A food packet is dropped from a helicopter and is modeled by the function f(x) = -16x2 + 14400. The graph below shows the height
f(x), in feet, of the food packet at different times x, in seconds:
Use the graph to determine the reasonable domain of f(x) based on the context.
a.) 0 _ x _ 30
b.)0 _ x _ 14400
c.) -30 _ x _ 30
d.) All real numbers
Use the graph to determine the reasonable domain of f(x) based on the context.
a.) 0 _ x _ 30
b.)0 _ x _ 14400
c.) -30 _ x _ 30
d.) All real numbers
2 answers:
Response:
The acceptable domain is .
Detailed explanation:
The function provided is
Where f(x) represents the height (in feet) of the food packet and x denotes time (in seconds).
Given that the leading coefficient is negative, it forms a parabola that opens downwards.
The time is consistently a positive value; thus, the domain of f(x) must be at least zero or greater.
.... (1)
The equation can also be formulated as
The graph shows that the x-intercepts occur at -30 and 30. Values outside of that range (-30 and 30) yield negative outputs for f(x). Consequently, the valid domain lies between -30 and 30.
.... (2)
From (1) and (2), we determine
Hence, the acceptable domain is .
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The illustration is omitted. Please see the attachment below.
Answer:
The area of the shaded sector is 144π square units.
Step-by-step breakdown:
Given:
The central angle for the sector is,
The circle's radius is,
The area of a sector with radius 'R' and angle can be determined with:
Substituting gives
Thus, the area of the shaded sector calculates to 144π square units.
