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Home Question Bank Math Geometry Archive 2025 January 05

Geometry Questions from Jan 05,2025

Browse the Geometry Q&A Archive for Jan 05,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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PTKQ is a cyclic quadrilatera A stick 2 m long is placed vertically at point \( B \). The top of the stick is in line with the top of a tree as seen from point \( A \), which is 3 m from the stick and 30 m from the tree. How tall is the tree? 2. A stick 2 m long is placed vertically at point \( B \). The top of the stick is in line with the top of a tree as seen from point \( A \), which is 3 m from the stick and 30 m from the tree. How tall is the tree? le plan étant rapporte à un reppere othonormé \( (0, \vec{v}, \vec{j}) \), on considère les points \( A(2,1) ; B(1,3) ; C(-1,2) \) et les vectewns \( \vec{u}(m+3,2) \) et \( \vec{v}(1, m+2) \) où \( m \in \mathbb{R} \) 1) Donner une équation cartisienne de la hait ( \( A B \) ) Pour éviter les accidents, un fermier en- toure sa nuare d'un grillage. Le tour de la mare nacsure 18 m et entre 2 piquets l'intervalle est de 3 m . De combien de piquets a-t-il hesoin? The real length of a road is 10 km . (b) Work out the length of the road on the map. Give the units of your answer. A map has a scale of 1 cm represents 4 km . On the map, the distance from town A to town B is 8 cm . (a) Work out the real distance, in km . from town A to town B . The size of the interior angle of a regular polygon \( 6 \% \), times the size of the exterior angle. Colculate tho sum of the interior angles of the polygon \[ \text { Q: } x y+x z+y z=0 \text {. } \] La quadrica nom muta se, per comodith, molliplichiamo if nool coefficienti per 2 . Alboy (2) \( : 2 x y+2 x z+2 y z=0 \). Le matrici ansociate a \( B \) sonno \( A=\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0\end{array}\right)=Q= \) \( \left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right) \), Abbiamo che rk \( A=r k Q=3 \). Ci aspettiamo un quardrica di tipo crealima Poiche 2 pansa per l'origine, si tratta di un cono ellittico reale. Gli autovalori di \( q \) somo \( \lambda=-1 \) con molteplicitaे 2 e \( \lambda=2 \) che e semplice. Ora, sicoome 2 non contiotion termini di grado uno ne termine noto, abbiamo finito. La sua forma carionica e \( Z^{2}=\frac{x^{2}}{(\sqrt{2})^{2}}+\frac{y^{2}}{(\sqrt{2})^{2}} \), che come ci aspettavamo, rappresenta un cono. Esencizio syotto 19.4 Variamo legecrmente l'eguazione dell'esercizio precedent SERCIzIO svolto 19.3 Classificare e portare in forma canonica la quadrica \[ \mathscr{Q}: x y+x z+y z=0 \]
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