15. Эгерде \( 4^{2 x}=8^{3 y} \) жана \( y \neq 0 \) болсо, анда \( \frac{x}{y}=? \) А) \( \frac{1}{2} \) Б) \( \frac{2}{3} \) В) \( \frac{3}{2} \) Г) \( \frac{9}{8} \) д) \( \frac{9}{4} \)

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

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

The height \( h \), in feet, of a projectile can bo modelod 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 ini 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 lacrosse playor throws a ball into the air from a hoight of 8 foet with an initial vertical volocity of 30 feot per second. When will the ball hit the groun Round to the nearest tenth of a second. Enter the correct value in tho box. Show Hints The ball will hit the ground in \( \square \) seconds.

Factor completely: \[ 32 v^{3}-2 v^{3} x^{4} \]

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 \( g(-6) \).