The Pyraminx is a Rubik's cube-type toy in the shape of a tetrahedron (not a pyramid). The Pyraminx shown below has edges 15\,\text{cm}15cm15, space, c, m long and vertical height h=12.2\,\text{cm}h=12.2cmh, equals, 12, point, 2, space, c, m. The triangle drawn with dashed lines is a right triangle. What is the distance rrr? Round your answer to the nearest tenth.

Robots with telescoping arms are sometimes used to perform tasks (e. g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

An english teacher would like to divide 8 boys and 10 girls into groups, each with the same combination of boys and girls and nobody left out. what is the greatest number of groups that can be formed?

The initial tableau of a linear programming problem is given. use the simplex method to solve it. x 1 x 2 x 3 s 1 s 2 z 1 2 4 1 0 0 8 3 4 1 0 1 0 10 minus3 minus12 1 0 0 1 0 the maximum is nothing when x 1equals nothing, x 2equals nothing, x 3equals nothing, s 1equals3, and s 2equals0. (be sure to simplify to lowest terms if necessary.)