Pre-calculus Questions from Nov 22,2024

Browse the Pre-calculus Q&A Archive for Nov 22,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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I. \( f: x \rightarrow x^{2}-2 \) and \( y x \rightarrow 2 x-1 \), find \( f \circ g(x) \quad \) (B) \( \operatorname{gof}(x) \) Sketch the graph of the following polar equation by transforming it to rectangular coordinates. \( \mathrm{r}=-\frac{6}{\cos \theta+\sin \theta} \) The rectangular equation for \( \mathrm{r}=-\frac{6}{\cos \theta+\sin \theta} \) is (Type an equation. Use integers or decimals for any numbers in the equation.) Find an equivalent equation in rectangular coordinates and graph the equation. \( \mathrm{r}=9 \csc \theta \) Choose the rectangular equation that is equivalent to \( \mathrm{r}=9 \csc \theta \). A. \( y=9 \) B. \( x=9 \) C. \( \sqrt{x^{2}+y^{2}}=9 x \) D. \( \sqrt{x^{2}+y^{2}}=9 y \) Find an equivalent equation in rectangular coordinates and graph the equation. \( r=-8 \cos \theta-10 \sin \theta \) A. \( (x-5)^{2}+(y-4)^{2}=41 \) B. \( (x+4)^{2}+(y+5)^{2}=41 \) C. \( 41=8 x-10 y \) D. \( y=-8 \sin x-10 \cos x \) Convert the polar equation to rectangular form and identify the graph. \( r r=-18 \sin \theta \) The polar equation \( \mathrm{r}=-18 \sin \theta \) is equivalent to the rectangular equation (Type an equation. Type your answer in standard form.) Fort 1 of 2 \( x^{2}+y^{2}=64 \) The polar form of the rectang rectangular equation, give the equivalent polar equation and sketch its graph. (Use a comma to separate answers as needed. Type each answer only once.) For the following rectangular equation, give the equivalent polar equation and sketch its graph. \[ x^{2}+y^{2}=81 \] The polar form of the rectangular equation is (Use a comma to separate answers as needed. Type each answer only once.) For the following rectangular equation, give the equivalent polar equation and sketch its graph. \[ \mathrm{x}^{2}+\mathrm{y}^{2}=81 \] The polar form of the rectangular equation is (Use a comma to separate answers as needed. Type each answer only once.) \( \leftarrow \begin{array}{l}\text { Use transformations to sketch a graph of } f \text {. } \\ f(x)=(x+1)^{2}-2 \\ \text { Use the graphing tool to graph the function. }\end{array} \) For the following rectangular equation, give the equivalent polar equation and sketch its graph. \( x-y=12 \) The polar form of the rectangular equation is (Use a comma to separate answers as needed. Type each answer only once.)
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