Thursday
March 30, 2017

Post a New Question

Posted by on .

The altitude of a triangle is increasing at a rate of 2.500 centimeters/minute while the area of the triangle is increasing at a rate of 1.500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.500 centimeters and the area is 93.000 square centimeters?

  • Math (: - ,

    Given
    A=bh/2, b=2*93/10.5=17.714
    differentiate with respect to t (by the product rule on the right hand side).
    The only unknown left is the rate of change of the base.
    Hint: it is negative.

  • Math (: - ,

    let the area be A
    let the base be x
    let the height be y

    given: at a time of t minutes,
    dA/dt = 1.5 cm^2/min
    dy/dt = 2.5 cm^2/min

    find:
    dx/dt when A = 93 and y = 10.5

    A = xy/2 or
    2A = xy (equ#1)

    differentiate implicitly with respect to t, using the product rule
    2dA/dt =x(dy/dt) + y(dx/dt) (equ#2)

    we know A=93 when y = 10.5, so x = 17.714
    sub into equ#2
    2(1.5) = 17.714(2.5) + 10.5dx/dt

    solve for dx/dt

  • Math (: - ,

    My answer is -3.9319, but it's wrong.

  • Math (: - ,

    I have -3.932 too.
    Can you check the numbers in the question?

  • Math (: - ,

    I copied & pasted this from my online homework. It said the answer is wrong.

  • Math (: - ,

    I also had -3.932

    What answer did the book have?

  • Math (: - ,

    I use an online homework program called WebWork. It just tells you if your answer is correct or not.

  • Math (: - ,

    Try -3.93, -3.932.

  • Math (: - ,

    The answer is -3.9300. Thanks!

Answer This Question

First Name:
School Subject:
Answer:

Related Questions

More Related Questions

Post a New Question