90 is 1 half of what
2 answers:
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Answer:
The input value or independent variable is number of questions that you answer correctly on this quiz (variable x)
Step-by-step explanation:
Let
x ----> the number of questions that you answer correctly on this quiz
y ----> the total number of points you score on this quiz
In this problem
The output value or dependent variable is the total number of points you score on this quiz (variable y)
The input value or independent variable is number of questions that you answer correctly on this quiz (variable x)
we have
This linear equation represent a proportional relationship between the variables x and y
where
k=10
K is the constant of proportionality or slope of the linear equation
The power series is
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence
The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.
Its radius of convergence is 0.5
Let,
f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....
The power series expansion (geometric series),
valid for I2xI < 1 , IxI < 0.5
so, radius of convergence = 0.5
The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5
Now, g(x) = ln(1-2x)
= -2
=-2
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
is the power series expansion for g(x).
radius of convergence =0.5
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