Exercise 22.1 1. Plot points \( \mathrm{A}(2 ; 3), \mathrm{B}(5 ;-3) \) and \( \mathrm{C}(-4 ; 2) \) on a coordinate plane. 1.1 Translate point A 5 places down and 4 places left and name the image \( A^{\prime} \).

Exercice 2: (1) Montrer les implications suivantes: a \( (\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}) ; \quad \mathrm{Si} \quad(|\mathrm{x}| \leq 1 \) et \( |y| \leq 1) \quad \) alors \( \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}} \leq 2 \sqrt{1-\left(\frac{\mathrm{x}+\mathrm{y}}{2}\right)^{2}} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{*}\right) ; \quad 2 \mathrm{x}+4 \mathrm{y}=1 \Rightarrow \frac{1}{\mathrm{x}^{2}+\mathrm{y}^{2}} \leq 20 \) (2) En utilisant "Le raisonnement par les équivalences successives", montrer que: a \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{+}\right) ; \quad \mathrm{x} \sqrt{\mathrm{x}^{2}+1}=\mathrm{y} \sqrt{\mathrm{y}^{2}+1} \Longleftrightarrow \mathrm{x}=\mathrm{y} \) \( \mathrm{b}\left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}_{+}^{*}\right) ; \quad \mathrm{x} \prec \mathrm{y} \quad \Longleftrightarrow \quad \frac{\mathrm{x}}{\mathrm{y}} \prec \frac{2 \mathrm{x}+5 \mathrm{y}}{5 \mathrm{x}+2 \mathrm{y}} \prec \frac{\mathrm{y}}{\mathrm{x}} \)

2. \( f(x)=2 x^{2}+3 x-4 \) and \( g(x)=2 x+3 \), find the \( (f-g)(x) \) 3. \( f(x)=3 x-5 \) and \( g(x)=x \), Find the \( (f \bullet g)(x) \) 4. \( f(x)=3 x^{2}+4 x-3 \) and \( g(x)=x \), find the \( (f / g)(x) \)

Guide Question: After the exercise routine, answer the following question. 1. Categorized aerobic, muscle strengthening, and bone strengthening activities from the sets of exercises you performed.

guientes sum b. \( 7 / 3+4 / 5 \)

8) A roller coaster starts at the top of the hill at \( 0 \mathrm{~m} / \mathrm{s} \) and then races down to the bottom until it gets to \( 22.7 \mathrm{~m} / \mathrm{s} \) with an acceleration of \( 2.5 \mathrm{~m} / \mathrm{s}^{2} \). How long did it take to get from the top of the hill to the bottom in seconds?