Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.ln 

A. ln e3 + ln 8
B. ln e3 - ln 8
C. 3 + ln 8
D. 3 - ln 8


Answer: D

Mathematics

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Graph the function.f(x) = 2- x - 2

A.

B.

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D.

Mathematics

The monthly demand for a certain brand of table wine is given by the demand equation ?  where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded. ? Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000. ? __________ cents per case ? What is the price per case when  x = 1,000. ? $__________ / case

What will be an ideal response?

Mathematics

Solve the problem.A rock is thrown vertically upward from the surface of the moon at a velocity of 32 m/sec. The graph shows the height y of the rock, in meters, after x seconds. Estimate and interpret the turning point (the point at which the graph reaches its maximum value).

A. The turning point is at approximately (20, 320). This is the point at which the rock reaches its maximum velocity and starts to slow down. B. The turning point is at approximately (40, 320). This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. C. The turning point is at approximately (20, 320). This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. D. The turning point is at approximately (40, 0). This is the point at which the rock reaches the surface of the moon again.

Mathematics

Find the angle ? between the given vectors to the nearest tenth of a degree. ? ?

A.
B. ?
C. ?
D. ?
E. ?

Mathematics