Find the error in the following proof that 2 = 1. consider the equation a = b. multiply both sides by a to obtain a 2 = ab. subtract b 2 from both sides to get a 2 − b 2 = ab − b 2 . now factor each side, (a + b)(a − b) = b(a − b), and divide each side by (a − b) to get a + b = b. finally, let a and b equal 1, which shows that 2 = 1.

If you were designing a bumper for a car, would you prefer it to exhibit elastic or plastic deformation? why? consider the functions of a bumper in both a minor "fender-bender" and a major collision.

What precautions should you take to prevent injuries when dealing with heavy loads?

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