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zzz [600]
3 years ago
9

What is 2.161616 as a fraction?

Mathematics
1 answer:
Komok [63]3 years ago
8 0

repeating fraction, nice

2.16161616...=2+0.16161616...
solve the repeating part
let's say x=0.16161616
2 places repeat, multiply x by 10^2 or 100
100x=16.161616

now subtract x from taht
100x-x=16.161616-0.16161616
the repeats cancel and we get
99x=16
divide both sides b 99
x=16/99

so
16/99=0.16161616...

2+16/99 is the fraction
if ya wanted 1 fraction then
2+16/99=
198/99+16/99=
214/99

2.161616=214/99
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For the subinterval [1.5,2]:

f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(2)=3^2-(2)^4=9-16=(-7)

f(1.5) and f(2) have opposite signs, this means there's a zero between the subinterval [1.5,2].

C)We have to repeat the same steps of A)

For the subinterval [1,1.25]:

f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5

f(1) and f(1.25) have the same signs, this means there's no zero in the subinterval [1,1.25].

For the subinterval [1.25,1.5]:

f(x)=3^x-x^4\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13

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f(1.5) and f(1.75) have opposite signs, this means there's a zero between the subinterval [1.5,1.75].

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f(1.75) and f(2) have the same signs, this means there isn't a zero between the subinterval [1.75,2].

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