Saturday, March 21, 2009

Question set 2


  1. You fire a cannonball upward so that its distance (in feet) above the ground
    t seconds after firing is given by h(t) = −16t^2 + 144t. Find the maximum height (dh/dt = 0) it reaches and the number of seconds it takes to reach that height.
  2. The daily profit, P, of an oil refinery is given by
    P = 8x − 0.02x^2,
    where x is the number of barrels of oil refined. How many barrels will give maximum profit (dP/dx = 0) and what is the maximum profit?
  3. A rectangular storage area is to be constructed along the side of a tall building. A security fence is required along the remaining 3 sides of the area. What is the maximum area that can be enclosed with 800 m of fencing?
  4. A box with a square base has no top. If 64 cm2 of material is used, what is the maximum possible volume for the box?
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15 comments:

  1. crazykidMarch 22, 2009 at 2:18 PM

    question 4
    the area of a box = (S x S) 6
    since there is no top the surface area,
    64cm^2 = (S x S)5
    64/5 = S^2
    12.8 = S^2
    square root 12.8 = S

    therefore S= 3.58

    the volume of a sqaure box = S^3

    since S= 3.58cm,
    V= (3.58)^ 3

    the max possible V = 45.8 cm

    ReplyDelete
  2. Swanky ThingMarch 26, 2009 at 8:28 PM

    This comment has been removed by the author.

    ReplyDelete
  3. Swanky ThingApril 3, 2009 at 8:54 AM

    Question 1
    You fire a cannonball upward so that its distance (in feet) above the ground
    t seconds after firing is given by h(t) = −16t^2 + 144t. Find the maximum height (dh/dt = 0) it reaches and the number of seconds it takes to reach that height.


    h(t) = −16t^2 + 144t
    dh/dt = -32t + 144

    the number of seconds it takes to reach.
    0 = -32t + 144
    32t = 144
    t = 144/32
    = 4.5

    ReplyDelete
  4. Swanky ThingApril 3, 2009 at 9:00 AM

    Question 2
    The daily profit, P, of an oil refinery is given by
    P = 8x − 0.02x^2,
    where x is the number of barrels of oil refined. How many barrels will give maximum profit (dP/dx = 0) and what is the maximum profit?

    P = 8x − 0.02x^2
    dP/dx = 8 - 0.04x

    The number of barrels that will give the maximum profit is 0.04.

    The maximum profit
    0 = 8 - 0.04x
    0.04x = 8
    x = 8/ 0.04
    = 200

    ReplyDelete
    Replies
    1. David JamesAugust 20, 2018 at 1:24 PM

      how did you get the number of barrels? i really need help

      Delete
  5. Swanky ThingApril 3, 2009 at 9:02 AM

    I need help with Question 3

    ReplyDelete
  6. Low riderApril 4, 2009 at 10:19 AM

    Me to i need help in question three at least to derive the equation.

    ReplyDelete
  7. empressApril 7, 2009 at 11:22 AM

    P = 8x - 0.02x^2
    dP/dx =8 - 0.04x
    when dP/dx = 0
    8 - 0.04x = 0
    8 = 0.04x
    this is where the maximum profit occurs which is 0.04.
    hence, x = 8/0.04
    x = 200
    therefore,200 barrels will give the maximum profit.

    ReplyDelete
    Replies
    1. David JamesAugust 20, 2018 at 1:30 PM

      oh so the number of barrels is 200 and not 0.04 as swanky thing stated?

      Delete
  8. empressApril 7, 2009 at 11:23 AM

    I myself needs help with question 3.
    LORD, plz send an angel.

    ReplyDelete
  9. empressApril 7, 2009 at 11:25 AM

    I totally agree withSwanky Thing, the answer is 4.5 seconds.

    KEEP UP THE GOOD WORK!

    ReplyDelete
  10. empressApril 7, 2009 at 11:27 AM

    Good work crazykid I couldn't think of any other accurate way to do that question.

    ReplyDelete
  11. Low riderApril 14, 2009 at 10:24 AM

    Yes swanky thing and crazy kid good way of explaining the questions

    ReplyDelete
  12. Chun-LiApril 27, 2009 at 7:37 PM

    hey just wondering for Q2 wouldn't x=200 be the amount of barrels and to find profit P we have to substitute that back into the equation

    The daily profit, P, of an oil refinery is given by
    P = 8x − 0.02x^2 ??

    ReplyDelete

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