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    Kayak Question

    Homework Statement A woman lives on an island 2km from the mainland. Her fitness club is 4km along the shore from the point closest to the island. To get to the fitness club, she paddles her kayak at 2km/h. Once she reaches the shore she jogs at 4km/h. Determine where she should land to reach...
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    Minimize Distance

    Homework Statement Mike, who i standing on the deck of a yacth that is travelling due west at 6km/h, sees a sailboat sailing southwestat 4km/h, 3km northwest of the yacht. How close to each other do these boats get? Homework Equations The Attempt at a Solution My drawing is: |...
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    Really hard related rates problem

    CAN SOMEONE PLEASE HELP ME UNDERSTAND THIS PARAGRAPH. I THINK HE HAS THE WRONG DRAWING, SET UP
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    Really hard related rates problem

    So what exaactly do I do with the first paragraph? And the second paragraph isn't it suppost to be V=(0.4+0.4+2x)h\frac{1}{2}(2.5) ???
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    Finding closest distance

    Yea I got it thanks Halls of Ivy... I get to stay in school :D
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    Finding closest distance

    OMG YOU ARE CORRECT! Thanks man. I'm slow. What's your paypal how much do I owe you. :tongue2: And now I have another similar one i'm struggling with it :S
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    Finding closest distance

    NO! but we only have found the time man not the distance
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    Finding closest distance

    The ships get 0.707km to each other btw thanks for all your help so far
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    Finding closest distance

    I got it to be: After the expansion and derivative dD/dt=200t-98.84/(the rest here doesn't matter cause i'm setting other side to zero)
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    Finding closest distance

    D^2=(-3.53+6t-0)^2+(3.53-8t)^2 I did derivative. Set it to 0. Got 0.7 Thats not the answer I'm suppost to plug time into the D^2 and get the distance correct?
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    Finding closest distance

    **** or is it A(8t,0) B(3.53,-3.53+6t) My guess is that's right if not I quit school
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    Finding closest distance

    ah crap.... A is (8t,0)
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    Finding closest distance

    A's position at t=0 is (0,0) A's position as a function of time is (3.53-8t,0) B's position as a function of time is (3.53,-3.53-6t)
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    Finding closest distance

    yes those are the coordinates.from the origin (0,0) using pythagorean theorem, i use 5sin45=a=3.53, b=3.53
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    Finding closest distance

    yes I have a drawing. I used the sin law to find the distance of the 2 sides. Coordinates (3.53,0) and (3.53,-3.53) By the way how do you put spaces in latex coding I tried \\ it didnt work
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    Finding closest distance

    ok D^2=(-3.53+6t^2)+8t^2 dD/dt=(200t-42.36)/whatever\\0=200t-42.36\\t=0.212\\ I plugged that in the distance formula and got a wrong answer
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    Really hard related rates problem

    yea the differentiation part is easy just the similar triangles part i don't get how do i find the volume equation, and i guess area
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    Really hard related rates problem

    Homework Statement A trough has an isosceles trapezoidal cross section as shown in the diagram. Water is draining from the trough at 0.2m^3/s At what rate is the surface rea of the water decreasing? Dimensions are: base width=0.4m, top width= 0.8m...
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    Finding closest distance

    Homework Statement Ship A, sailing due east at 8 km/h, sights ship B 5km to the southeast when ship B is sailing due north at 6km/h. How close to each other will the two ships get? Homework Equations The Attempt at a Solution I drew the picture. Ship a distance is 8t and B is 6t...
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    Rates of Change in business

    Homework Statement A Real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, each unit requires $75 in maintenance and repairs each month. How much rent...
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    Keep getting an indeterminate answer for limit

    Homework Statement Determine the limit: lim as x->-2 [1/(1+x)+1]/[2x+x^2] Homework Equations The Attempt at a Solution I can't seem to work around it, I keep getting an indeterminate answer.
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    Explaining the chain rule

    DERIvative of g(x)...
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    Explaining the chain rule

    Homework Statement The question is: How would you explain the chain rule to a classmate? My teacher wants: 1.a graph, 2. in words, 3. using math Homework Equations The Attempt at a Solution I said: for the function y=f[g(x)], the chain rule is d/dx[g(x)]. Whats the graph like?
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    Exponential Derivative

    i thought the law of y=x^x was: x^x(1+lnx)
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    Exponential Derivative

    How do you find the derivative of: y=x(3x)^x^2 ? I though it was yprime=(1)3x^x^2+x(3x^x^2)ln(1+3x)(2x)
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    Chain rule Derivative help

    Given: h=f\circ g , g(2)=5, g\prime(2)=3, and f\prime(5)=-2 Determine h\prime(2)
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