Answer: 48x/64
Work (assuming ^ is multiplication):
12x^4/4x^16
12x ^ 4x = 48x
4 ^ 16 = 64
<h3>
Answer: 5 cm</h3>
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Explanation:
Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).
Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:
20*cos(x)+25
20*(-1) + 25
-20 + 25
5
The height of the fan tip is 5 cm when it is the closest to the table.
Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is 
Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.
x+y=170 (We know that soda + dogs is 170)
x-50=y (We know that dogs is equal to 50 less than sodas)
We can use substitution to solve this system of equations.
x+y=170
Sub in the value of y from the second equation
x+(x-50)=170
2x-50=170
2x=220
x=110
We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.
x+y=170
110+y=170
y=60
So, there were 60 hotdogs sold and 110 sodas sold.
2
Divide both the top and bottom by 2 and you get 2/3