rate imply twice the increase in principle?
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RESPONSE --> I think it implies it, but I do not agree with it. I also do not know how to refute it though.
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13:17:37 Query problem 11.5.22 (3d edition 11.5.20) At 1 pm power goes out with house at 68 F. At 10 pm outside temperature is 10 F and inside it's 57 F. {}{}Give the differential equation you would solve to obtain temperature as a function of time.{}{}Solve the equation to find the temperature at 7 am.
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RESPONSE --> My equation was dH/dt = -k(H - 10). dH / H - 10 = -k dt -> ln[abs(H - 10)] = -kt + C -> abs(H - 10) = e^-kt * e^C -> H - 10 = Be^-kt where B = +-A and A = e^C -> To solve for B: 68 - 10 = B * e^-k(0) = 58 = B -> To solve for k, plug in B, 57 for H, and 9 for t: 57 - 10 = 58 * e^-9k -> 47/58 = e^-9k -> ln(47 / 58) = -9k -> ln(47 / 58) / -9 = k is approx. .023366 At seven a.m., which is 18 hours later: H - 10 = 58 * e^-k(18) -> H - 10 = 58 * e^[-(ln(47 / 58) / -9) * 18] -> H = 58 * e^[-.023366 * 18] - 10 = 28.08631421
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13:18:16 What assumption did you make about outside temperature, and how would your prediction of the 7 am temperature change if you refined your assumption?
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RESPONSE --> I made the assumption that it did not get colder outside. I think that as the night moved, say towards1 am, it became colder than 10 degrees.
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13:18:22 Query problem NOT IN 4th EDITION???!!! 11.6.16 (was 10.6.10) C formed at a rate proportional to presence of A and of B, init quantities a, b the same
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13:18:25 what is your differential equation for x = quantity of C at time t, and what is its solution for x(0) = 0?
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13:18:27 If your previous answer didn't include it, what is the solution in terms of a proportionality constant k?
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13:19:25 Query problem 11.6.25 (3d edition 11.6.20) F = m g R^2 / (R + h)^2.{}{}Find the differential equation for dv/dt and show that the Chain Rule dv/dt = dv/dh * dh/dt gives you v dv/dh = -gR^2/(R+h)^2.{}{}Solve the differential equation, and use your solution to find escape velocity.{}{}Give your solution.
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RESPONSE --> I couldn't figure this out because I couldn't find how to translate mgR^2 / (R + h)^2 into velocity and time.
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13:19:39 Query problem 11.6.20 THIS IS THE FORMER PROBLEM, VERY UNFORTUNATELY OMITTED IN THE NEW EDITION. rate of expansion of universe: (R')^2 = 2 G M0 / R + C; case C = 0
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13:19:41 what is your solution to the differential equation R' = `sqrt( 2 G M0 / R ), R(0) = 0?
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13:19:43 How the you determine the nature of the resulting long-term expansion of the universe, and what is your conclusion?
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13:19:48 Query problem 11.5.18 NOTE: THIS PROBLEM HAS BEEN OMITTED FROM THE NEW EDITION OF THE TEXT. VERY UNFORTUNATE. absorption of light in water
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13:19:50 what is your intensity function?
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13:19:52 If your previous answer didn't include it, what is the intensity function in terms of a proportionality constant k?
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13:19:54 if 50% is absorbed in 10 ft, how much is absorbed in 20 ft, and how much in 25 feet?
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13:20:29 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I didn't get alot out of 11.6 other than a good amount of practice. I feel like I know what I am doing, but I could be wrong.
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