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Old 11-12-2012   #1
someday
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Default Algebra word problem help?

1. A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet.
a. Express the amount A of material required to make the drum as a function of the radios r of the cylinder.
b. How much material is required if the drums radius is 3 feet?
c. How much material is required if the drums radius is 5 feet?
d. Graph and identify the radius that would require the least amount of material.

2. Suppose the population of species of fish (in thousands) is modeled by F(x)=x+10/0.5x^2+1, where x≥0 is in years.
a. find the equation of the horizontal asympytote.
b. Determine the initial population,
c. What happens to the population of the fish as the number of years increase?
d. Interpret the horizontal asymptote in terms of the fish population.

3. The Doppler effect is the change in pitch (frequency) of sound from a source (s) as heard by an observer (o) when one or both are in motion. If we assume both the source and the observer are moving in the same direction, the relationship is f^(')=f[a]((v-v[o])/(v-v[s]))
Where: f^()=perceived pitch by the observer
F[a]=actual pitch of the source
V=speed of sound in air (assume 772.4 mph)
V[o]=speed of observer
V[s]=speed of source
Suppose that you are traveling down the road at 45mph and you hear an ambulance (with siren) coming toward you from the rear. The actual pitch of the siren is 600 hertz (Hz).
A. Write a function f^()(v[s]) that describes this scenario.
B. If f^()=620 Hz find the speed of the ambulance.
C. Graph the function and determine using the trace function what is the pitch perceived by the observer when the speed of the source is 80mph.
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Old 11-14-2012   #2
MAS1

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Quote:
Originally Posted by someday View Post
1. A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet.
a. Express the amount A of material required to make the drum as a function of the radios r of the cylinder.
b. How much material is required if the drums radius is 3 feet?
c. How much material is required if the drums radius is 5 feet?
d. Graph and identify the radius that would require the least amount of material.

2. Suppose the population of species of fish (in thousands) is modeled by F(x)=x+10/0.5x^2+1, where x≥0 is in years.
a. find the equation of the horizontal asympytote.
b. Determine the initial population,
c. What happens to the population of the fish as the number of years increase?
d. Interpret the horizontal asymptote in terms of the fish population.

3. The Doppler effect is the change in pitch (frequency) of sound from a source (s) as heard by an observer (o) when one or both are in motion. If we assume both the source and the observer are moving in the same direction, the relationship is f^(')=f[a]((v-v[o])/(v-v[s]))
Where: f^()=perceived pitch by the observer
F[a]=actual pitch of the source
V=speed of sound in air (assume 772.4 mph)
V[o]=speed of observer
V[s]=speed of source
Suppose that you are traveling down the road at 45mph and you hear an ambulance (with siren) coming toward you from the rear. The actual pitch of the siren is 600 hertz (Hz).
A. Write a function f^()(v[s]) that describes this scenario.
B. If f^()=620 Hz find the speed of the ambulance.
C. Graph the function and determine using the trace function what is the pitch perceived by the observer when the speed of the source is 80mph.
1. Volume of a cylinder = pi*r*r*h where pi = 3.14159, r = radius (ft), and h = height of the cylinder.
pi*r*r*h = 100
h = 100/(pi*r*r)

I'm assuming the steel drum has a top and a bottom.
The surface area of a cylinder = A = 2*pi*r*h + 2*pi*r*r = 2*pi*r(h + r)

a. Substituting for h gives:
A = 2*pi*r((100/(pi*r*r)) + r)

b. For radius of 3 feet then
A = 2*pi*3((100/(pi*3*3)) + 3)
A = 123.22 sq ft

c. For a radius of 5 feet then
A = 2*pi*5((100/(pi*5*5)) + 5)
A = 197.08 sq ft

d. I graphed it and found the radius which requires the least amount of material to be about 2.515 ft. You can find the exact value by taking the derivative of A, setting it to 0, and solving for r.

2. a. Since the degree of the numerator polynomial is less than the denominator polynomial the horizontal asymptote is y = 0.

b. The initial population occurs at x = 0.
F(0)=(0+10)/(0.5*0^2+1) = 10/1 = 10 or 10,000 fish

c. As the number of years increases the number of fish goes to 0.

d. 0 fish

3. No time right now. Will try later.
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Old 11-15-2012   #3
someday
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Thank you so much! I really, really appreciate the help!
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