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shaqadry

  • 3 years ago

Let A be the total surface area of a rectangular container of square base and height, h. At a certain instant, the surface area is decreasing at 24 cm^2/s while the width of the base is 5 cm and increasing at 2 cm/s. Determine whether the height is increasing or decreasing at that instant if the height is 3 cm. (Ans: dh/dt = -4.4 cm/s) Somebody PLEAAAAAASSSEEE explain this to me. :(

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  1. radar
    • 3 years ago
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    This appears to be a related rate problem, but the answer tells you that the height is decreasing (note the - in the -4.4cm/sec.

  2. shaqadry
    • 3 years ago
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    okay :/ how do i solve it?

  3. radar
    • 3 years ago
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    Where did the answer come from? If that is your answer, then you have already solved it.

  4. shaqadry
    • 3 years ago
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    got it from the lecturer. but i have no idea how to solve it.

  5. radar
    • 3 years ago
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    O.K. First you need to express the total surface area (A) in terms of the base and height. The base is square (given) so assign x as the dimension of the base. The surface area of the base is then x^2 (x squared). This is not the total A, just the base area. The area of the rest of the container is to be expressed in terms of x (base dimension) and h (height). There are 4 sides each having an area hx, so that equals 4hx. Now the total surface area A is:\[x ^{2}+4hx\]. You must understand this before proceeding. Do you?

  6. shaqadry
    • 3 years ago
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    okay. go on.

  7. shaqadry
    • 3 years ago
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    so the top of the rectangle doesnt count?

  8. radar
    • 3 years ago
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    Do you understand rate of change or derivatives? No it is a container, no mention of a lid, but if it did count the terms which is now x^2 would become 2x^2. we can work it both ways, because it might be a closed container.

  9. shaqadry
    • 3 years ago
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    okay i understand. so then we find dA/dh? and the x remains? after that what?

  10. radar
    • 3 years ago
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    A'=-24 (cm)^2 given You are also given x' as 2cm/s you are given x (x = 5) you are given h (h=5) solve for h'

  11. radar
    • 3 years ago
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    I am kind of rusty here on implicit differentiation, hopefully you are current.

  12. radar
    • 3 years ago
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    *h=3

  13. radar
    • 3 years ago
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    I come up with -3.666 not the approved answer. I will try with the lid!

  14. shaqadry
    • 3 years ago
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    thank you so much! appreciate your help :)

  15. radar
    • 3 years ago
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    With the lid I get -5.55 somewhere I've erred, suggest going over it or did you get the -4.4

  16. shaqadry
    • 3 years ago
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    no i didnt get it :/

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