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Sorry rarinstraw I thought your answer was different. ://

this means

-3*-1   -1

and -3*-1=+3

so it is  +3-1  =  2

log₂24-log₂3=log₅x     using a log rule, we can write

log₂ [ 24/3]  = log₅x

log₂ [8]  = log₅x

3  = log₅x

This says that, in exponential form,

5^3  = x   =  125

how many ways can 9 people be seated to round table?'

Almost guest.

It is actually     (9-1)! = 8!

NOT 9! as it would be if they were in a row.  You see, you are supposed to only concern yourself with where people are sitting wrt each other NOT in regards to the room that the table is in.  So there is no beginning or end to this circle like there is with a line. :)

OK......but shouldn't that be,  " Thanks a 1 x 10^6  ??  "

CPhill, that's exactly what I was looking for. Thank you 1e3 times!!

No!!! Some other dude...

Hit the equal sign twice

Example

Multiplying 6.7 *  6.999  and hitting the equal sign twice  gives  4.68933e1  = 4.68933 x 10^1

was that me?

-6x = 3y - 2

X intercept....let y = 0

-6x  = 3(0)  - 2

-6x  = -2

x = -2/-6   = 1/3         so the x intercept  = (1/3, 0)

y intercept......let x = 0

-6(0)  = 3y - 2

0  = 3y - 2

2 = 3y

2/3  = y         so the y intercept  = (0, 2/3)

Height, H, after d days is given by :

a. H  = 5 + 1.5d

b.   after 20 days, we have

H = 5 + 1.5 (20)  =   5 + 30   = 35 cm

Hi OneDirection

What is the value of x2 - 2xy + y2 if x=0 and y=1 ?

just substitute those values of x and y in :)

\(x^2-2xy+y^2\quad where \;x=0\;\;and\;\;y=1\\ 0^2-2*0*1+1^2\\ =0-0+1\\ =1\)

Now he just needs to read it...

We can solve this as follows :

Let the height of the ceiling  = H

So, from the observer's position........we have

tan (45) = x/H        and      tan (20)  = (6 -x)/H        

Where x  and 6-x are the horizontal distances from the observer to lines drawn from each light perpendicular to the floor [ i.e, the ceiling height under both lights]

Solving for H, we have

x / tan(45)  =  (6-x)/tan(20)         cross-mutiply

xtan(20 )= (6-x)tan(45)   simplify

xtan(20) = 6tan(45) - xtan(45)

xtan(20) + xtan(45)  = 6tan(45)

x[ tan(20) + tan(45)]  = 6tan(45)

x = 6tan(45) / [ tan(20) + tan(45)]  =  about 4..399 m

So....the height of the ceiling  is given by 4..399/tan(45)  = about  4.399 m

P.S.   ....check that   (6 - 4.399)/ tan(20)   also gives you, roughly, 4.399m

Here's a pic .....

The observer is at A and the lights are at D and C  .... AB is the ceiling height =   about 4.399 ...  [4.4 rounded]

No problem 

Thanks Bree! I can now truthfully use exclamation points!!!!! Oh, and person who is ignoring my texts (I won't use ur name) plz respond and stop being such a jerk...

Circumference = 2pi*r = 2pi*4 = 8pi

so

\(\frac{5}{8\pi}=\frac{\theta\;radians}{2\pi}\\ \frac{5*2\pi}{8\pi}=\theta\;radians\\ \theta=\frac{5}{4}\;radians\\~\\ now\\ \pi radians=180 degrees\\ so\\ 1 radian = \frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{5}{4}*\frac{180}{\pi}degrees\\ \frac{5}{4}\;radians=\frac{225}{\pi}degrees\\~\\ \theta\approx 71.6 \;degrees\)

The problem is written as  2  x  -2       - 3   =  -4  -3  = -7

f(x) =  3^x

8.4 x 10^4

This is an ORIGINAL VOLUME = FINAL VOLUME problem

Original volume  pi x d x h   =  pi x 30 x 50 =4712.39 cm^3

This is also the FINAL VOLUME (though it is in a different shape!)

40 x 20 x h  =  4712.39

h = 4712.39/ (40 x 20) =  5.89 cm deep

Solve for x:
(log(24))/(log(2))-(log(3))/(log(2)) = (log(x))/(log(5))

(log(24))/(log(2))-(log(3))/(log(2)) = (log(x))/(log(5)) is equivalent to (log(x))/(log(5)) = (log(24))/(log(2))-(log(3))/(log(2)):
(log(x))/(log(5)) = (log(24))/(log(2))-(log(3))/(log(2))

Multiply both sides by log(5):
log(x) = (log(5) log(24))/(log(2))-(log(3) log(5))/(log(2))

Cancel logarithms by taking exp of both sides:
Answer: | x = e^((log(5) log(24))/(log(2))-(log(3) log(5))/(log(2)))

                x=125

This means that 29.73 is 85% of the original number 'x'.

Lets set up a ratio       x/29.73  =   100/85

then  x  = 100/85 x 29.73 = 34.98    

Wow, I thought that was a spam question...

*didn't                         

2.1958×10¹⁰ km³