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Home Question Bank Math Pre Calculus Archive 2024 November 10

Pre-calculus Questions from Nov 10,2024

Browse the Pre-calculus Q&A Archive for Nov 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the vector \( \mathbf{v} \) with the given magnitude and the same direction as \( \mathbf{u} \). \[ \begin{array}{l}\text { Magnitude Direction } \\ \|\mathbf{v}\|=20 \quad \mathbf{u}=\langle-3,4\rangle\end{array} \] \( \mathbf{v}=\square \) Need Help? Read It Find a unit vector \( \mathbf{u} \) in the direction of \( \mathbf{v} \). Verify that \( \|\mathbf{u}\|=1 \). \[ \mathbf{v}=\langle-6,6\rangle \] \( \mathbf{u}= \) Need Help? Read It Dada la función \[ H(x)=\operatorname{sen}\left(\ln \left(x^{2}+2\right)\right) \] tres funciones \( f(x), g(x) \) y \( h(x) \) tales que \( (f \circ g \circ h)(x)=H(x) \) son: Seleccione una: \( f(x)=\operatorname{sen} x, g(x)=\ln x, h(x)=x^{2}+2 \) \( f(x)=x^{2}+2, g(x)=\operatorname{sen} x, h(x)=\ln x \) \( f(x)=x^{2}+2, g(x)=\ln x, h(x)=\operatorname{sen} x \) \( f(x)=\ln x, g(x)=\operatorname{sen} x, h(x)=x^{2}+2 \) Sean \( f(x)=\frac{4}{x-6}, g(x)=\frac{x}{x-3} \) hallar el dominio y simplifica la expresión de \( (f+g)(x) \) Seleccione una: a. Dominio: \( \mathbb{R}-\{3,6\} \) Expresión: \( (f+g)(x)=\frac{x^{2}-2 x-12}{(x+6)(x+3)} \) Dominio: \( \mathbb{R}-\{-3,-6\} \) Expresión: \( (f+g)(x)=\frac{x^{2}-2 x-12}{(x-6)(x-3)} \) Dominio: \( \mathbb{R}-\{3,6\} \) Expresión: \( (f+g)(x)=\frac{x^{2}+2 x+12}{(x-6)(x-3)} \) Dominio: \( \mathbb{R}-\{3,6\} \) Expresión: \( (f+g)(x)=\frac{x^{2}-2 x-12}{(x-6)(x-3)} \) A driver has something to do with his or her chance of getting into a fatal car crash. The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups. For example, 25 -year-old drivers are involved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25 -year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died. The number of fatal vehicle crashes per 100 million miles, \( \mathrm{f}(\mathrm{x}) \), for drivers of age x can be modeled by the following quadratic function. \( \mathrm{f}(\mathrm{x})=0.013 \mathrm{x}^{2}-1.19 \mathrm{x}+28.24 \) Consider the function \( g(x)=2^{x-3}-8 \) a. Write down the range of \( g(x) \) Graph the function \( f(x)=-(x-5)^{2}-5 \) using the graph of \( f(x)=-x^{2} \) and your knowledge of translations. Graph the function \( f(x)=-(x-1)^{2}+2 \) using the graph of \( f(x)=-x^{2} \) and your knowledge of translations. Answer Drag the point on the graph to complete the horizontal and vertical translations. Points can be moved by dragging or using the arrow keys. Enable Zoom/Pan Considere a função \( f(x)=-x^{2}-4 x+2 \) e as afirmações a seguir: I-O gráfico da função possui concavidade para cima. II -0 gráfico da função intercepta o eixo OY em \( P(0,2) \). III -0 vértice da função será o ponto \( V(-2,6) \). IV - Trata-se de uma função crescente. V - Para \( x=0 \), temos \( f(x)=-3 \). É CORRETO AFIRMAR que: You go to the doctor and he gives you 12 milligrams of radioactive dye. After 20 minutes, 4.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend
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