potaeto 1,933 Posted September 23, 2014 Share Posted September 23, 2014 Hi. I'm offering 25,000 won per each question answered and explained to me CORRECTLY. If a question has more than one blank or box, i will award double. You can answer as many as you like. Although there is a time limit. You have until 11:59pm PST. Thank you. 1) Determine the equation of the tangent line at the indicated domain value. f(t) = 8t; t = 1 y(t) = ____________ 2) Answer the question by using the Exponential Rule or the Logarithmic Rule, as appropriate.Based on data from 1994 to 2001, the quarterly tuition of a resident student at Green River Community College may be modeled byE(t) = 430.6(1.042)t dollars where t is the number of years since 1994.†How quickly was quarterly tuition increasing in 2002? (Round your answer to the nearest cent.)____________dollars per year 3) Answer the question by using the Exponential Rule or the Logarithmic rule, as appropriate.Based on data from the 1990-1991 through the 2002-2003 school year, the total school expenditure, in billions of dollars, may be modeled by T(E) = −2915 + 366.6 ln E where E is the per pupil expenditure in dollars.†CalculateT'(2000). (Round your answer to four decimal places.)T'(2000) = _________________ billion dollars in total school expenditure per dollar of per pupil expenditure 4)Use implicit differentiation to find dy dx . 2x2 + y2 = 8 dy dx = _________________ Evaluate the derivative function at the designated point. (If an answer is undefined, enter UNDEFINED.)(2, 0) At (2, 0), dy dx = _______________ 5) Use implicit differentiation to find dy dx . x2− y2 = 65 dy dx = __________ Link to comment Share on other sites More sharing options...
gayness 2,400 Posted September 23, 2014 Share Posted September 23, 2014 1. 8 2. 8 3. 8 4. 8 5. 8 Link to comment Share on other sites More sharing options...
Souloist 3,634 Posted September 23, 2014 Share Posted September 23, 2014 Good luck. I'd help if I wasn't so bad at math. Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 Good luck. I'd help if I wasn't so bad at math. Thanks I was just in tutoring for the past 4 hours and we still weren't able to reach these questions so i have to get to this option since my teacher is HORRIBLE at teaching. Link to comment Share on other sites More sharing options...
Souloist 3,634 Posted September 23, 2014 Share Posted September 23, 2014 Thanks I was just in tutoring for the past 4 hours and we still weren't able to reach these questions so i have to get to this option since my teacher is HORRIBLE at teaching. Oh my goodness I feel your pain. My professor is absolutely horrible as well (she literally makes mistakes all the time, and my classmates have to correct it for her). I'm either going to have to teach myself or get a tutor. Link to comment Share on other sites More sharing options...
Meiko 329 Posted September 23, 2014 Share Posted September 23, 2014 4) dy/dx = -2x/ydy/dx(at 2,0) = -4/0 = undefined5) dy/dx = x/y Are these correct? Link to comment Share on other sites More sharing options...
KoreaxxLove 194 Posted September 23, 2014 Share Posted September 23, 2014 Now, I haven't had calculus for two years, but I did get a five on both AB/BC, so maybe I still remember a little. For implicit differentiation, you want to make it become dy/dx, so I think it's 2x^2 + y^2 = 8 y^2 = 8 - 2x^2 2y(dy) = -4x(dx) dy = -4xdx/2y dy/dx = -4x/2y Right? It's probably wrong; it's been so long since I've done it. But, I think it's basically you need to remember to do the chain rule, take the derivatives correctly, and make sue dy is over dx, right? IDK Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 4) dy/dx = -2x/y dy/dx(at 2,0) = -4/0 = undefined 5) dy/dx = x/y Are these correct? #5 is CORRECT #4 aren't tho. You'll be awarded 25K congrats!!! EDIT: CORRECTION #4 are correct too!! 50K more for you!! Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 Now, I haven't had calculus for two years, but I did get a five on both AB/BC, so maybe I still remember a little. For implicit differentiation, you want to make it become dy/dx, so I think it's 2x^2 + y^2 = 8 y^2 = 8 - 2x^2 2y(dy) = -4x(dx) dy = -4xdx/2y dy/dx = -4x/2y Right? It's probably wrong; it's been so long since I've done it. But, I think it's basically you need to remember to do the chain rule, take the derivatives correctly, and make sue dy is over dx, right? IDK Sorry, #4 was answered earlier but you can try the other questions!! Link to comment Share on other sites More sharing options...
Taelent 9,485 Posted September 23, 2014 Share Posted September 23, 2014 Do you need the working out too or nah? Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 Do you need the working out too or nah? I'd appreciate it, since i want to learn how to do these properly... my teacher sucks and doesn't explain. But it's fine if you don't include it. Link to comment Share on other sites More sharing options...
