this is based on Analytical Geometry, Transformations, Spheres, Cylinders, Prisms, Circles and all the questions which I am asking. I am just curious on how to solve these problems
Bonus Question: A star-polygon is drawn on a clock face by drawing a chord from each number to the fifth number counted clockwise from that number. That is, chords are drawn from 12 to 5, from 5 to 10, from 10 to 3, and so on, ending back at 12. What is the degree measure of the angle at each vertex in the star-polygon?
Question 1: Points (1, -5) and (11, 7) are the opposite vertices of a parallelogram. What are the coordinates of the point where the diagonals of the parallelogram intersect?
Question 2: The center of a circle has coordinates (6, -5). The circle is reflected about the line y = x.What are the x, y coordinates of the center of the image circle? State the x coordinate first.
Question 3: Twenty-seven solid gold spherical beads each of radius 3 are melted down and recast into a larger, solid gold sphere. How many units are in the radius of this larger gold sphere?
Question 4: A round pizza is 1/3 of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece? Express your answer in terms of pi.
Question 5: A recipe for crispy rice treats results in a mixture that fills a 9-inch by 13-inch pan to a depth of one inch. If a crispy rice treats mixture resulting from 1.5 times the original recipe is poured into a pan that is 10 inches by 15 inches, to what depth, in inches, will the pan be filled? Express your answer as a decimal to the nearest hundredth.
Find the volume of one bead: 4/3*pi*r^3=4/3*pi*3^3=36pi
27 x 36pi =972pi - combined volume of 27 beads
972pi =4/3*pi*r^3, solve for r
r = 9 - units - radius of new larger gold sphere.
Volume of cylinder =Pi x r^2 x h
Volume of pizza =Pi x 6^2 x 1/3 =12pi
Volume of 1 slice =12pi/12 =pi - cubic inches