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Home Question Bank Math Pre Calculus Archive 2024 December 18

Pre-calculus Questions from Dec 18,2024

Browse the Pre-calculus Q&A Archive for Dec 18,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( (\mathrm{y})^{*} \) Calculate the following sums: (1) \( \left(\frac{1}{4}+\frac{3}{4}\right)+\left(\frac{1}{6}+\frac{3}{6}+\frac{5}{6}\right)+\left(\frac{1}{8}+\frac{3}{8}+\frac{5}{8}+\frac{7}{8}\right)+\ldots+\left(\frac{1}{50}+\frac{3}{50}+\frac{5}{50}+\ldots+\frac{49}{50}\right) \) (2) \( 100^{2}-99^{2}+98^{2}-97^{2}+96^{2}-95^{2}+\ldots+2^{2}-1^{2} \) (3) \( 1+\sin ^{2} 2^{\circ}+3+\sin ^{2} 4^{\circ}+5+\sin ^{2} 6^{\circ}+\ldots+85+\sin ^{2} 86^{\circ}+87+\sin ^{2} 88^{\circ} \) The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=-5+\sqrt{x-1} \quad g(x)=\frac{2 x^{2}-6}{x^{2}} \quad h(x)=2|-3+x| \] Find \( f(6), g(-2) \), and \( h(-5) \). Simplify your answers as much as possible. Represent graphically the function \( f: f(x)=-x^{2}-2 x \) where \( x \in[-4,2] \) , from the graph deduce : 1 The coordinates of the vertex point of the curve. (2) The equation of the axis of symmetry. 3) The maximum value of the function. Exercicio 3. (10pts) Use o TVI para mostrar que \( p(x)=2 x^{3}-5 x^{2}-10 x+5 \) possui uma raiz no intervalo \( [-1,2] \). A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 5 hours there are 50,000 bacteria. At the end of 9 hours there are 80,000 . How many bacteria were initially present? A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 5 hours there are 50,000 bacteria. At the end of 8 hours there are 70,000 . How many bacteria were initially present? Déterminer le domaine de définition de la fonction \( f(x)=\sqrt{\frac{2 x+3}{4 x+7}} \). Écrire la réponse sous forme \( D_{f}=\ldots \) Réponse : La suite \( \left(v_{n}\right) \) est géométrique de raison 0.5 et \( v_{3}=16 \). La somme \( S=v_{3}+v_{4}+\ldots+v_{9} \) est égale à : a. \( 16 \times \frac{1-0.5^{3}}{1-0.5} \) b. \( 16 \times \frac{1-0.5^{6}}{1-0.5} \) c. \( 16 \times \frac{1-0.5^{10}}{1-0.5} \) d. \( 16 \times \frac{1-0.5^{7}}{1-0.5} \) Déterminer le domaine de définition de la fonction \( f(x)=\ln \left((x-9)^{2}\right) \). Ecrire la réponse sous forme \( D_{f}=\ldots \) Réponse : Déterminer le domaine de définition de la fonction \( f(x)=\ln \left(x^{2}+3 x-4\right) \). Ecrire la réponse sous forme \( D_{f}=\ldots \) Réponse:
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