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Wislar

  • 2 years ago

Please help! One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?

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  1. experimentX
    • 2 years ago
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    perhaps the Q meant this |dw:1350751784378:dw|

  2. Wislar
    • 2 years ago
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    I thought this was related rates, but I'm in calc 3, and we are doing differentials and tangent approximations, so I'm kinda lost here. Plus, I don't really remember related rates too well

  3. experimentX
    • 2 years ago
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    |dw:1350751819497:dw| yeah this is related rate.

  4. experimentX
    • 2 years ago
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    |dw:1350751925717:dw|

  5. experimentX
    • 2 years ago
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    Given that \( {x = 20} , {dx \over dt} = 3 \) \( {y = 30} , {dy \over dt} = -2 \) \[ A = {1 \over 2} xy \; \sin \theta \\ {dA \over dt} = 0, \\ \text{Find } {d \theta \over dt }\]

  6. experimentX
    • 2 years ago
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    If i interpreted the problem correctly ...

  7. Wislar
    • 2 years ago
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    How did you get z=16.14?

  8. experimentX
    • 2 years ago
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    forget that ... it's not necessary.

  9. Wislar
    • 2 years ago
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    It's been along time since I've done related rates, so I may be wrong, but would I take the derivative of dA/dt first?

  10. experimentX
    • 2 years ago
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    also given that \( \theta = {\pi \over 6} \) differentiate the above ... put the values and get the rest.

  11. experimentX
    • 2 years ago
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    Given area is constant ... dA/dt = 0

  12. Wislar
    • 2 years ago
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    Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?

  13. experimentX
    • 2 years ago
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    time ... t, also you are given the values of dx/dt and dy/dt

  14. Wislar
    • 2 years ago
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    dA/dt=.5 (dx/dt)ysin(theta)+x(dy/dt)sin(theta)+xy(theta)(cos(theta))(dtheta/dt) ?

  15. experimentX
    • 2 years ago
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    yes ... put the values dA/dt = 0, all values are given, you only need to find the value of d(theta)/dt

  16. Wislar
    • 2 years ago
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    Got it! Thanks!

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