Help! Hint: A nickel is worth $0.05 and a dime is worth $0.10
1 answer:
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Answer:
Step-by-step explanation:
It is given that,
Amy wants to sell at most 25 cookies ,
Let number of cookies be '' , then
should be less than or equal to 25
Which is represented by ,
Further,
Let number of sprites be '', then '
' should be greater than or equal to 10
Which is represented by
Also,
Given,
she profits $.50 on every cookie
and $1.00 on every sprite.
So total profit on selling cookies would be
= Profit on each cookie times the number of cookies
=
=
Similarly, total profit on selling sprites would be
=profit on each sprite times the number of sprites
=
=
Now, combining these two should be greater than or equal to $30
representing this through an equation,
Thus the sysytem of equations is given as:
Answer:
Anything in the form x = pi+k*pi, for any integer k
These are not removable discontinuities.
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Explanation:
Recall that tan(x) = sin(x)/cos(x).
The discontinuities occur whenever cos(x) is equal to zero.
Solving cos(x) = 0 will yield the locations when we have discontinuities.
This all applies to tan(x), but we want to work with tan(x/2) instead.
Simply replace x with x/2 and solve for x like so
cos(x/2) = 0
x/2 = arccos(0)
x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k
x = pi + 4pi*k or x = -pi + 4pi*k
Where k is any integer.
If we make a table of some example k values, then we'll find that we could get the following outputs:
- x = -3pi
- x = -pi
- x = pi
- x = 3pi
- x = 5pi
and so on. These are the odd multiples of pi.
So we can effectively condense those x equations into the single equation x = pi+k*pi
That equation is the same as x = (k+1)pi
The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).
