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3. Find a vector perpendicular to the plane of using the points \( P=(1,2,-4) \), \( Q=(2,5,-7) \) and \( R=(3,-5,-1) \). Also find area of the parallelogram and area of triangle. Furthermore find a unit vector perpendicular to the plane using these points.

Un cône a un rayon de base de 2 m et une hauteur de 6 m, et il est posé sur un prisme rectangulaire ayant des dimensions de 4 m de longueur, 3 m de largeur et 2 m de hauteur. Quelle est la surface totale du solide composite ?

\begin{tabular}{l} Considérons la fonction numérique \( f \) de la variable \\ réelle \( x \) définie sur \( \mathbb{R} \) par : \( f(x)=\frac{1}{2} \sqrt{x^{2}+3} \) \\ 1. a) Montrer que : \( f^{\prime}(x)=\frac{x}{2 \sqrt{x^{2}+3}} \) pour tout \\ \( x \geq 0 \), puis dresser le tableau de variations de la \\ fonction \( f \) sur \( \mathbb{R} \). \\ a) Montrer que : \( f([0 ; 1] \subset[0 ; 1[ \). \\ \hline 2. a) Résoudre dans \( \mathbb{R} \) l'équation \( (E): f(x)=x \). \\ b) Montrer que : \( f(x)>x \) pour tout élément \\ \( x \) de l'intervalle \( [0 ; 1[ \). \end{tabular}

Simplify: \[ \frac{2^{x}-2^{-x}}{4^{x}-1} \]

Найдите частную производную по переменной у функции \( x^{2}-3 y^{2}+2 z^{2}=4 \)

Explain the difference between exponential growth and exponential decay.

\begin{tabular}{l} Find the third proportion of each \\ \( \begin{array}{ll}{[1] 6,12} & {[2] \mathrm{x}^{2},-5 \mathrm{x}}\end{array} \) \\ \hline\end{tabular}

If \( x \% \) of Rs. 440 is Rs. 22 , then find \( x \)

If \( 2 \mathrm{a}-\frac{1}{2 \mathrm{a}}=3 \) then \( 16 \mathrm{a}^{4}+\frac{1}{16 \mathrm{a}^{4}} \) is?

3. On windy days, we will feel cooler compared to calm days without wind. The rate of heat loss, \( H \) (in kilocalories per square meter per hour), when the air temperature, \( t \) (in degrees Celsius), and the wind speed, \( w \) (in meters per second), are determined by the equation \( H=(10.45+10 \sqrt{w}-w)(33-t) \). Evaluate \( H \) when \( t=0 \) and \( w=4 \). a. Evaluate \( \frac{\partial H}{\partial t}, \frac{\partial H}{\partial w} \) when \( t=0 \) and \( w=4 \). Interpret the results! c. When \( t=0 \) and \( w=4 \), Which one has a greater influence on \( H \). a change in wind speed of \( 1 \mathrm{~m} / \mathrm{s} \) or a change in temperature of \( 1{ }^{\circ} \mathrm{Cl} \) ?