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Home Question Bank Math Geometry Archive 2025 January 21

Geometry Questions from Jan 21,2025

Browse the Geometry Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Untersuche die gegenseitige Lage der beiden Ebenen \( \mathrm{E}:-7 x_{1}+6 x_{2}+6 x_{3}=84 \) und \( \mathrm{F}:-7 x_{1}+6 x_{2}+6 x_{3}=205 \) Berechne ggf. den Abstand. \( \begin{array}{l}\text { Ebenen sind identisch } \\ \text { Ebenen sind parallel, Abstand der parallelen Ebenen } \mathrm{d}= \\ \text { Ebenen schneiden sich }\end{array} \) Find the missing quantities for the following circle. Use the \( \pi \) key for \( \pi \). Radius Diameter Circumference (Type an integer or decimal rounded to the nearest tenth as needed.) Radius \( \approx \square \) ? (Type an integer or decimal rounded to the nearest tenth as needed.) L'area di un trapezio rettangolo è dí 960 cm la sua altezza è 30 cm e il suo lato obliquo m sura 34 cm . Calcola il perimetro del trapezio. [128 Untersuche die gegenseitige Lage der beiden Ebenen E: \( -7 x_{1}+4 x_{2}+4 x_{3}=-56 \) und F: \( 21 x_{1}-12 x_{2}-12 x_{3}=411 \) Berechne ggf. den Abstand. Ebenen sind identisch Ebenen sind parallel, Abstand der parallelen Ebenen d \( = \) 1 The minute hand on a dock is 15 cm long. What area does it pass over in 1 hour? 2 What area does the minute hand described in question 1 cover in 20 minutes? A circle is centered at \( D(-1,3) \). The point \( G(-10,1) \) is on the circle. Where does the point \( J(-3,12) \) lie? Aufgabe: \( (2 \) Punkte \( ) \) Gegeben sind zwei zueinander parallele Ebenen \( \mathrm{E}_{1}:-16 x_{2}-2 x_{3}=-16 \) und \( \mathrm{E}_{2}: \) \( +8 x_{2}+x_{3}=56 \). Die Ebene F ist parallel zu \( \mathrm{E}_{1} \) und \( \mathrm{E}_{2} \) und hat von beiden Ebenen den gleichen Abstand. Bestimme eine Gleichung der Ebene F . \[ \mathrm{F}:+\hat{v} \square \mathrm{x}_{1}+\hat{\mathrm{v}} \square \mathrm{x}_{2}+\hat{\mathrm{v}} \square \mathrm{x}_{3}=+\hat{\mathrm{v}} \] A circle is centered at \( O(0,0) \) and has a radius of \( \sqrt{29} \). Where does the point \( T(5,-2) \) lie? A circle is centered at \( C(0,0) \). The point \( M(0, \sqrt{38}) \) is on the circle. Where does the point \( N(-5,-3) \) lie? Untersuche die gegenseitige Lage der Gerade \( \mathrm{g}: \vec{x}=\left(\begin{array}{c}0 \\ 2 \\ 10\end{array}\right)+t \cdot\left(\begin{array}{c}-1 \\ 3 \\ 2\end{array}\right) \) mit der Ebene \( \mathrm{E}:-6 x_{1}-9 x_{2}+2 x_{3}=36 \) Berechne ggf. Abstand bzw. Durchstoßpunkt. \( \begin{array}{ll}\text { Gerade schneidet Ebene, Durchstoßpunkt } \mathrm{D}( \end{array} \) Gerade ist parallel zur Ebene, Abstand der Gerade von der Ebene d \( =\square \)
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