Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make
a gravel border. After he completes his gravel border, the area of the new garden is 25 feet2.
2 answers:
If you want the original garden dimensions before the gravel border, you need the side length of the current square. Since a square's sides are equal and A = s², 25 ft² = 5², so the new garden's side measures 5 ft. Removing one foot all around means the previous square's side measured 7 ft × 7 ft (not 6 × 6 as might be assumed) — see attachment
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Answer:
To identify the critical point, we set the derivative equal to zero, resulting in:
Calculating the second derivative yields:
This indicates that t = 3.4375 marks the minimum value for the function. Substituting this back into the original function gives us:
Thus, the minimum annual income is found at t = 3.43 (between the years 2008 and 2009), with a value of 25.094
Step-by-step explanation:
In this scenario, we have the function:
Where P represents the annual net income from 2007-2011, and
t is the number of years since early 2005
To discover the lowest income, we utilize the derivative given by:
Setting this derivative to zero allows us to find the critical point, leading to:
Calculating the second derivative reveals:
Therefore, we conclude that t = 3.4375 is the minimum value, substituting into the original function results in:
Thus, the minimum annual income occurs at t = 3.43 (between 2008 and 2009) with the value being 25.094