The rate of change 
of the total number, in thousand of articles, of research articles in the prominent journal Physics Review written by researchers in Europe is shown in the graph, where t is time in years 
represents the start of 1983). Use both left and right Riemann sums with 8 subdivisions to
estimate the total number of articles in Physics Review written by researchers in Europe in the 16-year period beginning 1983. (Estimate each value of 
to the nearest 0.5). Use the sums to obtain an estimate of 
.
? 
?
A. 9,000 articles
B. 50,500 articles
C. 46,000 articles
D. 4,500 articles
E. 55,000 articles
Answer: B
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Find the center of mass of a thin plate covering the given region with the given density function.The region bounded by the curves y = ± 
and the lines x = 1 and x = 9, with density ?(x) = 
A. 
= 4, 
= 0
B. 
= 5, 
= 0
C. 
= 3, 
= 0
D. 
= 2, 
= 0
Check to see if the given number is a solution for the equation.3 - (x + 3) = 3(4x - 4); check x = 
A. 
is not a solution.
B. 
is a solution.
Graph the function over a one-period interval.y = 
sin (2x - ?) + 3
A. 
B. 
C. 
D. 
Solve the problem.Approximately 23.3% of all students at a city college commute to school. Write this percent as a fraction or mixed number in simplest form.
A. 23
B. 
C. 
D. 2