ETB5 4,512 Posted September 23, 2014 Share Posted September 23, 2014 #3 T’(E) = (366.6)(1/E) T’(2000) = (366.6)(1/2000) T’(2000) = 0.1833 Is it right? Link to comment Share on other sites More sharing options...
Taelent 9,485 Posted September 23, 2014 Share Posted September 23, 2014 Is the answer to the first one 16.64x - 8.64? Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 #3 T’(E) = (366.6)(1/E) T’(2000) = (366.6)(1/2000) T’(2000) = 0.1833 Is it right? CORRECT!!! congrats you get 25K won~ Is the answer to the first one 16.64x - 8.64? Incorrect, sorry :/ Link to comment Share on other sites More sharing options...
amix 12,096 Posted September 23, 2014 Share Posted September 23, 2014 #1: derivative of a point d/dt of f=8 the slope of the line is 8 f(t) is 8 so point (1,8) slope 8 y-8 = 8(x-1) y-8 = 8x-8 y = 8x? Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 #1: derivative of a point d/dt of f=8 the slope of the line is 8 f(t) is 8 so point (1,8) slope 8 y-8 = 8(x-1) y-8 = 8x-8 y = 8x? Incorrect, sorry :/ Link to comment Share on other sites More sharing options...
ETB5 4,512 Posted September 23, 2014 Share Posted September 23, 2014 #1 F(t) = 8^t t=1 F(1) = 8^1 = 8 so the point is (1,8) F’(t) = 8^(t)ln(8) F’(1) = 8^(1)ln(8) = 8ln(8) = m y-8=8ln(8)(t-1) y-8 = 8(t)ln(8) – 8ln(8) y(t) = 8(t)ln(8) – 8ln(8) + 8 --> (you could add the 8ln(8) and the 8 but that would give you a decimal and that is usually frowned upon, instead by leaving it like I left it, you can get a more accurate answer when you evaluate for any value of t.) Is it right? Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 #1 F(t) = 8^t t=1 F(1) = 8^1 = 8 so the point is (1,8) F’(t) = 8^(t)ln(8) F’(1) = 8^(1)ln(8) = 8ln(8) = m y-8=8ln(8)(t-1) y-8 = 8(t)ln(8) – 8ln(8) y(t) = 8(t)ln(8) – 8ln(8) + 8 --> (you could add the 8ln(8) and the 8 but that would give you a decimal and that is usually frowned upon, instead by leaving it like I left it, you can get a more accurate answer when you evaluate for any value of t.) Is it right? YES CORRECT!!! 25K more to you~~ Link to comment Share on other sites More sharing options...
amix 12,096 Posted September 23, 2014 Share Posted September 23, 2014 any chance that #2 is $82.04? (i'm probably wrong tho lmao) Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 any chance that #2 is $82.04? (i'm probably wrong tho lmao) Incorrect :/ sorry Link to comment Share on other sites More sharing options...
Taelent 9,485 Posted September 23, 2014 Share Posted September 23, 2014 YES CORRECT!!! 25K more to you~~ BRUH 8(t)ln(8) – 8ln(8) + 8 = 16.64t - 8.64 which was what I posted before. But it would probs be better to leave it in exact form anyway (i just got lazy and didnt wanna type all that up) Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 BRUH 8(t)ln(8) – 8ln(8) + 8 = 16.64t - 8.64 which was what I posted before. But it would probs be better to leave it in exact form anyway (i just got lazy and didnt wanna type all that up) hmm.. i typed it into the website the same exact form you submitted your answer and it counted it as incorrect. :/ This website is stupid and only accepts things in certain forms.. sorry Link to comment Share on other sites More sharing options...
ETB5 4,512 Posted September 23, 2014 Share Posted September 23, 2014 #2 E(t) = 430.6(1.042)t dollars They are asking you for the slope E’(t). E’(t) = (430.6)((1.042^t)ln(1.042)) Since t=the number of years SINCE 1994 (as in not counting 1994), then the value of t would be 2002-1994= 8 = t E’(8) = (430.6)((1.042^8)ln(1.042)) = 24.6 Is it right? Link to comment Share on other sites More sharing options...
potaeto 1,933 Posted September 23, 2014 Author Share Posted September 23, 2014 #2 E(t) = 430.6(1.042)t dollars They are asking you for the slope E’(t). E’(t) = (430.6)((1.042^t)ln(1.042)) Since t=the number of years SINCE 1994 (as in not counting 1994), then the value of t would be 2002-1994= 8 = t E’(8) = (430.6)((1.042^8)ln(1.042)) = 24.6 Is it right? CORRECT!!! damn girl you're smart 25K more won~~ ALL QUESTIONS HAVE BEEN ANSWERED. THERE IS NO MORE TO REWARD. THANKS TO ALL THE GENIUSES WHO PARTICIPATED I APPRECIATE IT!! Link to comment Share on other sites More sharing options...
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