Pg. 324 Homework Pg. 385 #57 – 68 all # π rad./min

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Presentation transcript:

Pg. 324 Homework Pg. 385 #57 – 68 all #70 2400π rad./min #71 37,699.11 ft/min #72 1200π rad./min #73 10,555.75 ft/min #74 2,661,120 in/hr; 177,408 rad./hr; 55,440 rad./hr #75 16π in #76 48π in

Angular and Linear Velocity A wheel with radius of 18 in. is rotating 850rpm (revolutions per minute). Determine: The angular speed of the wheel in radians per second (Hint: 1 rpm = 2π rad./min) The linear speed in feet per second of a point on the circumference of the wheel.

Angular and Linear Velocity #74 Elena can reach 42 mph on her exercise bike in high gear. The bike wheels are 30 in. in diameter, the pedal sprocket is 16 in. in diameter, and the wheel sprocket is 5 in. in diameter (in high gear). Find the angular speed of the wheel and both sprockets. (Note: The linear speed of a point on the wheel’s circumference also is 42mph.)

Applications of Trig Functions The cross section of a tunnel is a semi-circle with a radius of 20 ft. The interior walls of the tunnel form a rectangle. An engineer is asked to find the width and height of the tunnel opening with the maximum cross-sectional area.

Applications of Trig Functions A hole is drilled through the center of a sphere of radius 10. The portion drilled out is a right circular cylinder and two spherical caps. Find the dimensions of the cylindrical hole with the maximum volume that can be drilled out of a sphere.