\( 1.4 \quad \frac { 5 ^ { 2 x } - 1 } { 5 ^ { x } + 1 } = 4 \)

The height \( h \), in feet, of a projectile can be modeled by the equation \( h(t)=-16 t^{2}+v_{0} t+h_{0} \) where \( t \) is the time in seconds, \( h_{0} \) is the projectile's initial height in feet, and \( v_{0} \) is the projectile's initial vertical velocity in feet per second. Solve the projectile motion problem by completing the square. A soccer player kicks a soceer ball from the ground with an initial vertical velocity of var : \( v 0 \) feet per secoad. When will the ball land back on the ground? Round to the nearest tenth of a second. Enter the correct value in the box. Show Hints The ball will land on the ground again in \( \square \) second(s).

(a4) The solution set of the equation : \( \sqrt[3]{x^{2}}-3 \sqrt[3]{x}+2=0 \) is \( \{1,8\} \) \( \begin{array}{llll}\text { (a) }\{1, & \text { (b) }\{9,3\} & \text { (c) }\{8\} & \text { (d) }\{1\}\end{array} \)

Determine the geometric sequence if the second term is \( \frac{1}{9} \) and the sixth term is \( \frac{1}{729} \)

Factor completely: \[ 2 u^{4} w^{4}-2 w^{4} \]

Le plan est muni d'un repère orthonormé \( (O, I, J) \). Soit la fonction \( g \) définie sur \( \mathbb{R} \backslash\{-1\} \) par : \( g(x)=\frac{2 x+5}{x+1} \). On désigne par (C) la courbe représentative de \( f \) dans le plan muni du repère \( (O, I, J) \). 1. a) Démontre que pour tout \( x \) élément de \( \mathbb{R} \backslash\{-1\} g(x)=2+\frac{3}{x+1} \). 2. Démontre que: \( \frac{g(-1-x)+g(-1+x)}{2}=2 \). 3. Justifie que le point \( A(-1 ; 2) \) est un centre de symétrie de (C). 4. a) Calcule \( g(4) \). b) Sans utiliser une des expressions de \( g \), calcule \( g(-6) \).