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anonymous
 5 years ago
ok, last question in the assignment that i can't seem to get, [derivative = hard ;_;], once again the question is attached in next post.
anonymous
 5 years ago
ok, last question in the assignment that i can't seem to get, [derivative = hard ;_;], once again the question is attached in next post.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, what i know so far: after 3 seconds, the x[t] = 42ft and the s[t]=58.7 while the y[t] is given as 41ft. so now im not exactly sure what the question wants cause wouldnt the rate of s[t] remain the same after 3 seconds? o:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is the same as the problem you posted earlier, Instead of the diagonal of the rectangle, you have the hypotenuse of the triangle in this problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ya, i know that, but the question is asking "how fast is the distance s[t] between bike and balloon increasing 3 seconds later".... so i mean, won't the s[t] have the same rate increasing after 3 secs? why would the rate change?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, i see a mistake i made... the 41ft i used to fine the s[t] i didnt account that after 3 secs it would also increase like the x[t] is... so the y[t] after 3 secs would be 56ft, the x[t] 42ft and the s[t] = 70

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, so now i calculated the s[t], x[t] and y[t] would be after 6 secs and i got, y[t] = 86ft, the x[t] = 126ft and s[t] = 153. So using these, i did: 15370/63 = 27.5ft/sec and i believe this is the rate s[t] is increasing by.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0soooo, is this correct? o:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get x(t) = 126 ft for t =6sec?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0um, at 3 sec the x[t] is = 42ft so at 6 sec its 14ft/sec times 6s = 84 ft + 42 ft = 126 ft

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hold on. Do you mean to say that If i am travelling at a constant rate of 1ft/sec, I will cover 3 feet in 3 seconds and 3+6 = 9 feet in 6 seconds?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OHHHHHHHHHHHHHHHHHH, ok ok ok... my bad. i see now, k. so the x[t] after 6 seconds will be 84ft not 126ft... ok. so now, 12070/63 = 16.7 ft/sec.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get y(t) = 86 feet at t = 6 seconds?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, looking at the y[t] im stuck.... now they got 41ft at the rate of 5 ft/s which means that was after 8.2 seconds... so after 6 seconds would be AFTER that 8.2 seconds....? so wouldn't i add them or wait, would it be 8.2+6 = 14.2 and then i use 14.2 x 5 =71 ft... so i'd use 71 ft then?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0define when you start your timer. Suppose you had a timer to time these events. Tell me when you would start your timer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x, y and s are functions of time, correct? So you have to start your time at some point. When do you start your time?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you have an answer? or do you want me to explain?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0at the 41ft, when the cycle and balloon are in a vertical line to each other... i'd start my timer then.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets define y(t) then. Can you give an expression for y(t)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so at t = 6 seconds, y(t) = 30 feet?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you sure your definition is correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets look at this another way. When you start your timer, how high is the balloon?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, at t = 0, y(t) = 41 ft

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how high is the balloon 1 second after you started your timer?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get 46 ft?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.046 = 41ft+5ft/second*1second. correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what is the general expression for y(t)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 6 seconds later, what is y(t)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0have you done derivatives?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this question is part of chapter on applications of derivatives.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay.so you are asked to find ds(t)/dt at t = 3 seconds

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets define s(t). What is s(t)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0s[t] = square root of y[t]^2 plus x[t]^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay, so \[ds(t)/dt = d(y(t) ^{2}+x(t)^{2})^{0.5}/dt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right? and you know that dy/dt = 5 ft/sec and dx/dt = 14 ft/sec

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0solve the above expression in terms of dy/dt and dx/dt. Substitute for dy/dt and dx/dt and find the value of ds/dt at t = 3.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, i think i get it, lemme have a shot at it and ill post my answer in a bit.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0note that dy/dt = d(41+5t)/dt = 5 and dx/dt = d(14t)/dt =14

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0note also that x(t) = 14t

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright, finding the derivative of teh first equation is: 0.5(y[t]^2 + x[t]^2)^0.5 times (2y[t]+2x[t]) ok, using this differentiation, and knowing: y[t]^2=3136 2y[t]=112 x[t]^2=1264 2x[t]=84 substituting it all in, i get the answer of 1.4 ft/sec.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay great, I dont know what the answer is, but your differentiation seems correct.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alriiiight, thanks SO MUCH, you really were a GREAT help :] thanks ^^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you are welcome. You should do the other problem the same way too. the earlier one with the rectangle i mean.
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