Mathematics
7 Online
OpenStudy (nincompoop):
omg
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OpenStudy (nincompoop):
can someone break this down for me to see
OpenStudy (zzr0ck3r):
what is f?
OpenStudy (nincompoop):
\[=\frac{ 2 }{ 5 }\sum_{i=1}^{5}\frac{ -4i^2+125 }{ 25 }\]
OpenStudy (nincompoop):
oh f = -x^2 + 5
OpenStudy (ikram002p):
f(x)=-x^2+5
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OpenStudy (abb0t):
Separate them in to seperate fractions.
OpenStudy (abb0t):
\(\sf \color{red}{i^2} = \color{blue}{\frac{n(n+1))2n+1)}{6}}\)
OpenStudy (nincompoop):
\[\frac { 2 }{ 5 } \left[ \frac{ 4 }{ 5 }\sum_{i=1}^{5}\ i^2 + \sum_{i=1}^{5} 5 \right]\]
OpenStudy (abb0t):
yep. U got it.
OpenStudy (nincompoop):
2/5[4/5 * (n(n+1)(2n+1))/6 + 25]
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OpenStudy (nincompoop):
I am not getting 6.48
OpenStudy (abb0t):
constant also has an \(n\) remember.
OpenStudy (abb0t):
n = 5 in this case.
OpenStudy (nincompoop):
8/25 * (55 + 25)
OpenStudy (abb0t):
\[\sf \color{red}{i^2} = \color{blue}{\frac{n(n+1)(2n+1)}{6}}.........5\sum = 5n\]
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OpenStudy (abb0t):
and just plug n chug.
OpenStudy (nincompoop):
it's what I did
OpenStudy (nincompoop):
first sum is 55 second is 5*5
OpenStudy (nincompoop):
now I have 2/5 * 4/5 = 8/25
OpenStudy (nincompoop):
8/25 * (55 + 25)
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OpenStudy (nincompoop):
my arithmetic is effed up somewhere
OpenStudy (abb0t):
I GET 25.6
OpenStudy (nincompoop):
see?
OpenStudy (nincompoop):
if I didn't use summation, it would have been easier laughing out loud
OpenStudy (nincompoop):
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OpenStudy (ikram002p):
u oly have i = 1,2,3,4,5
if i^2 dint work just check the sum if it the same to 6.48
check ur sol again
OpenStudy (abb0t):
yeah, maybe it's \(i\)?
OpenStudy (nincompoop):
I found the error, it should be 4/25
OpenStudy (nincompoop):
2/5 (220/25 +25)
OpenStudy (nincompoop):
still... LAUGHING OUT LOUD wow this is terrible
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OpenStudy (ikram002p):
f=-x^2+5
\[\int\limits_{0}^{2} -x^2+5\]
\[ -x^3/3+5x from 0 to 2\]
\[ -8/3 +10 =10-2.6666=7.3333\]
lol !
OpenStudy (nincompoop):
it cannot be i only because we're talking about
f(x) = -x^2 + 5
the height must maintain the (2i/5)^2
OpenStudy (nincompoop):
i know.. I tried that also, @ikram002p
OpenStudy (abb0t):
mayb the books wrong?
OpenStudy (nincompoop):
since 6th edition all the way to 9th edition LAUGHING OUT LOUD it can happen
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OpenStudy (anonymous):
i don't think the book is wrong
OpenStudy (ikram002p):
its actully correct
the area btw
6.48 and 8.08
OpenStudy (ikram002p):
i wanna do the sum ^^
ganeshie8 (ganeshie8):
- is missing i think.. nin
ganeshie8 (ganeshie8):
minus sign
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ganeshie8 (ganeshie8):
\(\large =\frac{ 2 }{ 5 }\sum_{i=1}^{5}\frac{ \color{red}{-}4i^2+125 }{ 25 }\)
OpenStudy (ikram002p):
if he miss minus sighn he wud get num >than 8 or so
ganeshie8 (ganeshie8):
hmmk... i just had a cursory glance.. .
OpenStudy (nincompoop):
thank you guys, I'll take a nap and restore some of that brain juice
i might be able to do it tomorrow... I am so depleted to n00b level at the moment
OpenStudy (ikram002p):
i got -3.52+10=6.48
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OpenStudy (nincompoop):
I think it's that -4/5 I did a 4/5 instead
OpenStudy (ikram002p):
its 2/5[(-4/25sum i^2) +(5×125/25)]
OpenStudy (ikram002p):
2/5[(-4/25 (330/6)) +(25)}
=2/5[-8.8+25}
=-3.52+10=6.48