? 發問於 科學及數學數學 · 1 十年前

#@Application of Differentiation#(F.5)

Red ink is poured onto a white shirt forming a circular stain on it .The area of the stain grows a steady rate of 1 cm^2 /s. Calculate , in terms of π,

a) the radius ,in cm , of the stain 4 seconds after the ink first touched the shirt,

b)the rate , in cm/s , of increase of the radius of the stain at this instant.

1 個解答

評分
  • 1 十年前
    最愛解答

    a)

    After 4 seconds, the area of circle = 4*1 = 4 cm²

    The radius = √(4/π) = 2/√π cm (or 1.13 cm in 3 sig. fig.)

    b)

    Let A be the area of the circle and r be its radius.

    Then A = πr²

    dA/dt = 2πr dr/dt

    Since the area of the stain grows a steady rate of 1 cm² /s, dA/dt = 1

    1 = 2πr dr/dt

    dr/dt = 1/(2πr)

    Since at that moment, r = 2/√π,

    dr/dt = 1/[2π 2/√π] = 1/(4√π) cm/s (or 0.141 cm/s in 3 sig. fig.)

    Hope it helps! ^^

    資料來源: Myself
還有問題嗎?立即提問即可得到解答。