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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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A bicycle wheel has a diameter of 63 cm . Calculate how many times the wheel turns round in travelling 19.8 km . Use the value \( 3 \frac{1}{7} \) for \( \pi \). 24.2 Trovare la forma canonica e riconoscere il tipo della quadrica \[ \mathscr{Q}: x y+y z=z . \] To È più conveniente riscrivere la quadrica come \( \mathscr{Q}: 2 x y+2 y z-2 z=0 \). Le sociate sono allora \( A=\left(\begin{array}{llll}0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1\end{array}\right) \quad Q=\left(\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right) \) A right triangle has a hypotenuse measuring 13 units and one leg measuring 5 units. Determine the length of the other leg. Find the equation of a circle whose end points of any diameter are \( (2,-1) \) and \( (-2,2) \). Calculate the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Find the equation of a circle whose centre is \( (2,-1) \) and which passes through the point \( (3,6) \) ? Con la traslazione (T) \( \left\{\begin{array}{l}x^{\prime \prime}=x^{\prime}+\frac{\sqrt{2}}{10} \quad \text { la conica diventa } \mathscr{C}^{\prime \prime \prime}: 5 x^{\prime \prime 2}-y^{\prime \prime 2}=\frac{1}{10}: 0,0 \\ y^{\prime \prime}=y^{\prime}\end{array}\right. \) in forma canonica euclidea \[ \mathscr{C}^{\prime \prime}: \frac{x^{\prime \prime 2}}{\left(\sqrt{\frac{1}{50}}\right)^{2}}-\frac{y^{\prime \prime 2}}{\left(\sqrt{\frac{1}{10}}\right)^{2}}=1 \] Riscalando gli assi cartesiani con \( \oint \cdot\left\{\begin{array}{l}X=\sqrt{50} x^{\prime \prime} \\ Y=\sqrt{10} y^{\prime \prime}\end{array} \quad\right. \) si trova la forma canonica affion \( \mathscr{I}: X^{2}-Y^{2}=1 \). L'affinità che ha trasformato \( \mathscr{C} \) in \( \mathscr{I} \) è \( f=\phi \circ \tau \circ \rho \). Passiampo a \( \mathscr{D} \). Gli autovalori di \( Q^{\prime} \) sono 3 e -1 con gli autospazi \( E(3)=\mathcal{L}(\sqrt{3}, 1) \) e \( E(-1) \) \( \mathcal{L}(-1, \sqrt{3}) \). Usiamo allora la matrice ortogonale \( N=\left(\begin{array}{cc}\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ 1 & \sqrt{3}\end{array}\right) \) con la rotario 11. Prostorija je duga 4 m i široka 256 cm . Ob pločicama kvadratnog oblika što većih di svake takve pločice? Radius of the base of a cone is 7 cm and its slant height is 10 cm . Find its i) curved surface area ii) total surface area. ( choose suitable value of pi) Find the radius of \( a \) sphere whose surface area is 616 cm
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