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?
3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
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