Approximate the value of the series to within an error of at most 10−510−5. ∑n=1[infinity](−1)n+1n7 ∑n=1[infinity](−1)n+1n7 Acco
rding to Equation (2): |SN−S|≤aN+1 |SN−S|≤aN+1 what is the smallest value of NN that approximates SS to within an error of at most 10−510−5?
1 answer:
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The evaluation of 84 2/3% to a fraction in its lowest term is
Fractions are sections or parts of a whole. They are divided into two parts, the numerator, and the denominator.
From the given information, we are to convert a mixed fraction into its lowest terms. By doing that, we are to convert it to an improper fraction.
Divide both the numerator and denominator by (2)
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Substitute 
, so that
![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%2B%5Cdfrac1x%5Cleft%28%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D%5Cright%29%3D%5Cdfrac1%7Bx%5E2%7D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D-%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%29)
Then the ODE becomes
which has the characteristic equation
with roots at 
. This means the characteristic solution for 
is
and in terms of
, this is
From the given initial conditions, we find
so the particular solution to the IVP is
Then the ODE becomes
which has the characteristic equation
and in terms of
From the given initial conditions, we find
so the particular solution to the IVP is
Answer:
The possible numbers of songs that you can burn onto the CD is 11.
Step-by-step explanation:
The total storage capacity of CD = 70 minutes
Storage already used = 25 minutes
Hence, The available storage = Total available storage - Used Storage
= 70 minutes - 25 minutes = 45 minutes
Hence, the CD has 45 minutes storage left.
Now, each song takes up 4 minutes of storage.
⇒
=
⇒The number of songs possible = 11.25 ≈ 11
Hence, the possible numbers of songs that you can burn onto the CD is 11.