@robtobey A geometric sequence is obtained by placing five terms between 10 and 640. What is the common ratio equal to ?

- anonymous

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- jim_thompson5910

If r is the common ratio, then what is the next term right after 10?

- anonymous

nothing the question was just like this

- jim_thompson5910

do you agree that it would be 10*r or 10r ?

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## More answers

- jim_thompson5910

since to get the next term, you multiply the last term by r
hopefully that makes sense

- anonymous

nope mate the answer will be 4 2 3 5 or 6

- jim_thompson5910

don't worry about the answer choices right now

- anonymous

ok

- anonymous

11

- jim_thompson5910

idk what you mean
the term that comes after 10 is 10r
the term after 10r is 10r*r = 10r^2
etc etc until you get to 640

- jim_thompson5910

you should get this sequence:
10, 10r, 10r^2, 10r^3, 10r^4, 10r^5, 640

- anonymous

ok

- jim_thompson5910

the next term after 10r^5 is 10r^6
therefore,
10r^6 = 640

- jim_thompson5910

solve 10r^6 = 640 for r to get your answer

- anonymous

which is 4

- zzr0ck3r

I agree, to see an example look at
1,2,4,8,16,32,64
64/1=2^6

- jim_thompson5910

r = 4 is false

- anonymous

sorry it will be 2

- jim_thompson5910

r = 2 is true

- anonymous

thanks man can I ask 1 more question

- jim_thompson5910

sure

- anonymous

thank you then now I am writing

- anonymous

|dw:1439165401472:dw|

- anonymous

Did you get the question because my drawing is not good enough ?

- jim_thompson5910

what is the area of the circle given

- jim_thompson5910

hint: use A = pi*r^2

- anonymous

it has given no area

- jim_thompson5910

use that formula I gave to compute the area

- jim_thompson5910

r = 5 in this case

- anonymous

ok but how

- jim_thompson5910

A = pi*r^2
A = pi*5^2
A = ???

- anonymous

25pi then wat will happen

- jim_thompson5910

now we will have another circle with the same center at point A
this new circle will have radius 3
|dw:1439165882115:dw|

- anonymous

ok

- jim_thompson5910

the goal is to find the area of this shaded region and divide it by the 25pi found earlier
|dw:1439165892979:dw|

- jim_thompson5910

what is the area of the smaller circle?

- anonymous

9pi

- anonymous

but the answer is not 9/25 mate

- jim_thompson5910

it would be 9pi/25pi = 9/25 IF we wanted to land inside the inner circle
but we want to land in that ring I shaded above

- jim_thompson5910

area of ring = (area of larger circle) - (area of smaller circle)

- jim_thompson5910

answer = (area of ring)/(area of larger circle)

- anonymous

yes which will be 16/25

- jim_thompson5910

good

- anonymous

can I ask more please

- jim_thompson5910

one last one

- anonymous

ok

- anonymous

##### 1 Attachment

- jim_thompson5910

which one?

- anonymous

10

- anonymous

if you can all of them :D

- jim_thompson5910

are you able to compute f ' (x) ?

- anonymous

not at all

- jim_thompson5910

|dw:1439166519002:dw|

- jim_thompson5910

what is the derivative of sin(x) ?

- anonymous

cosx

- jim_thompson5910

so we just derive the outer function sin(...) to get cos(...)
|dw:1439166578842:dw|

- jim_thompson5910

then we use the chain rule to derive cos(x) to get -sin(x)
so derive cos(...) to get -sin(...)
that gets multiplied to what we have
|dw:1439166647000:dw|

- jim_thompson5910

we then go in further
derive 5x to get 5
that gets tacked on too
|dw:1439166679192:dw|
I placed it up front

- anonymous

ok

- jim_thompson5910

so
\[\Large f \ ' (x) = 5\cos(\cos(5x))*(-\sin(5x))\]

- jim_thompson5910

now just replace every x with pi/10 and evaluate

- anonymous

ok

- anonymous

the answer I think will be -5

- jim_thompson5910

yep it's -5

- anonymous

can I PLease PLease ask one more question

- anonymous

just one more and thats it

- anonymous

thank you

- anonymous

##### 1 Attachment

- anonymous

57

- anonymous

did you find the answer mate

- anonymous

Recall that \(sec^2(x) - tan^2(x) =1 \)
\(cos^2(x) - cos(x)sin(x) = cos^2(x)[1 - tanx] = \frac{1}{sec^2(x)}[1-tanx] = \frac{1}{1+tan^2(x)}[1-tan(x)]\)
Now put the value of tan(x) that's given.

- anonymous

ok carry on

- anonymous

*
\(\frac{1}{1+tan^2(x)}[1-tan(x)]\)

- anonymous

yeah but thats not my answer

- anonymous

Substitute the tan(x)= 2 and get the answer.

- anonymous

wat you think will be the answer

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