Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections perpendicular to the x-axis are circles whose diameters stretch from the curve  to the curve  

A. 81?2
B. ?2
C. ?2
D. 81?


Answer: C

Mathematics

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Set up a definite integral that gives the arc length of the given curve.x = t, y = , -  ? t ? 

A.
B.
C.
D.

Mathematics

Find the unit tangent vector of the given curve.r(t) = (cosh t)i   + (sinh t)j  + k 

A. T(t) = -  (tanh t sech t)i  + j  + (sech t)k
B. T(t) = - (tanh t)i  + j  + (sech t)k
C. T(t) = (tanh t sech t)i  + j  + (sech t)k
D. T(t) = i  + j 

Mathematics

Determine whether the source of error represents random or systematic error.A survey is conducted on smoking amongst teenagers. When questioned by adults, teenagers tend to underreport how much they smoke.

A. Systematic error B. Random error

Mathematics

A study on worldwide oil use was prepared for a major oil company. The study predicted that the amount of oil used to fuel productivity in a certain country is given by

?

?
where f (t) denotes the number of barrels per $1,000 of economic output and t is measured in decades ( corresponds to 1965). Compute f '(0) and f ?'(2).
?
Round the answer to the nearest hundredth.
?

A.

?


B. ?

?


C. ?

?


D. ?

?


E. ?

?


Mathematics