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Mathematics 14 Online
OpenStudy (khantahmina):

This is the new question

OpenStudy (khantahmina):

HELP WITH NUMBER 6 7 8

OpenStudy (agent0smith):

\[\large 0 = 2[e^{-t}(-1)+(1-t)e^{-t}(-1)]\]divide by 2, take out common factor of e^-t\[\large 0 = e^{-t}[(-1)+(1-t)(-1)]\]set each equal to zero and solve.

OpenStudy (khantahmina):

no solution

OpenStudy (khantahmina):

e^-t

OpenStudy (agent0smith):

The other factor has solutions.

OpenStudy (khantahmina):

\[(1-t)=0\] t=1

OpenStudy (khantahmina):

-1 doesnt =0 no solution Thats all iget

OpenStudy (agent0smith):

The other factor was not 1-t... look closer. 7.\[\large 0 = -2x^2(e^{(-x)^2})(-2)-2e^{(-x)^2}\]take out common factor \(-2e^{(-x)^2}\)\[\large 0 = -2(e^{(-x)^2})(x^2(-2)+1)\]

OpenStudy (agent0smith):

"-1 doesnt =0 no solution Thats all iget " none of that makes any sense.

OpenStudy (khantahmina):

wow i need seroius help with that

OpenStudy (agent0smith):

\[\large 0 = e^{-t}[(-1)+(1-t)(-1)] \]if one factor is e^-t, then what is the other factor?

OpenStudy (khantahmina):

1?

OpenStudy (khantahmina):

im not sure

OpenStudy (agent0smith):

You can also factor out a -1 \[\large 0 = e^{-t}[(-1)+(1-t)(-1)] \]\[\large 0 = -e^{-t}[1+(1-t)]\]

OpenStudy (khantahmina):

so from now do u use the zero property rule

OpenStudy (agent0smith):

Yes. The * separates the factors\[\large 0 = -e^{-t}*[1+(1-t)]\]

OpenStudy (khantahmina):

so then 0=-e^(-t) simplify that then 1+(1-t)=0 -1 -1 (1-t)=-1 -t=-2 t=2

OpenStudy (khantahmina):

right?

OpenStudy (agent0smith):

Yes

OpenStudy (khantahmina):

how would i then simplify then 0=e....

OpenStudy (khantahmina):

i think theres no solution bc theres a 0

OpenStudy (agent0smith):

There is a solution. You just found it.

OpenStudy (agent0smith):

Back to 7.\[\large 0 = -2(e^{(-x)^2})[x^2(-2)+1]\]solve.

OpenStudy (khantahmina):

i got one answer which is 2. bc i did the zero property.

OpenStudy (khantahmina):

THIS IS WHAT I MEAN

OpenStudy (khantahmina):

u see the question mark thats what i was talking about. will that be no solution

OpenStudy (khantahmina):

n for number 7 \[0=x^2 (e^(-x)^2)(-1)-e^(-x)^2\]

OpenStudy (agent0smith):

e^t never equals zero. Onto number 7.

OpenStudy (khantahmina):

ah i got u nowwww :)

OpenStudy (khantahmina):

so i divided by -2

OpenStudy (agent0smith):

Already factored 7, see earlier post \[\large 0 = -2(e^{(-x)^2})[x^2(-2)+1]\]

OpenStudy (khantahmina):

so then \[-2x^2+1=0\]

OpenStudy (agent0smith):

I assume you can solve that. Onto 8.\[\large 0 = -2 w^2 e^{(-w)^2}+e^{(-w)^2}\]factor out \(e^{(-w)^2}\)\[\large 0 = e^{(-w)^2}(-2 w^2+1)\]

OpenStudy (khantahmina):

\[-2x^2=-1\]

OpenStudy (khantahmina):

thats for number 7. ityped that 10 mins ago n it just sent. FREAKING WIFI

OpenStudy (khantahmina):

\[x=\sqrt{1/2}\]

OpenStudy (khantahmina):

for number 7^

OpenStudy (agent0smith):

You forgot the plus or minus sign, when taking a square root.

OpenStudy (khantahmina):

8. \[w ^{2}= 1/2\]

OpenStudy (khantahmina):

oh yeah 7. x= plus or minus \[\sqrt{1/2}\]

OpenStudy (khantahmina):

8. w= plus or minus radiccal 1/2

OpenStudy (khantahmina):

what u think?

OpenStudy (khantahmina):

THANK U SO MUCH FOR THE HELP @agent0smith

OpenStudy (khantahmina):

do u mind helping me with some other like word problems.??

OpenStudy (khantahmina):

its about average rate of change

OpenStudy (agent0smith):

Rationalize it\[\large \pm \sqrt{\frac{ 1 }{ 2 }} = \pm \frac{ 1 }{ \sqrt 2} = \pm \frac{ \sqrt 2 }{ 2 }\]I'm hungry though so maybe.

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