the Italian scientist Galileo Galilei dropped rocks o different weights from the top of the Leaning Towe of Pisa to prove his conjecture that the rocks would hit the ground at the same time. a. The original height of the tower was about 196 feet. Write a function \( h \) that gives the height (in feet) of a rock dropped from the top of the original tower after \( t \) seconds. Interpret each term. How long does the rock take to

1 In una circonferenza assegnata, di centro \( O \), traccia un diametro \( A B \) e su una delle semicirconferenze \( A B \) traccia nell'ordine i punti \( C, D, E, F e G \) in modo tale che gli archi \( \overparen{A C}, \overparen{C D}, \overparen{D E}, \widehat{E F}, \widehat{F G} \) e \( \overparen{G B} \) siano tutti tra loro congruenti. Dimostra che le corde \( A D, D F \) e \( F B \) sono congruenti. Dimostra poi che \( C G<2 D F \). Detto \( D^{\prime} \) il punto diametralmente opposto a \( D \), dimostra che \( C O / / A D \).

\( x + y = \left[ \begin{array} { c c } { - 1 } & { 0 } \\ { 3 } & { 5 } \end{array} \right] x - y = \left[ \begin{array} { l l } { 3 } & { 0 } \\ { 0 } & { 4 } \end{array} \right] \)

Consider the following problem: The radius \( r(t) \) of the base of a cylinder is increasing at a rate. of 1 meter per hour and the height \( h(t) \) of the cylinder is decreasing at a rate of 4 meters per hour. At a certain instant \( t_{0} \), the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume \( V(t) \) of the cylinder at that instant? Match each expression with its given value. \( h^{\prime}(t) \) \( \frac{d V}{d t} \)

Calcule o logaritmo. Arredonde sua resposta para a terceira casa decimal. \( \log _{2}\left(\frac{1}{50}\right) \approx \)

The graph of the function \( f(x)=x^{3}-3 x \) has one local maximum and one local minimum point. Find these points using the first derivative test. The function has a local maximum at the point (Type an ordered pair.)