If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.r(t) = (5 cos t)i + (8 sin t)jFind the acceleration vector.

A. a(t) = (-5 cos t)i + (-8 sin t)j
B. a(t) = (5 cos t)i + (8 sin t)j
C. a(t) = (5 sin t)i + (8 cos t)j
D. a(t) = (-5 sin t)i + (-8 cos t)j


Answer: A

Mathematics

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Solve the problem.The grading scale for a C in Amy's biology class is an average on tests between 70% and 80%, inclusive. Amy has 67%, 84%, and 77% on the first three tests this semester. What range of scores on the fourth test would give her a C?

A. Between 52% and 92%, inclusive B. 87% or better C. Between 70% and 80%, inclusive D. Between 57% and 87%, inclusive

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In an adiabatic process (one in which no heat transfer takes place), the pressure P and volume V of an ideal gas such as oxygen satisfy the equation where C is a constant. Suppose that at a certain instant of time, the volume of the gas is 2L, the pressure is 100 kPa, and the pressure is decreasing at the rate of 5 kPa/sec. Find the rate at which the volume is changing.

a. 14 L/sec
b. C–14 L/sec
c. C–
d.

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Evaluate the following:

1.
2.
3.

Mathematics

Perform the indicated matrix operations.Let A =  and B = . Find 3A + 4B.

A.
B.
C.
D.

Mathematics