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Home Question Bank Math Archive 2025 January 08

Math Questions from Jan 08,2025

Browse the Math Q&A Archive for Jan 08,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve for \( u \), where \( u \) is a real number. \[ \sqrt{u}=2 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( u=\square \square \) D. Look at Quadrant IV. What values can the \( x \)-coordinate of an ordered pair in this quadrant have? What values can the \( y \)-coordinate have? In an arithmetic sequence, if the first term is 5 and the common difference is 3, what are the first four terms of the sequence? |ll \( \begin{array}{l}4 x-5 y=-20 \\ 3 x+y=23\end{array} \) Look at Quadrant III. What values can the \( x \)-coordinate of an ordered pair in this quadrant have? What values can the \( y \)-coordinate have? 3.) \( \left(\frac{2}{3}\right)^{x}=\frac{16}{81} \) 131 Étudier la convexité d'une fonction Un ébéniste décide de refaire les accoudoirs d'un fauteuil. On modélise l'accoudoir à l'aide de la fonction \( f \) définie sur \( [0 ; 60] \) par : \[ f(x)=70+(14 x+42) \mathrm{e}^{-\frac{x}{5}} \text {. } \] Soit \( \mathscr{C}_{f} \) la courbe représentative de \( f \). On admet que la fonction \( f \) est deux fois dérivable sur l'intervalle \( [0 ; 60] \). On note \( f^{\prime} \) sa fonction dérivée et \( f^{\prime \prime} \) sa fonction dérivée seconde. 1. Montrer que pour tout nombre réel \( x \) de \( [0 ; 60] \), \( f^{\prime}(x)=\frac{1}{5}(-14 x+28) \mathrm{e}^{-\frac{x}{5}} \). 2. Étudier le signe de \( f^{\prime}(x) \) sur \( [0 ; 60] \) et dresser son tableau de variations. In \( \triangle A D C, \angle D=90^{\circ} ; \angle C=45^{\circ} \) \( A D=8 \) then find \( A C \). Simplify the expression. Do not use spaces between numbers or signs. \( 12 c-c= \) Consider the scores of 50 students of Grade 10 obtained in an examination. The maximum marks of the exam are 50 . \( 49,25,10,9,35,36,37,14,27,35,26,38,38 \), \( 29,37,37,8,38,28,30,39,40,42,42,15,16 \), \( 16,17,20,25,27,28,30,14,30,31,47,50 \), \( 12,14,12,21,45,46,11,25,30,33,34,45 \)
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