The quarter-circular slotted arm oa is rotating about a horizontal axis through point o with a constant counterclockwise angular velocity ω = 7 rad/sec. the 0.1-lb particle p is epoxied to the arm at the position β = 60°. determine the tangential force f parallel to the slot which the epoxy must support so that the particle does not move along the slot. the value of r = 1.4 ft.

1. are the triangles similar and if so why? what is the value of x? show your work.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

△abc is similar to △xyz. also, side ab measures 6 cm, side bc measures 18 cm, and side xy measures 12 cm. what is the measure of side yz ? enter your answer in the box.