hectictar

Pi is an irrational number, so it can't be expressed as just a fraction  

We have a book at my house called The Simple Solution to Rubik's Cube by James G. Nourse, and it's pretty good !!  If you can find one, I recommend it!

The best way to learn it is to practice doing it! 

mean = \(\frac{1+1+1+2+2+3+4+5+5+25}{10} = \frac{49}{10}=4.9\)

It is right above the  " log "  button.

Also, you can type in:   sqrt(   )

For example, to do:      \(\sqrt5\)

Type:                          sqrt(5)

64^4/3   =   64^1/3  *  64^3/3   =   4 * 64   =   4 * 4³   =   4⁴   =   256

x² + 4x + y² - 10y + 13  =  0

Subtract 13 from both sides of the equation.

x² + 4x + y² - 10y  =  -13

Add (4/2)² , or 4, and (10/2)² , or 25, to both sides of the equation.

x² + 4x + 4 + y² - 10y + 25  =  -13 + 4 + 25

Now we can factor the x part and y part like this....

(x + 2)² + (y - 5)²  =  16

Assuming the edges of the triangular faces are included in  " all sides " ......

Let's get the slant height and height in terms of  s  using the Pythagorean theorem.

slant height = √[ s² - (s/2)² ]

                   = √[ s²  -  s²/4  ]           Factor out an s² .

                   = √[ s²(1 - 1/4) ]

                   = √3s / 2

height = √[ (√3s / 2)² - (s/2)² ]

           = √[  3s² / 4    -  s²/4  ]

           = √[ s²(3/4 - 1/4) ]

           = √2s/2

volume = (1/3)(area of base)(height)

volume = (1/3)(s²)( √2s/2 )

volume = (√2/6)s³

surface area = (1/2)(perimeter of base)(slant height) + area of base

surface area = (1/2)(4s)( √3s / 2 ) + s²

surface area = √3s² + s²

What does  s  equal when    volume  =  surface area  ?

What does  s  equal when   (√2/6)s³  =  √3s² + s²       ?

(√2/6)s³  =  √3s² + s²                Divide through by s²

(√2/6)s  =  √3 + 1                      Multiply through by 6/√2

s = 3√6 + 3√2

Q1.)

(i)

Rearrange     v = u + at     so that     u     is made the subject of the equation.

This means:  Get     u     all by itself on one side of the equation.

v  =  u + at                    Subtract   at   from both sides of the equation.

v - at  =  u + at - at       Any number plus fifty bazillion minus fifty bazilion equals the original number.

v - at  =  u                     or we can write this as...

u  =  v - at

(ii)

I think the instructions are...

If    u  =  v - at     , what does  u  equal when    v = 4 ,    a = 2 ,    and    t = 1   ?

u  =  v - at                     Replace  " v "  with  4 , replace  " a "  with  2 , and replace  " t "  with  1

u  =  4 - (2)(1)

u  =  4 - 2

u  =  2

Q2.)

(i)

We want to get   u   all by itself on one side of the equation.

v²  =  u² + 2as                          Subtract   2as   from both sides of the equation.

v² - 2as  =  u² + 2as - 2as

v² - 2as  =  u²                          Take the square root of both sides of the equation.  *

\(\sqrt{v^2-2as}=\sqrt{u^2}\)               The square root of any number squared equals the number.

\( \sqrt{v^2-2as}\)  =  u

u  =  \( \sqrt{v^2-2as}\)

(ii)

u  =  \( \sqrt{v^2-2as}\)               Replace  " v "  with  10 , replace  " a "  with  4 , and replace  " s "  with  10

u  =  \( \sqrt{10^2-2(4)(10)}\)

u  =  \( \sqrt{100-80}\)

u  =  \( \sqrt{20} \)                          And the square root of 20 can also be written as...

u  =  \(2\sqrt5\)

* I only took the positive root because I think that is all you need to do, but I might be wrong. If you want to be a cool kid, you can say   u  =  \( \pm\sqrt{v^2-2as}\)          and          u  =  \(\pm2\sqrt5\)     

I hope this made some sense! If you have a question don't hesitate to ask!  

We can get the equation in " vertex " form,     y - k  =  a(x - h)²       , where (h,k) is the vertex.

y  =  -\(\frac14\)x² + 4x - 19                      Multiply through by -4.

-4y  =  x² - 16x + 76                     Subtract 76 from both sides of the equation.

-4y - 76  =  x² - 16x                      Add  (16/2)²  , that is,  64  , to both sides of the equation.

-4y - 76 + 64  =  x² - 16x + 64

Now the right side of the equation is a perfect square trinomial and can be factored like this...

-4y - 76 + 64  = (x - 8)(x - 8)

-4y - 12  =  (x - 8)²                         Multiply both sides of the equation by \(-\frac14\) .

y + 3  =  -\(\frac14\)(x - 8)²

Now that the equation is in this form, we can see that the vertex is the point  (8, -3) .