All Answers 358187 Answers

Which expression is equal to 6/sqrt(5) ?

\(\begin{array}{|rcll|} \hline && \dfrac{6}{\sqrt{5}} \\\\ &=& \dfrac{6}{\sqrt{5}}\cdot \dfrac{\sqrt{5}}{\sqrt{5}} \\\\ &=& \dfrac{6\sqrt{5}}{\sqrt{5}\sqrt{5}} \\\\ &=& \dfrac{6\sqrt{5}}{\sqrt{5\cdot 5}} \\\\ &=& \dfrac{6\sqrt{5}}{\sqrt{5^2}} \\\\ &=& \dfrac{6\sqrt{5}}{5} \\ \hline \end{array}\)

Happy bleedin’ birthday!  Sir CPhill

Simplify sqrt(162x^3y^2)

Assume x and y are nonnegative.

\(\begin{array}{|rcll|} \hline && \sqrt{162x^3y^2} \\ &=& \sqrt{81\cdot2x^2xy^2} \\ &=& \sqrt{81x^2y^2 2x} \\ &=& \sqrt{81}\sqrt{x^2}\sqrt{y^2}\sqrt{2x} \\ &=& \sqrt{9^2}\sqrt{x^2}\sqrt{y^2}\sqrt{2x} \\ &=& 9xy\sqrt{2x} \\ \hline \end{array}\)

Which expression is equal to 5*sqrt(20)-3*sqrt(45) ?

\(\begin{array}{|rcll|} \hline && 5\sqrt{20}-3\sqrt{45} \\ &=& 5\sqrt{4\cdot 5}-3\sqrt{9\cdot 5} \\ &=& 5\sqrt{4}\sqrt{5}-3\sqrt{9}\sqrt{5} \\ &=& 5\cdot 2\sqrt{5}-3\cdot3\sqrt{5} \\ &=& 10\sqrt{5}-9\sqrt{5} \\ &=& \sqrt{5} \\ \hline \end{array}\)

What a lovely poem. You’ve captured the essence of the legendary, mystical, and, mathematical (and lovable) Sir CPhill in nuanced, poetic detail. 

_{^{I’m too much of a troll to write something that nice, but not so much of one that I can’t see it.}} 

GA

What are the real and imaginary parts of the complex number?

The real  part is -6

The imaginary  part is 2i

Which expression is equal to (−8−3i)+(3+4i)?

\(\begin{array}{|rcll|} \hline && (-8-3i)+(3+4i) \\ &=& -8-3i+3+4i \\ &=& -8+3-3i+4i \\ &=& -5+i \\ \hline \end{array}\)

Which expression is equal to (5−2i)−(1+3i)?

\(\begin{array}{|rcll|} \hline && (5-2i)-(1+3i) \\ &=& 5-2i-1-3i \\ &=& 5-1 -2i - 3i \\ &=& 4-5i \\ \hline \end{array}\)

Which expression is equal to  −2i(−9+6i) ?

\(\begin{array}{|rcll|} \hline && -2i(-9+6i) \\ &=& 18i-12i^2 \quad & | \quad i^2 = -1 \\ &=& 18i-12(-1) \\ &=& 18i+12 \\ &=& 12 + 18i \\ \hline \end{array}\)

Multiply.

(−4−7i)(3−5i)

\(\begin{array}{|rcll|} \hline && (-4-7i)(3-5i) \\ &=& -12+20i-21i+35i^2 \\ &=& -12-i+35i^2 \quad & | \quad i^2 = -1 \\ &=& -12-i-35 \\ &=& -47-i \\ \hline \end{array}\)

I think I found your old post Melody, here.....

