A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? i got 8/400 but it was wrong
anonymous
 one year ago
A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? i got 8/400 but it was wrong

This Question is Closed

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434325170769:dw picture looks something like this

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434325227788:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1"A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? i got 8/400 but it was wrong "  Moves horizontally at a speed of 8ft/s this means x'=8ft/s we are looking for theta (in rad) when y=200ft

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well what is theta when y=200ft

freckles
 one year ago
Best ResponseYou've already chosen the best response.1what trig function can you use here

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434325371019:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1hint you have opp and hyp measurements given

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i did sin of 100/200 and got .479

freckles
 one year ago
Best ResponseYou've already chosen the best response.1arcsin(1/2)? which is pi/6

freckles
 one year ago
Best ResponseYou've already chosen the best response.1to solve sin(theta)=1/2 you normally take arcsin( ) of both sides since arcsin(sin(x))=x where x is between pi/2 and pi/2 dw:1434325633246:dw anyways we are going to use x (because we are given x's rate) and theta for sure and I will go ahead and use that constant side \[\tan(\theta)=\frac{100}{x}\] differentiate both side

freckles
 one year ago
Best ResponseYou've already chosen the best response.1how did you get that equation?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Like can you tell me what is confusing you please? Because I don't know how to help if I don't know where to start to help.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the derivative of tan=100/x thats where i got confused

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well the equation is actually \[\tan(\theta)=\frac{100}{x} \text{ or you can write it as } \\ \tan(\theta)=100x^{1}\] so you don't have to use quotient rule if you prefer

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you will need to use chain rule on both sides though

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to evluate either one of these: \[\frac{d \tan(t)}{dt}=? \\ \frac{d(t^{1})}{dt}=?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1for the first it is easy just to remember derivative of tan(t) w.r.t t is sec^2(t) and the second one I asked you about can be done by power rule have you every used power rule before? I hope so because this question is about application of chain rule

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\tan(\theta)=100x^{1} \\ \text{ differentiate both sides } \\ \sec^2(\theta) \cdot \frac{d \theta}{d t}=100 \cdot \frac{d(x^{1})}{dt}\] you still to differentiate the right hand side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be 100/x^2?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1don't forget you need to write times dx/dt

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\sec^2(\theta) \cdot \frac{d \theta}{ d t}=\frac{100}{x^2} \cdot \frac{dx }{dt}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1plug in all the values you found and are given and solve for dtheta/dt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be sec^2(pi/6)*dtheta/dt= 100/1ooroot3* 200?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well the x has a square on it and I thought dx/dt was given as 8ft/sec why you put 200 for dx/dt? dx/dt represents the rate and which the kite moves horizontally

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\sec^2(\frac{\pi}{6}) \cdot \frac{ d \theta}{ d t}=\frac{100}{(100 \sqrt{3})^2} \cdot 8\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i solved the right hand side but then how do i divide by the sec^2 im havinf trouble calculating that?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{d \theta}{dt} =\frac{1}{\sec^2(\frac{\pi}{6})} \frac{100}{(100 \sqrt{3})^2} \cdot 8 \\ \frac{d \theta}{ dt}=\cos^2(\frac{\pi}{6}) \frac{100}{(100\sqrt{3})^2} \cdot 8\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok and i have 1/50 those should be equal

freckles
 one year ago
Best ResponseYou've already chosen the best response.1don't forget to put your units

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my answer was 8/400 and i got it wrong?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or is it not supposed to be negative?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can try without did you put the units though ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the units are already tehre rad/s so i just had to type my answer in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i only have one more try so im scared to type it and get it wrong

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok don't know what to tell you we have the answer above says it is decreasing at a rate of 1/50 rad/sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know this thing is weird _ but thank you for your help though!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it was supposed to be positive got it right!!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.