Help!!!i need it quick
1 answer:
Answer:
A linear function is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
An exponential equation is written as:
y = A*(r)^x
Where A is the initial quantity and r is the rate of growth.
If a and A are both positives, the similar characteristic of both types of functions is that as x increases, then the value of y will also increase. Then both functions are increasing functions.
They are different in how they increase, while a linear function increases at a constant rate, an exponential function increases slow at the beginning and really fast as x increases, as you can see in the image below where we compare the two types of functions, the green one is the linear function, and the blue one is the exponential function.
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Assuming you want the cosine series expansion over an arbitrary symmetric interval ![[-L,L]](https://tex.z-dn.net/?f=%5B-L%2CL%5D)
, 
, the cosine series is given by
You have
Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of
and so
So the cosine series for
periodic over an interval is
You have
Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of
and so
So the cosine series for
So... if you notice the picture below, based on the given vertices, is a hyperbola with a vertical traverse axis
meaning for the equation, the fraction with the "y" variable is the positive fraction, thus
so... what' the point h,k for the center? well, just take a peek at the graph, the center is half-way between both vertices, that's h,k
what's the "a" component or the traverse axis... well, is the distance from one vertex to the center, notice the picture, notice how many units from either vertex to the center, that's "a"
now.. what's "b"? well, "b" comes from the conjugate axis, or the other runnning over the x-axis hmm the smaller one in this case.... well, we dunno what "b" is
however, we know the distance from either focus, to the center of the hyperbola, and that distance "c", is
notice the picture, notice the distance from either focus to the center, that's the distance "c", thus
that'd be "b"
bearing in mind that
meaning for the equation, the fraction with the "y" variable is the positive fraction, thus
so... what' the point h,k for the center? well, just take a peek at the graph, the center is half-way between both vertices, that's h,k
what's the "a" component or the traverse axis... well, is the distance from one vertex to the center, notice the picture, notice how many units from either vertex to the center, that's "a"
now.. what's "b"? well, "b" comes from the conjugate axis, or the other runnning over the x-axis hmm the smaller one in this case.... well, we dunno what "b" is
however, we know the distance from either focus, to the center of the hyperbola, and that distance "c", is
notice the picture, notice the distance from either focus to the center, that's the distance "c", thus
that'd be "b"
bearing in mind that