Solve by any method:

4x-y+z=-5

2x+2y+3z=10

5x-2y+6z=1

I tried using Gaussian Elimination

Gaussian Elimination:

\(\left( \begin{matrix} 4 & -1 & 1 \\ 2 & 2 & 3 \\ 5 & -2 & 6 \end{matrix} \left| \begin{matrix} -5 \\ 10 \\ 1 \end{matrix} \right. \right) \\ \overset{II^{*}= 2\cdot II - I}{\curvearrowright} \left( \begin{matrix} 4 & -1 & 1 \\ 0 & 5 & 5 \\ 5 & -2 & 6 \end{matrix} \left| \begin{matrix} -5 \\ 25 \\ 1 \end{matrix} \right. \right) \\ \overset{III^{*}= \frac45 \cdot III - I}{\curvearrowright} \left( \begin{matrix} 4 & -1 & 1 \\ 0 & 5 & 5 \\ 0 & -\frac35 & \frac{19}{5} \end{matrix} \left| \begin{matrix} -5 \\ 25 \\ \frac{29}{5} \end{matrix} \right. \right) \\ \overset{III^{*}= \frac{25}{3} \cdot III + II}{\curvearrowright} \left( \begin{matrix} 4 & -1 & 1 \\ 0 & 5 & 5 \\ 0 & 0 & \frac{110}{3} \end{matrix} \left| \begin{matrix} -5 \\ 25 \\ \frac{220}{3} \end{matrix} \right. \right) \\\)

\(\begin{array}{|rcll|} \hline \frac{110}{3}z &=& \frac{220}{3}\\ z &=& \frac{220}{110} \\ \mathbf{z} &\mathbf{=}& \mathbf{2} \\\\ 5y+5z&=& 25 \\ 5y + 10 &=& 25 \\ 5y &=& 15 \\ \mathbf{y} &\mathbf{=}& \mathbf{3} \\\\ 4x-y+z &=& -5 \\ 4x - 3 + 2 &=& -5 \\ 4x &=& -4 \\ \mathbf{x} &\mathbf{=}& \mathbf{-1} \\ \hline \end{array}\)

Happy Birthday! 

(Is your Birthday the 19th or the 20th?)

Wow..

Hey, is it true that profile pictures of unicorns decrease the number of points you have?

(Read it in an old post)

Hello, MyNameIsGuest

or...

Guest!

I do not remember using a picture like that, if i did it must have been a very long time ago.

It must have been way back when Camelot was a fledgling forum.  

Anyway the automatic censor has disallowed the pic, no moderator has anything to do with it. 

Hi Myna,

Would you be a feathered bird?

Welcome to our web2.0calc forum :)

Indian Myna    (or Mynah)

The autocensor is picking up on your rather gory knives and considering them unsuitable content. 

The horizontal velocity is unaffected by the drop..   also ....the weight of the marble is irrelevant..so....

The time it takes to drop  =  d / r  =    .51 m / 1.2 m/s   =  .425 s

So......the height of the table can be found  as

H  =  vi * t   +  (1/2) a  * t^2

Where  

H  =  the table height

vi =  the intital vertical velocity =  0

t  =  time to drop  =   .425 s

a  =  acceleration due to gravity =  9.81 m/s^2

So we have

H  =  0 * .425s +  (1/2) (9.81m/s^2) * (.425s)^2  

H  ≈   .886 m

We can use this equation

h  = vi * t   +  (1/2) * a * t^2

Where

h = height  =  8.5 m  

vi  =  initial velocity  = 0

a  = acceleration  due to gravity   

t  = time  =  5s

8.5 m  =  0 * 5s    +  (1/2) * a  * (5 s)^2

8.5  =  12.5  a

8.5 m / 12.5 s^2    =   .68 m/s^2 =  acceleration due to gravity

This  will  be  a negative quantity since it is directed downward

So..... this is      -.68  / -9.81    ≈  .069  that of Earth  ≈  6.9%  of that on Earth

Thanks, Donut  and Jeff......!!!

-1115  / 134   ≈  -8.32  ft / m   = - [ 8 + 32/100 ]  =  - [ 8 + 4/25  ]  ft / m

We need  this formula

vf^2  =  vi^2  +  2 (a)(d)

Where  

vi  is the initial velocity  = 0

a  =  acceleration due to gravity  =  -9/81m/s^2

d  = the displacement  =  321 m

vf   =  the final  velocity  ......so we have....

vf^2  = 0  +  2 (-9.81m/s^2)(321m)

vf^2  =   6298.02 m^2/s^2           take the square root

vf  ≈  79.36 m/s

Happy Birthday CPhill!!! Have a nice day!!!!