(a) Suppose that the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? O L²/L ✓L T OLX T² O T²/L O L/T O L/T² (b) A displacement is related to time as x = A sin(2лft), where A and fare constants. Find the dimensions of A. (Hint: A trigonometric function appearing in an equation must be dimensionless.) OL/T OLXT O T/L OL OT

A rectangle has a length of (5.1 ± 0.2) m and a width of (2.3 ± 0.1) m. Calculate: (a) the area and (b) the perimeter of the rectangle, Give the uncertainty in each value.

Convert the following measurements to metric units with power-of-ten prefixes. Do not use scientific or engineering notation. Numeric values must range from 1 to less than 1000. Metric prefixes, which are case-sensitive, must be one of the following: M, m, c, k, or µ. (You may use lower-case 'u' in place of 'p'.) Example: 2.00 × 105 m = 200 km Enter the numeric value in the first box, and enter the metric prefix in the second box. a. 3.51 x 10-5 L = b. 7.98 x 108 J = C. -0.000230 W = - W d. 11,200 K = K (note: upper-case 'K' is the abbreviation for the temperature unit 'kelvin')

A rectangle has a length of (2.8 ± 0.2) m and a width of (1.7 ± 0.2) m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value. (a) Calculate the area and give its uncertainty. (Enter your answers in m2.)   m2 ±  m2 (b) Calculate the perimeter of the rectangle and give its uncertainty. (Enter your answers in m.)   m ±  m