Challenge 1: Patterns Record all of the possible three place value patterns that use
only the circle and square shapes. A few are listed in the
diagram to the right
Try to make sure these patterns are in some type of order and
avoid putting down patterns randomly

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg. a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?

Apinion having 30 involute teeth of 6,5 module rotates at 220 r/min and transmits 2 kw to a gear wheel having 70 teeth; the addendum on both wheels is 4 of the circular pitch and the angle of obliquity is 200. determine; 3.1 the lengths of the path of approach and the arc of approach 3.2 the normal force between the teeth at an instant when there is only one pair of teeth in contact