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    Calculus Question

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    Ahmed
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    Calculus Question

    Post by Ahmed on Sun Dec 19, 2010 11:21 pm

    took me a while till I solved it:

    An Airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation is chancing when the angle (-)=30 degrees [(-) I made this symbol for theta].

    Last step was annoying as hell.

    If anyone wants to have some fun...


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    Re: Calculus Question

    Post by Doc on Sun Dec 19, 2010 11:30 pm

    related rates sonnnn

    the answer is the power cosmic!!
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    Re: Calculus Question

    Post by Doc on Sun Dec 19, 2010 11:41 pm

    wait u have to use position formula for this right?
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    Re: Calculus Question

    Post by Ahmed on Sun Dec 19, 2010 11:43 pm

    No you don't.
    --------------------

    BTW help me out with this one:

    If f(x)=4x^2-3x+2, at what point on the interval -2


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    Re: Calculus Question

    Post by Ahmed on Sun Dec 19, 2010 11:44 pm

    If f(x)=4x^2-3x+2, at what point on the interval -2 < x < 3, if any, is tangent to the curve parallel to the secant line.


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    Re: Calculus Question

    Post by Doc on Sun Dec 19, 2010 11:44 pm

    take derivative and find out where its 0 me thinks
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    Re: Calculus Question

    Post by Ahmed on Sun Dec 19, 2010 11:45 pm

    Huh? How did you figure that out?


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    Re: Calculus Question

    Post by Doc on Sun Dec 19, 2010 11:45 pm

    secant is 1/cos lol
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    Re: Calculus Question

    Post by Doc on Sun Dec 19, 2010 11:48 pm

    lol i dunno man im just saying random stuff

    howd u do the first problem tho?
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:03 am

    Draw a right triangle. The base of the triangle should be along the ground from where the plane is to where the observer is. The hypotenuse should extend from the observer to the plane and the other side is just vertical and it has a length of 5 miles. Theta is the angle beside the observer formed by the hypotenuse and the base.

    db/dt=-600 , b stands for base, t stands for time so the base is changing at a rate of 600 mi/h or in other words the derivative of the base with respect to time is 600. Note that I wrote db/dt=-600 because the length of the base is decreasing as the plane gets closer to the observer so the rate is negative.
    We are asked to find dθ/dt and we are given db/dt so we need some equation that relates θ and b.
    If you look at your triangle you'll notice tan(θ)=5/b
    by implicit differentiation(with respect to time) we get, sec(θ)dθ/dt=-5b^-2db/dt
    Now you simply plug in the numbers given and solve
    sec(30)dθ/dt=-5(5√3)^-2*-600
    dθ/dt=30 degrees per hour or if you use π/6 instead of 30 you get the answer 30 radians per hour
    If you're wondering where the 5√3 came from remember that tan(θ)=5/b so b=5/tan(θ)=5/tan(30)=5/(1/√3)=5√3


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 12:08 am

    LOL i drew the triangle, disregarded it and went for the position formula and didn't have enough info Hilarious
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:10 am

    How the hell do you do approximations?

    I have a table that has values of f(x) for the given x values for a unknown function. I have to approximate f'(0.10).




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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:18 am

    Also is this correct:

    If a particle moves along a line according to the law s=t^5+5t^4, then the # of times it reverses direction is?

    I would use the derivative (velocity) or the 2nd derivative (acceleration)?



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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 12:21 am

    Ahmed wrote:How the hell do you do approximations?

    I have a table that has values of f(x) for the given x values for a unknown function. I have to approximate f'(0.10).



    you mean that linear approx garbage??

    screww that
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:35 am

    So far you didn't help me in anything...


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 12:42 am

    dude i havent done calculus in over a year!

    i only remember easy stuff, not related rates and linear approx :S
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:46 am

    Remember evaluating the derivative of an inverse function?

    F My Cal teacher.


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 12:48 am

    no .. i suck at life Hilarious
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 12:53 am

    F my sh!tty teacher.


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 1:03 am

    dude just google it!

    damn

    this nigga has a sh!tload of videos

    http://www.youtube.com/user/patrickJMT
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 1:09 am

    He has videos on Trig, not Cal.


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 1:26 am

    yeah he does u noob .. just go to his play list for calc 1 or use the search function

    try this

    http://www.analyzemath.com/calculus/Differentiation/derivative_inverse.html
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 1:40 am

    FFFFF...hopefully this will help me on tomorrow's test

    http://216.101.58.17/hs/bchin/pdf/inversesT8/theme8sol.pdf

    I HAVE BEEN STARING AT THE SAME FREAKING QUESTION FOR HALF AN HOUR. I HOPE THE TEACHER TAKES A LONG SLEEP.


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    Re: Calculus Question

    Post by Doc on Mon Dec 20, 2010 1:53 am

    just post the damn question ... i suck at math if i dont do it in over a day (lol Rolling Eyes ) but ill try anyway
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    Re: Calculus Question

    Post by Ahmed on Mon Dec 20, 2010 2:02 am

    Forget it, this site:

    http://216.101.58.17/hs/bchin/pdf/inversesT8/theme8sol.pdf

    Somehow helped me...in a weird way. Like I don't know why you solve it like that, but I know how, and that's all I need to know for the test.

    Thank God

    Now to understand the approximation question.


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