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Home Question Bank Math Geometry Archive 2024 December 09

Geometry Questions from Dec 09,2024

Browse the Geometry Q&A Archive for Dec 09,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Determinar: (a) A equação da superfície de revolução gerada pela rotação da elipse \( 9 x^{2}+4 y^{2}=36 \), \( z=0 \), em torno do eixo \( y \). (Valor: 1,5 ); A circular garden has a radius of 5 meters. If you want to plant flowers around the entire edge, how many square meters of soil will you need for the flower bed? Complete the square and write the equation in standard form. Then give the center and radius of the circle. \( x^{2}+y^{2}+12 x-14 y=-81 \) A. \( (x+6)^{2}+(y-7)^{2}=4 \) Center: \( (-6,7) \), radius: 2 B. \( (x+6)^{2}+(y-7)^{2}=4 \) Center: \( (6,-7) \), radius: 4 C. \( (x-7)^{2}+(y+6)^{2}=4 \) Center: \( (7,-6) \), radius: 2 D. ( \( x-7)^{2}+(y+6)^{2}=4 \) Center: \( (-7,6) \), radius: 4 (a) A equação da superfície de revolução gerada pela rotação da elipse \( 9 \mathrm{x}^{2}+4 \mathrm{y}^{2}=36 \), \( \mathrm{z}=0 \), em torno do eixo y . (Valor: 1,5\( ) \); (b) A equação da superfície de revolução gerada pela rotação da parábola cujo foco é o ponto \( (0,0,0) \) e a diretriz é a reta \( 3 \mathrm{z}-7=0 \). em torno do eixo z . (Valor: 1,5 ). Hiku wants to create a rectangle in the coordinate plane. He plots \( (-4,-3),(6,2) \), and \( (6,-3) \). What is the other point that he needs to plot to complete his rectangle? Note: Do not use any spaces in your answer. The squm of the angles of a triangle is \( 180^{\circ} \). Find the three angles of the triangle if one angle is twice the sma angle and the third angle is \( 20^{\circ} \) greater than the smallest angle. A. \( 30^{\circ}, 60^{\circ}, 90^{\circ} \) B. \( 32^{\circ}, 64^{\circ}, 84^{\circ} \) C. \( 40^{\circ}, 80^{\circ}, 60^{\circ} \) D. \( 30^{\circ}, 50^{\circ}, 100^{\circ} \) (E) \( A B+B C<A C \) (B) \( \mathrm{m} \angle A+\mathrm{m} \angle B<90^{\circ} \) (1) \( \mathrm{m} \angle A+\mathrm{m} \angle B=90^{\circ} \) (1) \( A B+B C>A C \) Find the distance between the points \( (7,4) \) and \( (4,8) \). Write your answer as a whole number or a fully simplified radical expression. Do not round. \( \square \) units 10. Find the dimensions of the field if the width is at least 60 yds . Calculate the area of a circle with a radius of 5 m using \( \pi \\).
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