Solve the problem.An object at the end of a spring is immersed in liquid. Its velocity (in cm/s) is then described by the equation 
where t is the time (in s). Find the displacement s as a function of t if s = -4 cm for t = 0.
A. s = -e-2t - 
e-8t - 
B. s = e-2t + 
e-8t - 
C. s = -e-2t + 
e-8t + 
D. s = -e-2t - 
e-8t + 
Answer: A
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Simplify the complex fraction. Leave the answer in factored form when appropriate. 
A. 
B. 
C. 
D. 4
Change the order of integration and evaluate the integral.
A. 632
B. 316
C. 
D. 
Solve the problem.The linear equation y = 229x + 6320 provides an approximation of the annual cost (in dollars) to rent an apartment at the Leisure Village Retirement Community, where x = 1 represents 2011, x = 2 represents 2012, and so on. Write an equation that yields the same y-values when the exact year number is entered.
A. y = 229(2010 - x) + 6320 B. y = 229(2011 - x) + 6320 C. y = 229(x - 2011) + 6320 D. y = 229(x - 2010) + 6320
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Show that the formula 
obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some natural number k, it is also true for the next natural number 
. Then show that the formula is false for 
.
What will be an ideal response?