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Home Question Bank Math Pre Calculus Archive 2024 November 20

Pre-calculus Questions from Nov 20,2024

Browse the Pre-calculus Q&A Archive for Nov 20,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A fountain shoots water from a nozzle at its top. The function \( f(x)=-5 t^{2}+10 t+15 \) describes the height of the water \( h(t) \), in metres, \( t \) seconds after it leaves the nozzle. What is the maximum height of the water spout? What is the domain and range of the logarithmic function \( y = \log(x) \)? Colin has 42 cm of wood to make a rectangular picture frame. What dimensions will give Colin the maximum area for his picture frame? Colin has 42 cm of wood to make a rectangular picture frame. What dimensions will give Colin the maximum area for his picture frame? Resuelve otros problemas se Otra aproximación del número \( \pi \) se puede ha- llar realizando la operación: \[ 2 \cdot \frac{2 \cdot 2 \cdot 4 \cdot 4 \cdot 6 \cdot 6 \cdot 8 \cdot 8}{1 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7 \cdot 9} \] ¿Cuáles factores se deben tomar, tanto en el nu- merador como en el denominador, para obre- ner una buena aproximación de \( \pi \) ? Graph the following function and its inverse on the same Cartesian plane. \( f(x)=2^{x} ; f^{-1}(x)=\log _{2} x \) The area, in \( \mathrm{m}^{2} \), of a rectangular deck is modelled by the function \( A(x)=84 x-2 x^{2} \). What dimensions will give the maximum area for the deck? 13 Bosqueje la curva con ecuación \( x^{2 / 3}+y^{2 / 3}=1 \) emplee la simetría para hallar su longitud. Exercice1 : On considère la suite \( \left(U_{n}\right) \) définie par : \[ \begin{array}{l}U_{0}=1 \\ U_{n+1}=\frac{5 U_{n}}{3 U_{n}+5}\end{array} \] 1) calculer \( U_{1} \) et \( U_{2} \) puis montrer que la suite ( \( \left.U_{n}\right) \) n'est ni arithmétique ni géométrique 2) On introduit la suite \( \left(V_{n}\right) \) de terme général \( V_{n}=\frac{5}{U_{n}} \) 4a) \( a(x)=\frac{5 x}{x^{2}-4} \)
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