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Mathematics 21 Online
OpenStudy (anonymous):

Simplify: [3(n+1)!] / 5n!

OpenStudy (anonymous):

3(n+1)n! / 5n! = 3(n+1)/5

OpenStudy (anonymous):

how did u get that? do the factorials just cancel out??

OpenStudy (anonymous):

i mean the n!...do they just cancel?

OpenStudy (anonymous):

n! cancelled with n!

OpenStudy (anonymous):

oh i see..can u tell me if my answers are right for some q's...its about finding teh domain and range

OpenStudy (anonymous):

sure

OpenStudy (anonymous):

1) \[f(x) = \sqrt{x-4} \] \[D = x \ge 4 \] \[R = y \ge 0\]

OpenStudy (anonymous):

correct

OpenStudy (anonymous):

\[2) f(x) = \sqrt{x ^{2} - 4} \] D = x is greater tahn r equal to 2 R = all real numbers

OpenStudy (anonymous):

\[3) f(x) = \sqrt{4-x ^{2}} \] \[D = 2 \ge x \] \[R = 2 \ge y \]

OpenStudy (anonymous):

D = x is greater tahn r equal to 2 or x is less tahn r equal to -2

OpenStudy (anonymous):

so both ar the solutions?

OpenStudy (anonymous):

this for #2

OpenStudy (anonymous):

yes both

OpenStudy (anonymous):

ok...

OpenStudy (anonymous):

is the range correct

OpenStudy (anonymous):

for number 2

OpenStudy (anonymous):

R = all real numbers ( wrong)

OpenStudy (anonymous):

since we have a suare root the range always greater than or equal to 0

OpenStudy (anonymous):

so \[R = y \ge 0\]

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

now #3

OpenStudy (anonymous):

D= x greater than or equal -2 and less than or equal 2

OpenStudy (anonymous):

R= like # 2 Range

OpenStudy (anonymous):

what is the diffence between how u wrote teh domain for 2 was x is g=2 OR x is less =-2 and when u used AND for number 3

OpenStudy (anonymous):

|dw:1315443300915:dw|

OpenStudy (anonymous):

see the drawing we take the positive area only

OpenStudy (anonymous):

do you have an idea about the method of how to know the signs of quadratic experession?

OpenStudy (anonymous):

um i dont rember..dont u just substitute numbers to see if it fits teh solution

OpenStudy (anonymous):

yes this is one way, it's ok , but there is another one

OpenStudy (anonymous):

------ -2 -------- 2 ------ x2-4

OpenStudy (anonymous):

we have here 3 area, one less than -2, the 2nd betwn -2 and 2 , and the third are greater than 2

OpenStudy (anonymous):

to put signs look to the coefficent of X^2 is positive or negative?

OpenStudy (anonymous):

the middle area alway opposit to the sign of x^2 coeffcient

OpenStudy (anonymous):

and the other area are like the sign of x^ cofficient

OpenStudy (anonymous):

that's it

OpenStudy (anonymous):

but you can yours

OpenStudy (anonymous):

i have one more question to find domain n range

OpenStudy (anonymous):

ok , np

OpenStudy (anonymous):

\[f(x) = \sqrt{x ^{2}+44}\] d = all real #'s and r = y is greater tahn = sqrt of 44 ....im confused about this one

OpenStudy (anonymous):

d = all real #'s ( correct )

OpenStudy (anonymous):

range is the same as the one before

OpenStudy (anonymous):

but in y = [sqrt(x^-4) ] +3 ===? (domain greatrer or equal 3

OpenStudy (anonymous):

anyway I don wanna cuase you headache

OpenStudy (anonymous):

:)

OpenStudy (anonymous):

which q are u talkin about? but in y = [sqrt(x^-4) ] +3 ===? (domain greatrer or equal 3

OpenStudy (anonymous):

or is that sthn u just wanted to point out?

OpenStudy (anonymous):

that is from my mind :)

OpenStudy (anonymous):

oh i see...thnanks...how bout if smthng is f(x) cube root of x?? is the domain and range both all real numbers

OpenStudy (anonymous):

yes , exactly

OpenStudy (anonymous):

and for absolute value?? \[\left[ x+3 \right]-2 \] is teh d = all real numbers and r=[-2, infinity)

OpenStudy (anonymous):

perfect

OpenStudy (anonymous):

soory i'm such a bother but i just want to compeltely understand domain and ranges...

OpenStudy (anonymous):

\[x ^{2}+y ^{2} = 25\] D= [-5,5] and R = [-5,5] ...is this true?

OpenStudy (anonymous):

yes correct, and np ask anything sabrina

OpenStudy (anonymous):

can u help me explain how to write rectangular equation? liek the question is eliminate the parameter t and then write a rectangulat equation for \[x=t ^{2} + 3\] \[y=2t \]

OpenStudy (anonymous):

ok no problem...

OpenStudy (anonymous):

wat is ur email?

OpenStudy (anonymous):

ok?

OpenStudy (anonymous):

u can delete it now..i copied it..thnanks

OpenStudy (anonymous):

ok see ypu sabrian and don hesitate to ask anything here or email , g2g sabrina bye

OpenStudy (anonymous):

bye..thnks again

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