Prompt
you are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). a small square of the same size is cut from each corner, and each side folded up along the cuts to from a box with no lid.
1. anya thinks the cut should be 1.5 inches to create the greatest volume, while terrence thinks it should be 3 inches.
explain how both students can determine the formula for the volume of the box.
determine which student's suggestion would create the larger volume.
explain how there can be two different volumes when each student starts with the same size cardboard.
2. why is the value of x limited to 0 in. < x < 4.25 in.?
(quick response )

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

What is the difference between the equations of a vertical and a horizontal line?

Fast! find the length of cu. the triangles are similar. show your work.