91Ó°ÊÓ

\(\text { In } \triangle \mathrm{AOB}, \mathrm{A}=(6,0), \mathrm{B}=(0,8), \text { and } \mathrm{O}=(0,0)\) a. Find, to the nearest tenth, the volume of the solid formed by rotating the triangle about \(\overline{\mathrm{OA}}\). b. Find, to the nearest tenth, the volume of the solid formed by rotating the triangle about \(\overline{\mathrm{OB}}\). c. Find, to the nearest tenth, the volume and the total surface area of the solid formed by rotating the triangle about \(\overline{\mathrm{AB}}\).

Given the circles represented by \((x+9)^{2}+(y-4)^{2}=52\) and \((x-12)^{2}+(y-3)^{2}=13,\) find the length of a a Common internal tangent b Common external tangent

Find the center of the circle containing \(\mathrm{D}=(-3,5), \mathrm{E}=(3,3)\) and \(F=(11,19)\) Note The center of this circle is called the circumcenter of \(\triangle \mathrm{DEF}\)

Find the area of the quadrilateral with vertices at \((-3,2),(15,6)\) \((7,12),\) and \((-7,8)\)

Find the reflection of the point \((-9,7)\) over the reference line \(y=x\)

Find an equation of the reflection of the graph of \(y=\frac{3}{4} x-1\) over a The x-axis \(\quad\) b The y-axis \(\quad\) c The line \(y=x\)

A lattice point is a point whose coordinates are integers. How many lattice points are on the boundary and in the interior of the region bounded by the positive \(x\) -axis, the positive y-axis, the graph of \(x^{2}+y^{2}=25,\) and the line passing through \((-3,0)\) and \((0,2) ?\)

A green billiard ball is located at ( \(3,1\) ), and a gray billiard ball at (8, 9). Fats Tablechalk wants to strike the green ball so that it bounces off the \(y\) -axis and hits the gray ball. At what point on the \(\mathrm{y}\) -axis should he aim? (Hint: Use the reflection principle.)