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babymother [125]
2 years ago
10

In a West Texas school district the school year began on August 1 and lasted until May 31. On August 1 a Soft Drink company inst

alled soda machines in the school cafeteria. It found that after t months the machines generated income at a rate of f(t) = 300t/2t2 + 8 dollars per month. Find the total income, $Tscc, produced during the second semester beginning on January 1.
Mathematics
1 answer:
WINSTONCH [101]2 years ago
3 0

Answer:

$95.78

Step-by-step explanation:

f(t) = 300t / (2t² + 8)

t = 0 corresponds to the beginning of August.  t = 1 corresponds to the end of August.  t = 2 corresponds to the end of September.  So on and so forth.  So the second semester is from t = 5 to t = 10.

$T₂ = ∫₅¹⁰ 300t / (2t² + 8) dt

$T₂ = ∫₅¹⁰ 150t / (t² + 4) dt

$T₂ = 75 ∫₅¹⁰ 2t / (t² + 4) dt

$T₂ = 75 ln(t² + 4) |₅¹⁰

$T₂ = 75 ln(104) − 75 ln(29)

$T₂ ≈ 95.78

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General Idea:

The relationship between rate(R), distance(D) and time(T) given below:

R= \frac{D}{T}

Applying the concept:

We need to make use of the formula to find Kelly's walking rate before and after her snack

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Option C isn't correct because it doesn't took Kelly 2 hours longer to walk 1/6 mile than it did for her to walk 1/4 mile.  It took 1/112 hour longer.

\frac{1}{14}  - \frac{1}{16}  = \frac{1 \cdot 8}{14 \cdot 8}  - \frac{1 \cdot 7}{16 \cdot 7}  =  \frac{8}{112} - \frac{7}{112}  = \frac{1}{112}

Option D isn't correct because 2 2/3 miles per hour is slower than 3 1/2 miles per hour.

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Complete question is;

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Options A, B & C: ±6, ±1, ±3

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We are given the polynomial;

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