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Answered here :  https://web2.0calc.com/questions/homework_19

Rom: I got different result!!:

k =(0.2, 0.04, 0.008, 0.0016, 0.00032, 0.00006 4, 0.00001 28, 0.00000 256, 0.00000 0512, 0.00000 01024.....to infinity)

x = (2, 12, 62, 312, 1 562, 7 812, 39 062, 195 312, 976 562, 4 882 812......to infinity)
k = ∑[1/(1+2*(5^n - 1)/2), n, 1,∞] = 1/4

\(\text{digesting all this we see he's got 4 spots with 12 applicants that can fill any of them}\\ \text{there are }\dbinom{12}{4}\cdot 4! =11880 \text{ ways of assigning these distinguishable positions}\)

Ln   =  natural log

This is the log using   "e"  as a  base

If you hover your cursor over the "log" button on the calculator...you will see the Ln    function

x^2 - 6x + 2 = 0

x^2 -6x + 9  = -2 + 9

(x - 3)^2 =  7   take both roots

x - 3 =   ±√7

x = √7 + 3        or   x = -√7 + 3

So   ( r -s) =   2√7  =   √28

So   (r - s)^2   =    28

xxxx

circle:

\(|z-z_0|=1\\ if~z=x+yi ~and~z_0=1+2i\\ then~(x-1)^2+(y-2)^2=1\\ or~x^2+y^2-2x-4y+4=0\)

Formula:

\(z\overline{z}+pz+q\overline{z}+r=0\\ if~z=x+yi~and~\overline{z}=x-yi\\~and~z_0=1+2i\\ then~x^2+y^2+(p+q)x+(pi-qi)y+r=0\)

p,q = ?

\(p+q=-2\\\ (p-q)i=-4\\ r=4\\ \Rightarrow \\ q=-1-2i\qquad p=-1+2i\qquad r=4\)

(p,q,r) = ( -1+2i, -1-2i, 4 )

dizaztor, it doesn't ask for meters. It is for miles, in which case 1/4 would be correct.

I got this problem wrong on the homework.

3/60 = 1/20 of a mile - your friend speed per minute.

5 x 1/20 =5/20 =1/4 of a mile by the time you start walking. 

3 miles per hour is 1.34112 meters per second. 5 minutes = 60 * 5 = 300 seconds. She has walked 300 * 1.34112 = 402.336 meters.

2a^2=2*36=72

5b^2=5*4=20

72+20=92.

HOPE THIS HELPED!

Just divide:

2370 ISK / 120 ISK = $19.75 US.

PM it is not 1/1 

The top has + signs and the bottom has - signs. So the ansswer is more than 1

Your question is not complete. The numbers are missing.

The volume of any right pyramid is    1/3  *  the area of the base.

Actually I am not sure if it has to be a right pyramid, I think it can be any pyramid.

Tetre got it from (3x)^2 = 9x^2   Thanks Tertre and asdf   

There is an obscure circle geometry  law that says if A is a point external to the circle

then the square of the tangential distance from A to the circle 

is equal to the square of the distance from A to the furthest point on any chord that is collinear with A.

Maybe that can be worded better. :/

anyway it says     \((3x)^2=(9+16)^2\)

No one on this post has attempted to prove this.  They have simply used it to answer your question.

\(\text{suppose your friend sets out at time }t=0\\ \text{her distance from wherever she they started from is }3t\\ \text{similarly your distance from the same spot is }\\ 4\left(t - \dfrac{4}{60}\right)\\ \text{you meet your friend when these two are equal}\\ 3t = 4\left(t - \dfrac{4}{60}\right)\\ \dfrac{16}{60}=\dfrac{4}{15}=t\\ t = \dfrac{4}{15}~hr = 16~min\)

Ahr yes, that does look erroneous. Thanks for finding it. :)

I will have to go back and see what mistakes led to this one.  Afterall this was just the checking part. 

You are a guest, so it does not matter. If you have a real accout, then downvoting is truly dissappointing. (*hint hint* i am continuously donvoted by someone)

Vieta's formulas. 

Say we have a polynomial \(ax^2 + bx + c = 0\) with solutions X_1 and X_2.

Vieta's formulas prove that...

a) X_1 + X_2 = -b/a.

b) (X_1) * (X_2) = c/a.

- PM

There is a tag at the bottom left corner of the page that says "Online Users". If there are some profile pictures there, that means some experienced (or people that use the website a lot) users are online.

The radical in \(\dfrac{\sqrt{28}}{14}\) can be simplified to \(2 \sqrt{7}\). \(\dfrac{2 \sqrt{7}}{14}\) simplifies into \(\boxed{\dfrac{\sqrt{7}}{7}}\), the answer. 

Hope this helps,

- PM

Assuming that the numberator is the same as the denominator, the answer is \(\boxed{1}\). 

Treat \(\sqrt{45 + \sqrt{1}} + \sqrt{45 + \sqrt{2}} ... + \sqrt{45 + \sqrt{2024}}\) as X. We will have \(\dfrac{X}{X}\), which simplifies into 1. 

Hope this helps, 

- PM

But anyways, think of it this way. The whole trip takes her X minutes, from Home to Friend's House. Let's call the distance between the Post Office and Friend's House \(Y\). To walk (2+Y) miles, it takes her X minutes. 

If she can walk a mile in Z minutes, she can walk the distance from Home to Post Office in 2Z minutes. The time she takes to walk from Post Office to Friend's House is X - 2Z, which we will call A. To find the distance between PO and FH, we have (A minutes) * (1 mile / Z minutes). The minutes cancel out, giving us A miles / Z. Putting any values for A and Z will give us the answer for the distance from PO to FH. 

Hope this helps,

- PM