Daniel_Lougee_Wk6 Assignment
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Defense Language Institute *
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Mathematics
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Feb 20, 2024
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Running head: ASSIGNMENT WEEK 6 (MATH)
1
Assignment Week 6 (Math)
Question A
NAAQS were established for six principal pollutants. Describe each and give examples of each applicable pollutant.
The six principal pollutants established under the National Ambient Air Quality Standards in accordance with 40 CFR part 50 are Carbon Monoxide (CO), Lead (Pb), Nitrogen Dioxide (NO
2
), Ozone (O
3
), Particle Pollution (PM), and Sulfur Dioxide (SO
2
) (US EPA, 2021.)
Carbon Monoxide air pollutants are produced by exhaust byproducts of transportation, farming, energy production, and other industries. CO is measured in parts per million (US EPA, 2021.)
Lead air pollutants derive from leaded fuel and the metal production industry. Lead is measured in one-millionth of a microgram per cubic meter of air (US EPA, 2021.)
Nitrogen Dioxide like Carbon Monoxide comes from multiple sources to include transportation, farming, energy production, and other industries. NO
2 is measured in parts
per billion (US EPA, 2021.)
Ozone originates from both manmade gasses and natural occurring production when UV light radiates Oxygen in the atmosphere. O3 is measured in parts per million (US EPA, 2021.)
ASSIGNMENT WEEK 6 (MATH)
2
Particle Pollution comes from any finite airborne particle that is either solid or liquid less than 10 micrometers in size. PM like lead is measured in one-millionth of a microgram per cubic meter of air (US EPA, 2021.)
A great example of Sulfur Dioxide air pollution is any diesel vehicle’s emissions. However, it also occurs naturally through volcanic activity. Sulfur Dioxide is measured in
parts per billion (US EPA, 2021.) Question B
In Hepburn’s Speed Model, the coefficients of vehicles are indicated for C and D. As
the chief of operations in your organization, you are responsible for presenting the yearly budget for the semi-trucks in your company’s inventory. Since your safety officer is insisting that each of your drivers must maintain an average speed of 55mph, what would be the vehicle operating cost of your company for each semi-
truck in cent per mile? To determine the companies’ vehicle operating cost for each semi-truck in cents per mile one must use Hepburn’s Speed Model. Sinha & Labi define the formula as vehicle operating cost (VOC) = constant (a
0
)
– constant (a
1
) *
vehicle speed (S) + constant
(a
2
)
*
speed (S)
2 (2007.) The example defines speed as 55 miles per hour. Given the vehicle is a large automobile on the Sinha & Labi’s chart, constant (a
0
) is 38.1, constant (a
1
) is 0.093, and constant (a
2
) is 0.00033. The formula calculates as VOC = 31.1 – (0.093
* 55) + (0.00033 * 55
2
). This simplifies to VOC = 38.1 – (5.115) + (0.99825) and VOC then equals 33.98325 and rounds up to 33.9833 cents per mile for each semi-truck.
VOC = 31.1 – (0.093 * 55) + (0.00033 * 55
2
)
VOC = 38.1 – (5.115) + (0.99825)
ASSIGNMENT WEEK 6 (MATH)
3
VOC = 33.98325 or rounded up to 33.9833
Question C
A taxi driver plans to pick you up at the airport and drop you off at the bank so you
can complete some financial transaction before you head home. He notes that the change in vehicle operating cost (VOC) is 42 cents per mile. Given that his fuel consumption per minute is 0.2, what is the approximate price of fuel for this given arrangement if you delayed the driver for 36 minutes at the bank? To determine the approximate price of fuel for the 36-minute delay at the bank
Sinha & Labi’s formula for change in fuel vehicle operating cost is the best method. In
the formula Change in Fuel Vehicle Operating Cost (VOC) = fuel consumption per
minute (g) * (change in delay d
0 - d
1
) * price of fuel (P) or VOC = g * (d
0
-d
1
) * p (2007.)
The problem defines vehicle operating cost as 42 cents per mile, VOC = 42 cents / mile.
Fuel consumption per minute equals 0.2, g = 0.2. Change in delay is 36 minutes, (d
0
-d
1
) =
36. Therefore, the formula is 42 = 0.2 * (36) * p which simplifies to p = 42 / 0.2 * (36).
This reduces to p = 42 / 7.2 where price of fuel for a 36-minute delay at the bank =
$5.8333 and rounds down to $5.83.
42 = 0.2 * (36) * p
p = 42 / 0.2 * (36)
p = 42 / 7.2
p = $5.8333 = $5.83 Question D
ASSIGNMENT WEEK 6 (MATH)
4
The simple interest for buying a passenger transit rail is shown as the product of the
principal amount (P), time (in years), and annual rate (R). The City of Phoenix plans to buy five additional mass transit cars for $15 million, and pay off its loan in 30 years. What would the annual percentage rate be if the city plans to make an interest payment of $2 million? Simple interest formula is the way to find out the annual percentage rate if the city
plans to make an interest payment of two million dollars. Simple interest formula is annual interest rate (r) = interest paid (i) / (principal loan amount (p) * time (t)) or r = i / (p * t) (Sinha & Labi, 2007.) For this problem the following variables are defined, interest paid is $2,000,000, principal loan amount is $15,000,000, and time is 30 years. Therefore, in accordance with the formula r = 2,000,000 / (15,000,000 * 30) which yields
the annual percentage rate of 0.44% if the city plans to make an interest payment of two million dollars. r = 2,000,000 / (15,000,000 * 30)
r = 2,000,000 / (450,000,000)
r = 0.44%
Question E
In a box model, the maximum distance to transport particle across a city is calculated as follows: Approximate length of one side is 30 miles, width is 28 miles, and the mixing height is 2 miles. To the nearest mile, what will be this distance? To calculate this distance to the nearest mile Sinha and Labi’s box model formula represents the most accurate solution. This solution however postulates that where the problem does not define the precise disbursement of particles, they spread in a consistent
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