Mia is going out to eat with some friends and has a total of $15 to spend. She got a water to drink and plans to leave a $3 tip.
The price of the entrees range from $5.98 to $24.99. She must also remember that there is a 7% sales tax applied to the cost of her meal. The total cost she pays for her meal, including the tip, can be modeled by the function f(c), where c represents the price of the entree she orders. The domain of the function is__ ≤ c ≤ __.
Mia's friend Clara loans her $5 so that Mia has more entrees to choose from on the menu. With this additional $5, the domain of the function representing the price of an entree Mia can afford is now __≤ c ≤ __.
1. First we are going to find the cost function. We know for our problem that there is a 7% sales tax applied to the cost of her meal and she plans to leave 3$ as tip. Let represent the cost of the meal: where is the cost of the entree is the total cost she will pay
We know that the minimum cost of an entree is $5.98, so the domain of our functions so far is: Now, to find the upper limit of the domain, we are going to take advantage of the fact the she only has $15 to spend, so we can replace the total cost with 15 and solve for :
We can conclude that the domain of the function is
2. We know that Mia's friend Clara loans her $5, so Mia's total money now is $15+$5=$20. Since the minimum cost for an entree remains the same ($5.98), the lower limit of our domain remains the same: Now, to find the upper limit of our domain, we are going to replace the total cost with 20 an solve for :
We can conclude that the domain of the function representing the price of an entree Mia can afford is now
I'll guess the answer is <em>you can tell that pi is an irrational because it has a </em>non-terminating yet non-repeating decimal representation.<em>
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Of course it's not clear how we tell this. We can't know for sure just by looking at the first trillion digits we've figured out whether it repeats or not. Someone told us it didn't, that's really how we know.
1. If you join the top part and the bottom part of the figure, you obtain a sphere. Then, you must apply the formula for calculate the surface area of a sphere:
Where r is the radius ()
2. Then:
3. The formula for calculate the suface area of the red part, which is a cylinder, is: