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Home Question Bank Math Geometry Archive 2025 January 01

Geometry Questions from Jan 01,2025

Browse the Geometry Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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EsERCIzIo 16.8 Si considerino i vettori in \( \mathbb{R}^{3} \) \[ v_{1}=(1,2,-1) \quad v_{2}=(1,0,1) \quad v_{3}=(1,2,0) \] (i) Calcolare \( \left\|v_{1}\right\|,\left\|v_{2}\right\| \) e \( \left\|v_{3}\right\| \). (ii) Calcolare gli angoli individuati dai tre vettori. (iii) Determinare tutti i vettori contemporaneamente ortogonali a \( v_{1} \) e \( v_{2} \) e provare che formano un sottospazio vettoriale di \( \mathbb{R}^{3} \). (iv) Calcolare tutti i vettori ortogonali a \( w=\frac{1000}{873} v_{3} \). (v) Determinare la proiezione ortogonale di \( v_{1} \) e \( v_{3} \) sulla direzione del vettore \( v_{2} \). Svolgimento 2) Solve triangle \( D E F \) \( m \angle D=69,1^{8}, m \angle F=55,4^{8}, m \angle F=55,5^{\circ} \) \( m \angle D=59,1^{8}, m \angle B=62,4^{8}, m \angle F=58.5^{\circ} \) \( m \angle D=62.1^{\circ}, m \angle B=63,4^{\circ}, m \angle F=54.5^{\circ} \) \( m \angle D=59,1^{8}, m \angle E \equiv 67.4^{\theta}, m \angle F=53.5^{\circ} \) What is a circle? 30 M . Tako veut franchir à l'aide d'une échelle un mur vertical de \( 3,5 \mathrm{~m} \) de haut devant lequel se trouve un fossé rempli d'eau, large de \( 1,15 \mathrm{~m} \). Pour cela, il doit poser l'échelle sur le sommet du mur. Détermine la longueur minimum de cette échelle arrondie au centimètre près. 29 L'unité de longueur est le centimètre. un rectangle a une aire de \( 74 \mathrm{~cm}^{2} \) et une longu de \( 14,8 \mathrm{~cm} \). 1. Justifie que : sa largeur est de 5 cm . 2. Calcule la longueur de ses diagonales. (On donnera l'arrondi du résultat au \( 10^{\circ} \) près Ankit has a block of ice in the shape of a cube that has a volume of \( 27 \mathrm{ft}^{3} \). Ankit plans to cut the ice block into small ice cubes that measure 2 inches in all directions. How many such ice cubes can Ankit create? (Note: There are 1728 cubic inches in \( 1 f^{3} \).) EsERCIzio 16.2 Determinare l'angolo (anche a meno del segno) compreso tra i seguenti vettori : (i) \( v=(2,1) \) e \( w=(-1,2) \) in \( \mathbb{R}^{2} \) (ii) \( v=(0,1,1) \) e \( w=(1,2,1) \) in \( \mathbb{R}^{3} \); (iii) \( v=(-1,0,-1) \) e \( w=(1,2,0) \) in \( \mathbb{R}^{3} \). 22. Calcola I'area della superficie totale e il volume di un prisma quadrangolare rego- lare sapendo che la somma degli spigoli misura 192 cm e che lo spigolo laterale è congruente al doppio dello spigolo di base. \( \left[1440 \mathbf{c m}^{2} ; 3456 \mathbf{c m}^{3}\right] \) - Calcola I'area della superficie totale e il volume di un prisma quadrangolare rego- lare sapendo che la somma degli spigoli misura 192 cm e che lo spigolo laterale è congruente al doppio dello spigolo di base. [1440 cm²; \( \left.\mathbf{3 5 6} \mathbf{c m}^{3}\right] \) In a right triangle, the lengths of the legs are given as 12 units and 5 units. Use the Pythagorean theorem to find the length of the hypotenuse.
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