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Square roots

What do higher roots do to numbers. How do you even solve them.

Hello Guest!

I'll show you an example:

\(\sqrt[7]{1521517764.6953125} \)

= e^\(\large \frac{ln\ 1521517764.6953125}{7}\)

\(=20.5\)

  !

Thanks for giving that comprehensive answer  

I suspect there is a little problem with the English language here.

Half a sphere is a hemisphere

but

Half a circle is a semicircle.    

Don't ask me why ://

Going To The Picnic

Let p = people
Let w = wagon

\(\begin{array}{|lrcll|} \hline (1) & p &=& (w-10)(\frac{p}{w}+1) \\ & p &=& p + w - 10\frac{p}{w}-10 \\ & 0 &=& w - 10\frac{p}{w}-10 \\ & 10\frac{p}{w} &=& w -10 \\ &\mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{10} (w -10) } \\\\ (2) & p &=& (w-25)(\frac{p}{w}+3) \\ & p &=& p+3w - 25\frac{p}{w}-75 \\ & 0 &=& 3w - 25\frac{p}{w}-75 \\ & 25\frac{p}{w} &=& 3w-75 \\ &\mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{25} (3w-75) } \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline p= \mathbf{\frac{w}{10} (w -10) } &\mathbf{=}& \mathbf{\frac{w}{25} (3w-75) } \\ \frac{w}{10} (w -10) &=& \frac{w}{25} (3w-75) \\ 25 (w -10) &=& 10 (3w-75) \\ 5 (w -10) &=& 2 (3w-75) \\ 5w-50 &=& 6w-150 \\ \mathbf{ w } &\mathbf{ =}& \mathbf{ 100 } \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline \mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{10} (w -10) } \\ &=& \frac{100}{10} (100 -10) \\ &=& 10\times 90 \\ \mathbf{ p } &\mathbf{ =}& \mathbf{ 900 } \\ \hline \end{array}\)

y has many different values based on the value of x

The relationship is below:

y = (6(x/5)-1)

Area of top hemicircle + bottom semicircle = πr²​ = π*6² = 36π

Area of side rectangle = lh = 2*6(length is 2*radius)*10 = 120m²

Area of outer curve = lh = π*6(1/2 circumference is length)*10 = 60π 

Total surface area = 96π + 120

Hope this helps!

Edit: I cannot English anyway so...

Hmmm... Blarney MASTER does sound better..

Thank you Melody and CPhill

The sum of the elements of any row [ after the first one]  is always 1 greater than the sum of the elements of all the previous rows 

To see this....note that the sum of elements  on any row  [ starting with n = 0]  is just 2ⁿ

Note that, for example, the sum of the first 4 rows is

2⁰ + 2¹ + 2² + 2³  = 1 + 2 + 4 + 8  =   15  =  2⁴ - 1

And adding 1 to this sum  = 16  =   2⁴  which is just  the sum of the 5th row elements

There is another similar question here    (sept 17)

I found an old question that was a bit like this, I remember Bertie helped me with it. 

(1) A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?

I stuffed up on question 1 but it is very similar to question 2

Since you have never bothered to respond to my answers there is not point in me doing it properly now.

Number of ways to draw  2 black and 1 white  = C( 8,2) * C(7,1)        (1)

Number of ways to draw  1 black and 2 white  = C( 8,1) * C(7,2)       (2)

Number   of ways to draw  3 balls from 15  =  C( 15,3)     (3)

Total Probability  =   [ (1) + (2) ] / (3)  = 

[   C( 8,2) * C(7,1)  + C( 8,1) * C(7,2)  ] / [  C( 15,3) ]  = .8  =  80%  

y = 32    bounded above and below since this is a horizontal line

y =  2^x     bounded below by the x axis.....unbounded above

y = 2 - x²  this is an inverted parabola with a vertex at (2,0)....thus...it is bounded above and unbounded below

y = √ [ 1 - x² ]       this is the upper part of a circle with a radius of 1.....thus....it is bounded below and above

y = x² √ [ x + 4 ]  ......this one is hard to see......look at the graph here :

https://www.desmos.com/calculator/oblelcc1ie

Notice that it is bounded below but not above

5,976,000,000,000,000,000,000 IN EXPANDED FORM

Hallo guest!

\(\color{BrickRed}5\ 976\ 000\ 000\ 000\ 000\ 000\ 000\\ \color{blue}=5.976\times 10^{28}\\ =59.76 \times 10^{27}\\ \color{blue}=59.76\ a\ octillion\)

  !

The number of total possible sets....choose any 5 people from a total of 42  =   C(42,5)   (1)

The total sets  consisting only of women......choose any 5 of 24   = C(24,5)      (2)

Probability  =  (2) / (1)  =  C(24,5) /  C(42,5)  ≈ .05 =  5 percent

Mr. James wants to build a walkway around his school garden. The width of his garden is one-third the length.
The perimeter of the school garden is 32 feet.
What is the length and width of his garden?

L=3W

2(3W+W)=32 feet

8W=32 feet

W=4 feet

L=3W

L=3* 4 feet

L=12 feet

The width is 4 feet, the length is 12 feet.

  !

HELP PLEASE

I am glad I could help. 

You can expand your final answer to see if it is correct or not.

It is always good to check answers :)

Thanks! Wasn't exactly sure what he was asking, so good job!

No one really wants to do that... it's not a hard problem... why do you need help with it?

Solve for x:

\(\dfrac{x}{3}=\dfrac{x}{2}-2\rightarrow2x=3x-12\rightarrow x=12\)

Ohhhh. Okay. I see what I did wrong. I was only thinking about adding to 5 so I tried -1 and 6. Thanks!

\(3x^2+5x+2\\ \)

First you need to find two numbers that multiply to give 3*2=6  

Obviously they need to be of the same sign (positive or negative)

They also need to add to 5.    Since 5 is positive both numbers must be positive.

2 and 3 work

2+3=5

2*3=6

so now you need to write 5x as 3x+2x

\(3x^2+5x+2\\ =3x^2+3x+2x+2\\ =3x^2+3x\quad+\quad2x+2\\ \text{Now factor in pairs}\\ =3x(x+1)\quad + \quad 2(x+1)\\ =(3x+2)(x+1) \)