Sarah has sold $33 worth of tickets to the comedy show. She has 4 tickets left to sell for $11 per ticket?
1 answer:
Answer:
Part A)
Part B) The domain is the interval [0,1,2,3,4] and the range is the interval [$33,$44,$66,$77]
Part C) This problem is a discrete function
Step-by-step explanation:
Part A) What is the function notation?
Let
x -----> the number of tickets left to sell
f(x) -----> amount of money for ticket sales
we know that
The amount of money for ticket sales is equal to the cost of each ticket by the number of tickets left to sell plus the amount of money from tickets already sold.
so
The function notation is
Part B) What is the domain and range?
A reasonable domain is the number of tickets left to sell
so
[0,1,2,3,4] -----> The domain is a set of input values consisting of only certain numbers in an interval
Find the range
For x=0 ----->
For x=1 ----->
For x=3 ----->
For x=4 ----->
so
The range is the interval -----> [$33,$44,$66,$77]
Part C) Is this problem continuous or discrete?
we know that
A <u><em>discrete functio</em></u><u>n</u> allows the x-values to be only certain points in the interval, usually only integers or whole numbers, and the <u>continuous function</u> allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values.
In this problem
the x-values are only certain points in the interval
therefore
Is a discrete function
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The equation is 
the -30 expression, is subtracting, if negative, from the 60
if the cosine returned is negative, you'd end up with a +30,
negative * negative = positive
and then the 30 expression will ADD to the 60 amount
so the temperature "t" is highest, when the 30 expression, is
positive and and it's highest
when does that happen, when cosine is negative and at its highest,
well, cosine range is
so the lowest value cosine can provide is -1, when is cosine -1?
well, at
so... let's find a value that makes that expression to
![\bf t=60-30 cos (x \frac{\pi}{6}) \qquad x=6 \\\\ thus \\\\ t=60-30 cos (6 \frac{\pi}{6})\implies t=60-30 cos (\pi ) \\\\ t=60-30[-1]\implies t=60+30\implies t=90](https://tex.z-dn.net/?f=%5Cbf%20t%3D60-30%20cos%20%28x%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%5Cqquad%20x%3D6%0A%5C%5C%5C%5C%0Athus%0A%5C%5C%5C%5C%0At%3D60-30%20cos%20%286%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%5Cimplies%20t%3D60-30%20cos%20%28%5Cpi%20%29%0A%5C%5C%5C%5C%0At%3D60-30%5B-1%5D%5Cimplies%20t%3D60%2B30%5Cimplies%20t%3D90)
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so...for August, that'll mean
the -30 expression, is subtracting, if negative, from the 60
if the cosine returned is negative, you'd end up with a +30,
negative * negative = positive
and then the 30 expression will ADD to the 60 amount
so the temperature "t" is highest, when the 30 expression, is
positive and and it's highest
when does that happen, when cosine is negative and at its highest,
well, cosine range is
so the lowest value cosine can provide is -1, when is cosine -1?
well, at
so... let's find a value that makes that expression to
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so...for August, that'll mean