need help, calculus
Lagt inn: 29/10-2015 00:27
A tumbler stands on a flat table. The glass consists of a right circular cylindrical shell with inner radius 33 cm, height 1010 cm and mass $m_s = 50$ grams in the top of a massive, cylindrical base with height 1 cm and mass mbmb = 10 grams. For each $x \in [0, 10]$, let $h (x)$ be the height of the center of gravity of the glass with content across the table, when water height from the bottom of the glass is xx cm. We have then
\begin{equation} h(x) = \dfrac {m_b h_b + m_s h_s + m_v h_v}{m_b + m_s + m_v} \end{equation}
where hbhb cm is the height of the center of gravity for the glass bottom of the table, hshs cm height the center of gravity of the glass sidewall of the table, etc. gram is the mass of water and hvhv cm, the height of center of gravity above the water table. a) Explain why $h_b = 0.5$, $h_s = 6$, $m_v = 9π x$ and $h_v = 1 + x/2$. You can think that 11 cubic centimeter of water has lots of exactly 11 gram.
b) Calculate $h (0)$ and $h (10)$. How can these function values interpreted?
c) Determine where hh wax and wane on scoping $D_h = [0, 10]$. Find any local and global extremal for hh.
d) What water height xixi glass gives the lowest height $h (x)$ for the center of gravity?
e) Calculate the value of the function $h (x$) corresponding value for xx that was in d). What you discover?
\begin{equation} h(x) = \dfrac {m_b h_b + m_s h_s + m_v h_v}{m_b + m_s + m_v} \end{equation}
where hbhb cm is the height of the center of gravity for the glass bottom of the table, hshs cm height the center of gravity of the glass sidewall of the table, etc. gram is the mass of water and hvhv cm, the height of center of gravity above the water table. a) Explain why $h_b = 0.5$, $h_s = 6$, $m_v = 9π x$ and $h_v = 1 + x/2$. You can think that 11 cubic centimeter of water has lots of exactly 11 gram.
b) Calculate $h (0)$ and $h (10)$. How can these function values interpreted?
c) Determine where hh wax and wane on scoping $D_h = [0, 10]$. Find any local and global extremal for hh.
d) What water height xixi glass gives the lowest height $h (x)$ for the center of gravity?
e) Calculate the value of the function $h (x$) corresponding value for xx that was in d). What you discover?