Answer :
Sure, let's determine the correct values for the domain and range within the context of this situation.
### Domain:
The function [tex]\( p(t) \)[/tex] represents the change in pressure over time. Since time [tex]\( t \)[/tex] cannot be negative, the domain of the function is [tex]\( t \geq 0 \)[/tex].
### Range:
The function given is [tex]\( p(t) = 5 \sin(880 \pi t) \)[/tex].
The sine function, [tex]\( \sin(x) \)[/tex], oscillates between -1 and 1 for any real number [tex]\( x \)[/tex]. Therefore, when we multiply the sine function by 5, the range of [tex]\( 5 \sin(880 \pi t) \)[/tex] will be between [tex]\( -5 \)[/tex] and [tex]\( 5 \)[/tex].
So, the range of the function [tex]\( p(t) \)[/tex] is:
[tex]\[ -5 \leq p(t) \leq 5 \][/tex]
### Final Answer:
- The domain of the function is [tex]\( t \geq 0 \)[/tex].
- The range of the function is [tex]\( -5 \leq p(t) \leq 5 \)[/tex].
Therefore, the correct answers are:
The domain of the function is [tex]\( t \geq 0 \)[/tex].
The range of the function is [tex]\( -5 \leq p(t) \leq 5 \)[/tex].
### Domain:
The function [tex]\( p(t) \)[/tex] represents the change in pressure over time. Since time [tex]\( t \)[/tex] cannot be negative, the domain of the function is [tex]\( t \geq 0 \)[/tex].
### Range:
The function given is [tex]\( p(t) = 5 \sin(880 \pi t) \)[/tex].
The sine function, [tex]\( \sin(x) \)[/tex], oscillates between -1 and 1 for any real number [tex]\( x \)[/tex]. Therefore, when we multiply the sine function by 5, the range of [tex]\( 5 \sin(880 \pi t) \)[/tex] will be between [tex]\( -5 \)[/tex] and [tex]\( 5 \)[/tex].
So, the range of the function [tex]\( p(t) \)[/tex] is:
[tex]\[ -5 \leq p(t) \leq 5 \][/tex]
### Final Answer:
- The domain of the function is [tex]\( t \geq 0 \)[/tex].
- The range of the function is [tex]\( -5 \leq p(t) \leq 5 \)[/tex].
Therefore, the correct answers are:
The domain of the function is [tex]\( t \geq 0 \)[/tex].
The range of the function is [tex]\( -5 \leq p(t) \leq 5 \)[/tex].