Please Show your work and Solve. What is the answer to these 5 questions?
1 answer:
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Answer:
y = 0
Step-by-step explanation:
The given sinusoidal equation is
The general form of the sin function is presented as follows;
y = A·sin(B·(x - C)) + D
Where;
A = The amplitude
The period, T = 2·π/B
The frequency, f = B/2·π
C = The horizontal shift
D = The vertical shift
By comparison with the given sine function, we have;
The amplitude, A = 2
The frequency, f = B/2·π = π/2/(2·π) = 1/4
The frequency, f = 1/4 Hz
C = The horizontal shift = 3/(π/2) = 6/π
The vertical shift, D = 0
Given that the mid line of the parent function, sin(x), is the line y = 0, and that the vertical shift is 0, the midline of the function, , is therefore, the line;
y = 0.
Answer:
The x-intercept represents that after 10 in. of rain there are mosquitoes.
Or
The x-intercept represents that after 0 in. of rain there are no mosquitoes.
Step-by-step explanation:
We are given a table that represents the population of mosquitoes in a certain area as a function of inches of rainfall :
RAINFALL(in.) POPULATION (millions.)
0 0
1 9
3 21
4 24
5 25
6 24
We will first find the function P(t) which denotes the number of mosquitoes after t inches of rainfall.
As the function is quadratic.
Hence , let:
At t=0 we have, P(t)=0
at t=1 we have: P(t)=9
i.e.
Also at t=2 we have: P(t)=21
i.e.
On solving equation (1) and (2) we get:
a= -1 and b=10
Hence,
We know that the x-intercept of a graph is a point where the y-value is zero.
i.e. it is the inches of rainfall when the population of mosquitoes is zero i.e. there are no mosquitoes.
i.e. we have to find t such that:
P(t)=0
i.e.
Hence, we have got two x-intercept.
one at t=0 and the other at t=10.
The x-intercept represents that after 10 in. of rain there are no mosquitoes.
Or
The x-intercept represents that after 0 in. of rain there are no mosquitoes.