Saturday, March 21, 2009

Real LIfe Differentiation

  1. A closed box has a fixed surface area A and a square base with side x .
    (a) Find a formula for the volume V of the box, as a function of x .
    (b) Find the rate of change of V with respect to x.
  2. The revenue from selling q items is given by the formula R(q) = 500q - q^2
    and the total cost is given by C(q) = 150 + 10q . Write down a function that gives the total
    profit earned. Find the rate of change of total profit with respect to q.
  3. For positive constants A and B, the force between two atoms in a molecule is given by
    f(r) = A/r^2 + B/r^3 where r > 0 is the distance between the atoms.
    What is the expression for the instantenous rate of change of force between the atoms with respect to distance?
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8 comments:

  1. ghetto_celebMarch 21, 2009 at 11:40 AM

    question 1:

    remember not to get caught up in the background of real life questions. always keep focus on what ur looking for.

    with this question i will be looking for info to help me formulate an equation that connects the sides of the box and the volume of the box.well i interpret the fixed surface area to mean the object has equal sides all around.

    therfore:

    V = x^3

    now to differentiate, i will check for notted terms, sheds and what i;m suppose to differentiate with respect to what.since its the volume with respect to the side x, i will go ahead an differentiate the above eqaution i have formulated to give

    dy/dx = 3*1 x^3-1

    dy/dx = 3x^2

    ReplyDelete
  2. poopsiepumkinpieMarch 22, 2009 at 8:45 AM

    (3)

    f(r)= A/r^2 + B/r^3

    bring all d downstairs upstairs..

    = Ar^-2 + B^ -3

    df/dr = -2Ar^-3 + (-3)Br^-4

    = -2A/r^3 + 3B/r^-4

    ReplyDelete
  3. mysticwings*March 22, 2009 at 12:40 PM

    no 2

    ok well i know that we have to find P(q) which is the profits made and somehow we have to find this using R(q) and C(q) and then differentiate P(q). but what exactly do we have to do with R(q) and C(q) to find P(q)???
    if R is revenue and C is cost, then P in normal maths would be R - C .....

    does anyone have ideas ???????????

    ReplyDelete
  4. maths hate or love itMarch 23, 2009 at 8:01 PM

    mysticwings* i think you are correct, it would
    Profit = Revenue earned - Cost in order to obtain the profit.

    P(q) = R(q)- C(q) = [500q - q^2] - [150 + 10q]
    = 490q - q^2 - 150

    d(P)/d(q) = 490 - 2q

    ReplyDelete
  5. Swanky ThingMarch 24, 2009 at 4:09 PM

    I totally agree with the answer above...

    ReplyDelete
  6. Swanky ThingApril 3, 2009 at 9:30 AM

    A closed box has a fixed surface area A and a square base with side x .
    (a) Find a formula for the volume V of the box, as a function of x .
    (b) Find the rate of change of V with respect to x.


    a) V = x^3 where x is the side

    b) dV/dx= 3x^-2

    ReplyDelete
  7. Swanky ThingApril 3, 2009 at 9:37 AM

    Question 3

    For positive constants A and B, the force between two atoms in a molecule is given by
    f(r) = A/r^2 + B/r^3 where r > 0 is the distance between the atoms.
    What is the expression for the instantenous rate of change of force between the atoms with respect to distance?

    f(r) = A/r^2 + B/r^3

    Make the equation simplier
    f(r) = Ar^-2 + Br^-3

    df/dr = -2Ar^-3 + -3Br^-4

    ReplyDelete
  8. Low riderApril 13, 2009 at 10:40 AM

    Swanky thing i agree with your answers

    ReplyDelete

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