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Home Question Bank Math Archive 2025 January 18

Math Questions from Jan 18,2025

Browse the Math Q&A Archive for Jan 18,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A partir de la identidad pitagórica, deriva la relación entre \( \cot(x) \), \( \sin(x) \) y \( \cos(x) \). EXERCISE 2 Consider the following functions: \( \begin{array}{lll}\text { (a) } f(x)=2 x+4 & \text { (b) } f(x)=3 x-6 & \text { (c) } f(x)=\frac{1}{2} x+3 \\ \text { (d) } f(x)=4 x-1 & \text { (e) } f(x)=-2 x & \text { (f) } f(x)=2 x-5\end{array} \) \( \begin{array}{ll}\text { (1) For each function determine } f^{-1} \text {, the inverse function in the form } f^{-1}(x)=\ldots \ldots \\ \text { (2) Hence draw neat sketch graphs of both functions on the same set of axes. } \\ \text { (3) Draw the line of symmetry on the same set of axes as the two graphs. } \\ \text { (4) Determine the coordinates of the point of intersection of both graphs and } \\ \text { then indicate this point on the diagram. }\end{array} \) Name: G5 Lessons 11-13 Review Multiplying and Dividing with Fractions Homework 1. Rocky finished a 200 -meter race in \( \frac{5}{12} \) of a minute. The winner of the race used \( \frac{21}{25} \) of Rocky's time to finish the race. How much time did the winner use to finish the race? Sia \( f \) una funzione derivabile su \( \mathbb{R} \), tale che \( \lim _{x \rightarrow+\infty} f^{\prime}(x)=3 \). È vero che: Scegli un'alternativa: \( f \) è limitata su una semiretta \( (a,+\infty) \) \( \lim _{x \rightarrow+\infty} f(x)=3 \) \( f \) ha asintoto obliquo destro \( f \) è un infinito di ordine 1 rispetto a \( x \), per \( x \rightarrow+\infty \) © non è necessariamente crescente su una semiretta \( (a,+\infty) \approx \) 1. Rocky finished a 200 -meter race in \( \frac{5}{12} \) of a minute. The winner of the race used \( \frac{21}{25} \) of Rocky's time to finish the race. How much time did the winner use to finish the race? EXERCISE 2 Consider the following functions: \( \begin{array}{lll}\text { (a) } f(x)=2 x+4 & \text { (b) } f(x)=3 x-6 & \text { (c) } f(x)=\frac{1}{2} x+3 \\ \text { (d) } f(x)=4 x-1 & \text { (e) } f(x)=-2 x & \text { (f) } f(x)=2 x-5\end{array} \) \( \begin{array}{ll}\text { (1) For each function determine } f^{-1} \text {, the inverse function in the form } f^{-1}(x)=\ldots \ldots . \\ \text { (2) Hence draw neat sketch graphs of both functions on the same set of axes. } \\ \text { (3) Draw the line of symmetry on the same set of axes as the two graphs. } \\ \text { (4) Determine the coordinates of the point of intersection of both graphs and } \\ \text { then indicate this point on the diagram. }\end{array} \) \( \sum _ { i = 0 } ^ { m } ( 1 - 3 i ) = - 671 \) Data la funzione \( f(x)=\frac{x-1}{x^{3}+x^{2}-x-1} \), è vero che Scegli un'altemativa: \( f \) è limitata \( x \) \( f \) è un infinito di ordine 2 rispetto a \( \frac{1}{x+1} \), per \( x \rightarrow-1 \) \( \lim _{x \rightarrow-1} f(x) \) non esiste \( \lim _{x \rightarrow-1} f(x) \) esiste finito \( f \) è un infinito di ordine 1 rispetto a \( \frac{1}{x+1} \), per \( x \rightarrow-1 \) \( \sum _ { i = 0 } ^ { m } ( 1 - 3 i ) = - 671 \) L'equazione \( \operatorname{Im}\left(z \bar{z}+\frac{1}{z}+z+\bar{z}\right)=0: \) Scegli un'alternativa: ha un numero finito di soluzioni immaginarie pure ha un numero finito di soluzioni reali ha infinite soluzioni immaginarie pure \( \mathbf{x} \) non ha soluzioni
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