4. What is the radius of a circle (rounded to the nearest tenth) that has an area of 32 ? 3.2 5.1 10.2 6.4

Triangles \( \triangle A O B \) and \( \triangle A O C \) have vertices \( A(0,7), B(-1,-2), C(2,-1) \), and \( O(0,0) \). Show that \( m \angle A O B>m \angle A O C \). Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to the nearest thousandth as needed.) A. Since \( A B=\square \) and \( A C=\square, \overline{A B}>\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). B. Since \( A B=\square \) and \( A C=\square, \overline{A B}=\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \). C. Since \( A B=\square \) and \( A C=\square, \overline{A B}<\overline{A C} \), and thus \( m \angle A O B>m \angle A O C \).

If the diameter of a circle is doubled, how does it affect the circumference?

4. (30\%) Sean \( A=(-3,2,0), B=(0,0,4), C=(2,1,-1) \) y \( P=(-3,4,0) \) a. Encuentre la ecuación del plano \( \pi(A, B, C) \) b. Determine la distancia entre el plano \( \pi(A, B, C) \) y el punto \( P \) c. Hallar el volumen del tetraedro \( A B C P \)

Halla el centro y el radio de cada una de las siguientes circunferencias y realiza la gráfica. a. \( 2 x^{2}+2 y^{2}+14 x-10 y+35=0 \) b. \( x^{2}+y^{2}-8 x-10 y+40=0 \) c. \( x^{2}+y^{2}+4 x-6 y=5 \) d. \( x^{2}+y^{2}+10 x-6 y-24=0 \) e. \( x^{2}+y^{2}-23 x+35 y+1 / 75=0 \)

\( f(x)=x^{2}-2 x+2 \) centre de symetrie?