4. A pebble is flicked upward from a height of 0.81 meter. The position function \( s(t)=-4.756 t^{2}+2.590 t+0.810 \) gives the height (in meters) of the pebble after \( t \) seconds. a) Find \( s^{\prime}(t) \). b) Explain how you can use \( s^{\prime}(t) \) to determine the maximum height of the pebble. What is the velocity of the pebble when it reaches its maximum height? c) For which values of \( t \) is \( s^{\prime} \) positive? For which values of \( t \) is \( s^{\prime} \) negative? What does the graph of \( s^{\prime} \) tell you about the graph of \( s \) ?

Semplifica le seguenti espressioni. \( 222\left(\frac{1}{3}+\frac{5}{2}-\frac{7}{12}\right)+\left(\frac{5}{4}+\frac{9}{6}\right)-\left(\frac{1}{2}+2\right) \)

the function \( h(x) \) below, select the answer choice which correctly decomposes \( h(x) \) into component x). so that \( h(x)=f(g(x)) \). \[ h(x)=\sqrt{-5 x+9}-8 \]

\( \begin{array}{ll}\text { 1.) } h(x)=\frac{5}{4 x+6} & \text { 3.) } g(x)=\frac{x-2}{x+6} \\ \text { 2.) } f(x)=\frac{5 x}{2 x-8} & \text { 4.) } f(x)=\frac{x^{2}-9 x+20}{x-6} \\ \text { 5.) } g(x)=\frac{2 x^{2}-x+1}{x^{2}-6 x+9}\end{array} \)

1. Distancia entre dos puntos: a. Calcula la distancia entre los puntos \( A(3,4) \) y \( B(7,1) \) b. Halla la distancia entre \( P(-2,5) \) y \( Q(3,-4) \)

Question The hypotenuse of a right triangle is 10 cm long. One of the triangle's legs is three times the length of the other leg. Find the lengths of the three sides of the triangle. In case of non-integer answer(s), round your answer(s) to the nearest hundredth. Provide your answer below: