Question

How do you simplify this equation into a value for y ?

y = (Sqrt[2]/2) / E^((Sqrt[2]/2)^2) ​

Answer 1

oh wow what is this lol

Answer 2

y = (Sqrt[2]/2) / E^((Sqrt[2]/2)^2)
I think it's this..

​\[y =\frac{ \frac{\sqrt{2}}{2} }{ E^{\frac{\sqrt{2}}{2}^2} ​}\]

Answer 3

Im supposed to be able to do this by hand... :/

Answer 4

OMG who assigns this?

Answer 5

its the worst calculus course ever invented.. bill davis, horacio porta and Jerry Uhl

Answer 6

apparently a flipped curriculum.. where they explain nothing, and try to have the students work it out for themselves.

Answer 7

ffffffffffffffffffffffff

Answer 8

\[(\frac{\sqrt{2}}{2})^2\] I would start expanding this first.

Answer 9

how is this Calculus? More like torture.

Answer 10

maybe
\[ (\frac{2^.5} { 2 }) (\frac{2^.5}{ 2 })\]

\[ \frac{(2^.5)(2^.5)} { 4 } \]

Answer 11

Ive been thinking the same thing.. lol

Answer 12

ummm ...
\[\frac{\sqrt{2}}{2}(\frac{\sqrt{2}}{2}) = \frac{2}{4} \rightarrow \frac{1}{2}\]

Answer 13

woah.. is that true?

Answer 14

yes it is

Answer 15

\[\LARGE e^{\frac{1}{2}}\]

Answer 16

darn it ... I sort of forgot some of the e rules

I know for \[\large e^{2+x} \rightarrow e^2e^x\]

Answer 17

so I think I can move the 2 in the numerator down to the denominator

Answer 18

I need to relook it up... I think it involves one of em .

Answer 19

yes thats true..

Answer 20

can't remember =/

Answer 21

hey so you are suppose to "simplify" the expression called y?
and y is given as:
\[y=\frac{\frac{\sqrt{2}}{2}}{e^{(\frac{\sqrt{2}}{2})^2}}\]

Answer 22

yeah and I already expanded the bottom

Answer 23

because that's an easy place to start

Answer 24

so I think we get
y= 2^(1/2) / 2 E^(1/2)

Answer 25

where did that 2 come from? ^ at the denominator

Answer 26

btw is there an easy way to enter these equations? that equation tool takes me forever.

Answer 27

you can also write that as:
\[y=\frac{\sqrt{2}}{2} \cdot \frac{1}{e^\frac{1}{2}}\]

Answer 28

you can also chose to multiply the top and bottom by e^(1/2)
to rationalize the denominator

Answer 29

well sorta rationalize anyways since e isn't rational :p

Answer 30

\[\large y=\frac{\sqrt{2}}{2} \cdot \frac{1}{e^\frac{1}{2}} \]
I rather have this XD
can't we flip the second fraction over or use one of the exponent laws for that 1/e^{something}

Answer 31

I cant believe these questions aren't all over open study.. I must be the only idiot in the world doing this course..

Answer 32

cough common core cough xD

Answer 33

yes you can do this:
\[y=\frac{\sqrt{2}}{2 e^\frac{1}{2}} \cdot \frac{e^\frac{1}{2}}{e^\frac{1}{2}}\]

Answer 34

wasn't there also an ... I forgot what's it's called but if I have something like this... I can split it up...what's it called?
\[\large e^{2+x} \rightarrow e^2e^x \]

Answer 35

that is one the law of exponents

Answer 36

I have this in notes...
The main laws of exponents are
e^(a + b) = e^a e^b
e^(a - b) = e^a/e^b
(e^a)^b = e^(a b) .
a / E^n = a E^-n negative exponent law

Answer 37

ah... so would this work?
\[\large e^{\frac{1}{2}} \rightarrow e^{1}e^{-2}\]

Answer 38

no

Answer 39

\[e^1e^{-2}=e^{1-2}=e^{-1}=\frac{1}{e}\]

Answer 40

oh xD now I remember

Answer 41

have you considered getting rid of the square root part on bottom as I suggested earlier ?

Answer 42

e and the other exponent laws are different
\[n^{a-b} = \frac{n^a}{n^b}\]

Answer 43

n can be e

Answer 44

yeah \[\frac{\sqrt{2}}{2}(\frac{\sqrt{2}}{2}) = \frac{2}{4} \rightarrow \frac{1}{2} \]

Answer 45

oh whoops yeah for something else not the exponent law thing

Answer 46

maybe log.. can be applied?

Answer 47

remember this:
\[y=\frac{\sqrt{2}}{2 e^\frac{1}{2}} \cdot \frac{e^\frac{1}{2}}{e^\frac{1}{2}} \\ y= \frac{\sqrt{2} e^\frac{1}{2}}{2 e}=\frac{\sqrt{2 e}}{2e}\]

Answer 48

anyways that is the form I would leave it in but you may think the square thing looks better on bottom and if you think that you can multiply top and bottom by sqrt(2e)
and simplify from there

but this form above is the one I would leave it as

Answer 49

square root thing*

Answer 50

My calculator says this will end up being 1/Sqrt[2E]
and I would get a value of 0.428882

Answer 51

ok if you want that other result as I said you can put the square root thing in the bottom by multiplying top and bottom by sqrt(2e)
and simplifying from there

Answer 52

are we on track?

Answer 53

\[y=\frac{\sqrt{2e}}{2e} \\ \text{ this is my preferred form } \text{ multiply } \sqrt{2e} \text{ on bottom and \top and simplify from } \\ \text{ there if you want } y=\frac{1}{\sqrt{2e}}\]

Answer 54

sounds like a fun course :)

Answer 55

lol, dan you would own this course.. :)

Answer 56

is there a trick to turning this into a value that I can set into a chart.. I'm supposed to plot points with this, by hand.

Answer 57

example:
\[\frac{\sqrt{u}}{u} \\ \frac{\sqrt{u}}{u} \cdot \frac{\sqrt{u}}{\sqrt{u}} =\frac{u}{u \sqrt{u}}=\frac{1}{\sqrt{u}}\]

Answer 58

ah I like that perspective.. thnx. myininaya, I will add that to the list..

Answer 59

oh I see.. after we got \[e^\frac{1}{2}\] we changed it in radical form and rationalize!