A fishing boat captain charges $ 250 for an excursion. His fixed monthly expenses are $ 1200 for insurance, rent for the dock, and minor office expenses. He also has variable costs of $ 100 per excursion to cover gasoline, bait, and other equipment. a. Write a linear cost function representing the cost C x in $ for the fishing boat captain to run x excursions per month. b. Write a linear revenue function representing the revenue R x in $ for x excursions per month. c. Determine the number of excursions per month for the captain to break even. d. If 18 excursions are run in a given month, how much money will the fishing boat captain earn or lose?
A fishing boat captain charges $ 250 for an excursion. His fixed monthly expenses are $ 1200 for insurance, rent for the dock, and minor office expenses. He also has variable costs of $ 100 per excursion to cover gasoline, bait, and other equipment. a. Write a linear cost function representing the cost C x in $ for the fishing boat captain to run x excursions per month. b. Write a linear revenue function representing the revenue R x in $ for x excursions per month. c. Determine the number of excursions per month for the captain to break even. d. If 18 excursions are run in a given month, how much money will the fishing boat captain earn or lose?
Solution Summary: The author explains that a fishing boat captain charges 250 for an excursion while his fixed monthly expenses are
A fishing boat captain charges
$
250
for an excursion. His fixed monthly expenses are
$
1200
for insurance, rent for the dock, and minor office expenses. He also has variable costs of
$
100
per excursion to cover gasoline, bait, and other equipment.
a. Write a linear cost function representing the cost
C
x
in $
for the fishing boat captain to run
x
excursions per month.
b. Write a linear revenue function representing the revenue
R
x
in $
for
x
excursions per month.
c. Determine the number of excursions per month for the captain to break even.
d. If
18
excursions are run in a given month, how much money will the fishing boat captain earn or lose?
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
428 mph
41°
50 mph
a. The ground speed of the airplane is
b. The bearing of the airplane is
mph.
south of west.
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
a. The resultant force is
(Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°))
b. It's magnitude is
lb.
c. It's angle from the positive x-axis is
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
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