A simply supported beam with dimensions of b = 12 in., h = 24 in., d = 21.5 in., and L = 21 ft supports a uniform service (unfactored) dead load consisting of its own weight plus 1.7 kips/ft and a uniform service (unfactored) live load of 1.5 kips/ft. The concrete is normal-weight concrete. Determine the moment due to the factored loads, Mu.      

List the 5 health components of physical fitness.  Of those which two are YOU most in need of training?  Explain WHY?  

Find the limit of the function by using direct substitution. (6 points)

Express the complex number in trigonometric form. -4i (5 points)

(05.04 MC) The following reaction shows sodium carbonate reacting with calcium hydroxide.Na2CO3 + Ca(OH)2 → NaOH + CaCO3How many grams of NaOH are produced from 20.0 grams of Na2CO3?(Molar mass of Na = 22.989 g/mol, C = 12.01 g/mol, O = 15.999 g/mol, Ca = 40.078 g/mol, H = 1.008 g/mol)

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 12, 3, , …  (7 points)

Write the sum using summation notation, assuming the suggested pattern continues. 4 – 12 + 36 – 108 + … (5 points)

Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (8 points) 

Find the fifth roots of 243(cos 240° + i sin 240°). (5 points)

At high doses barbiturates can have a hypnotic effect, however, there is some evidence that barbiturate use can disturb normal sleep though _______________________.