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Why don't you get rid of all those unnecessay $ signs so that your post can be easily read ?

We know you appreciate us Juriemagic that is why we are always quick to answer your questions.

(At least we try to be and I think we usually are)

I always appreciate your good manners too  

yep yep....I have it...a square root ALWAYS has a positive and negative answer...my my...how could I forget that????.....Thank you to all who replied..I do appreciate..

x^(2/3) ⇒ (-512)^(2/3) = 64 (-1)^(2/3) ≈ -32. + 55.4256 i    ?????

that is not correct

x^(2/3)

when x=-512

⇒ (-512)^(2/3)

= (64) *(-1)^(2/3)   true

       (-1)^(2/3) = [(-1)^2]^(1/3) = [1]^(1/3) = 1

       or

      (-1)^(2/3) = [   (-1)^(1/3)   ]^(2) = [-1]^(2) = 1

      either way

= (64) *(-1)^(2/3) 

=  +64

I am glas you showed us your confusion.  People do not learn if they do not ask questions  :)

Suppose a is directly proportional to b, but inversely proportional to c. If a = 2 when b = 5 and c = 9, then what is c when b = 3?

\(a=kb\qquad \text{where k is a constant}\\ \text{When a=2, b=5 so}\\ 2=k*5\\ k=\frac{2}{5}=0.4\\ so\\ a=0.4b\)

\(a=\frac{m}{c}\qquad \text{where m is a constant}\\ \text{when a=2, c=9 }\\ 2=\frac{m}{9}\\ m=18\\ so\\ a=\frac{18}{c}\\ \text{sub in 0.4b for a}\\ 0.4b=\frac{18}{c}\\ when\; b=3\\ 0.4*3=\frac{18}{c}\\ 1.2=\frac{18}{c}\\ c=\frac{18}{1.2}\\ c=15 \)

When b=3  c=15

You need to check for careless errors   :)

x^(2/3) ⇒ (-512)^(2/3) = 64 (-1)^(2/3) ≈ -32. + 55.4256 i    ?????

https://artofproblemsolving.com/wiki/index.php/Law_of_Cosines

x^(2/3) - 20 = 44

x^(2/3) = 64

(x^2)^(1/3) = 64    cube both sides

x^2  = 64^3

x^2 = 262144    take both roots

x =  ±  √262144

x = ± 512

The only thing I can see wrong with your logic is that you that if

x^2 =64

x can be poitive or negative 8

other than that, your way is fine.  :)

\(x^{2 \over3}-20=44\\ \left( x^{\frac{1}{3}}\right)^{2}=64\\ x^{\frac{1}{3}}=\pm8\\ x=8^3 \qquad or \qquad x=(-8)^3\\ x=512 \qquad or \qquad x=-512\\ \)

x^(2/3) = 64     take sqrt of both sides

x^1/3 = + - 8     Cube both sides

x = 512   or -512  

Here is what MY dog finds as the answer (he may not be as bright as GA's dog...so he may be incorrect)

The WIND speed does not affect the AIRspeed...it DOES affect the GROUNDspeed

Vertical speed (z component) is also not affected by the wind speed and is equal to ( given )  120  (km/hr)

The y component of the airspeed is found with pythagorean theorem     490^2 = 120^2 + y^2     y = 475 km/hr

The x component of the ground speed is .707 (120) = 84.84    (this component is due to the wind ONLY)

The y component of the wind speed is     .707 (120) = 84.84   and is additive to the 475 km/hr

Only the x and y components contribute to the ground speed....the vertical speed does not

the x and y components  squared and added together are the resultant ground speed squared

x^2 + y^2  = GS^2

84.84^2  + (84.84 + 475)^2       = GS^2                  (yah?...no guarantee!)

GS = 566.2 km/hr

Its okay sorry if i was a little mean

No offence but you're really not helpful.  I understand that any help I get at all is completly out of good will but still.  The question is what is c WHEN B EQAULS 3.

Josh, this is a simple question.

Would you know how to solve this if the aircraft wasn’t ascending?

The solution method uses the law of cosines

\(\Large c^2 = a^2 + b^2 - 2ab \cos \normalsize (C) \)

My cat, who learned this from my dog, can solve it while catnapping.

Present your attempted solution (in coherent form) and my cat will respond with a critique. 

GA

Guess what......the graphs are still incorrect....but you solve them the same way as posed before.....try it and get back to us with your results

Omi67,

thank you very much!..I got to step 4....

I do appreciate!!

You are right Rom.  I didn't check them all carefully enough!

I checked it over first 10 million integers.

It appears to transition from 15048 at 19998 to 15049 at 19999

and remain there.

"what if it was a rational number like -5.2 or something, would that still be an integer? "

No!  An integer is a whole number.  Nothing after the decimal point.  No fractional part. 

I get 19999.

19999/101 = 198.00990099... ; ceil(19999/101) = 199;   ceil(19999/101) + 1 = 200;   19999/100 = 199.99

ceil(20000/101)+1 = 200;    20000/100 = 200

.

Hi good people,

please help me with this one. I really have tried all I could, but just do not get to the desired outcome.

\(u^3 -3uv^2 + 3u^2 v - v^3 = (u-v)(u^2 + 4uv+v^2) = 259-286= -27\)

\(\text{This has to be factored as }\\ (u-v)=9\\ (u^2+4uv+v^2)=-3\\ \text{in order to match the equation, and further must be that }\\ u=7, v=-2\\ u^2+v^2 = 49+4 = 53\)