数学应用题 一个球体状的气球被每秒钟13cm^3的速度充满 当气球有3800cm^3的空气时直径的瞬时增长速率是多
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:英语作业 时间:2024/07/26 13:37:27
数学应用题 一个球体状的气球被每秒钟13cm^3的速度充满 当气球有3800cm^3的空气时直径的瞬时增长速率是多
是英语题 原题是a spherical balloon is being filled at a rate of 13 cm^3 per second. how fast is the diameter growing at the instant when the balloon has 3800 cm^3 of air?
谢谢了 我特别着急
是英语题 原题是a spherical balloon is being filled at a rate of 13 cm^3 per second. how fast is the diameter growing at the instant when the balloon has 3800 cm^3 of air?
谢谢了 我特别着急
![数学应用题 一个球体状的气球被每秒钟13cm^3的速度充满 当气球有3800cm^3的空气时直径的瞬时增长速率是多](/uploads/image/z/18974498-50-8.jpg?t=%E6%95%B0%E5%AD%A6%E5%BA%94%E7%94%A8%E9%A2%98+%E4%B8%80%E4%B8%AA%E7%90%83%E4%BD%93%E7%8A%B6%E7%9A%84%E6%B0%94%E7%90%83%E8%A2%AB%E6%AF%8F%E7%A7%92%E9%92%9F13cm%5E3%E7%9A%84%E9%80%9F%E5%BA%A6%E5%85%85%E6%BB%A1+%E5%BD%93%E6%B0%94%E7%90%83%E6%9C%893800cm%5E3%E7%9A%84%E7%A9%BA%E6%B0%94%E6%97%B6%E7%9B%B4%E5%BE%84%E7%9A%84%E7%9E%AC%E6%97%B6%E5%A2%9E%E9%95%BF%E9%80%9F%E7%8E%87%E6%98%AF%E5%A4%9A)
The volume of the balloon V(t)=13t
Let D(t) be the diameter of the balloon at time t, then V(t) = 4π[D(t)/2]^3 / 3
which gives us D(t) = ∛[(78/π) * t]
Take its derivative, D'(t) = ∛[(26/9π) * t^(-2)]. This is the rate of change of the diameter at time t.
When V(t) = 3800, t = 3800/13
D'(t) = ∛[(26/9π) * (3800/13)^(-2)].
Then just use a calculator and get D'(t) = 0.022
Let D(t) be the diameter of the balloon at time t, then V(t) = 4π[D(t)/2]^3 / 3
which gives us D(t) = ∛[(78/π) * t]
Take its derivative, D'(t) = ∛[(26/9π) * t^(-2)]. This is the rate of change of the diameter at time t.
When V(t) = 3800, t = 3800/13
D'(t) = ∛[(26/9π) * (3800/13)^(-2)].
Then just use a calculator and get D'(t) = 0.022
高数 导数应用题一个球形气球充气时,其表面积以100π dm2/min的速度增长,当气球半径为10dm时气球半径的增长有
一个圆的半径增长3cm,直径增长( )cm,周长增长( )cm.
一圆球形气球,体积是8cm^3,再打入一些空气后,气球仍保持为球形,体积是27cm^3前后两次气球的半径之比.
微积分 若以10立方厘米/秒的速率给一个球形气球充气,那么气球半径为2cm时,它的表面积增加有多快?
为什么 手持一个充满空气的气球,松手后气球飞上天 有可能?
黄气球有32个,蓝气球是黄气球的4分之3,红气球是蓝气球的3分之2,红气球有多少个?
在恒温条件下有一个充满氢气的气球 气球的下端挂着称有澄清石灰水的烧杯开始时 气球在空中悬浮 经过一段时间后 气球将会
有红黄蓝三色气球共54个红气球是黄气球的3倍,蓝气球是红气球的2倍还多4个,求三种气球各多?
蓝汽球有15个,红气球是蓝气球的3倍,一共有气球多少个
红气球,黄气球和花气球一共有99只,已知花气球是黄气球的3倍,黄气球是红气球的两倍.球三种气球各有几只
某气球内充满了一定质量的气球,当温度不变时,气球内气球的压力p(千帕)是气球的体积V(米2)的反比例函数,其图象如图所示
为什么充满空气的气球不能悬浮在空气中?