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anonymous

  • one year ago

Related Rates Question Help!?!?! The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? a)25 b)-45 c)-50 d)45

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  1. anonymous
    • one year ago
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    only need help on this one and then i can do a whole bunch that are alike!!

  2. phi
    • one year ago
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    |dw:1438197781116:dw|

  3. phi
    • one year ago
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    the area of the triangle is \[ A = \frac{1}{2} x y\] take the derivative with respect to t: \[ \frac{dA}{dt} = \frac{1}{2}\left( x \frac{dy}{dt}+ y \frac{dx}{dt}\right)\]

  4. anonymous
    • one year ago
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    wouldn't the x and y disappear ?

  5. anonymous
    • one year ago
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    and also the .5

  6. phi
    • one year ago
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    both x and y are variables and you must use the product rule

  7. anonymous
    • one year ago
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    lovely okay got it thank you very much!

  8. phi
    • one year ago
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    d u v = u dv + v du if you have a constant, it can "go out front"

  9. phi
    • one year ago
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    unfortunately, I do not get any of your answer choices.

  10. anonymous
    • one year ago
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    wait would it be x dy/dt wouldn't it be x dx/dt

  11. anonymous
    • one year ago
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    okay nvm product rule forgot

  12. phi
    • one year ago
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    the rule is d (uv) = u * dv + v * du or with x and y d/dt (xy)= x d/dt y + y * d/dt x

  13. anonymous
    • one year ago
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    what are you getting?

  14. anonymous
    • one year ago
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    im getting -25

  15. phi
    • one year ago
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    dx/dt= -1 dy/dt= 2 x=10 y=70 x dy/dt + y dx/dt = 10*2 + 70*-1 = 20-70= -50 then multiply by 1/2 to get -25 sq ft/ sec

  16. anonymous
    • one year ago
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    -25 is an answer choice though. wheres the problem?

  17. phi
    • one year ago
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    which one ?

  18. anonymous
    • one year ago
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    oh woops a should be a -25

  19. anonymous
    • one year ago
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    sorry abut that :(

  20. anonymous
    • one year ago
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    Thank you very much !!

  21. phi
    • one year ago
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    good luck on the other problems

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