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This question has been answered on a different thread! 

I think it would be a good idea if you solve this for yourself. :)

Do some casework!

Set up some cases such as x >= 3, and where x < 3. Remember, just because x >= 3, doesn't mean that f(x) is also greater than or equal to 3, set up some cases there too! There may also be extraneous solutions! Get rid of those :)

unfortunately that's wrong.

By Lagrange Interpolation, p(7) = 548.

I typed the question wrong.. it's actually 

Let p(x) be a monic polynomial of degree 6 such that p(1) = 1, p(2) = 2, p(3) = 3, p(4) = 4, p(5) = 5, and p(6) = 6. Find p(7).

Simplify the equation to \(x^2 + 4x + 1 = 0\)

Note that\({1 \over (a - 1)} + {1 \over(b - 1)} = {(b-1) \over (a - 1)(b-1)} + {(a-1) \over(a-1)(b - 1)} = {{a + b - 2} \over ab−a−b+1} = {{(a + b )- 2} \over ab−(a+b)+1 }\)

Now, recall that \(a + b = -{b \over a} = -4\) and \(ab = {c \over a} = 1\). 

Substituting this in gives us \({{-4 - 2} \over 1 + 4 + 1 } = {-6 \over 6} = \color{brown}\boxed{-1}\)

The center of the cube is (3,-1,7).

Here is the answer: \(\mathbf{d} = \begin{pmatrix} 1/5 \\ -4/5 \end{pmatrix}\)

(b) There are 108/3 = 36 unique sets.

(c) For the first card, there are 3 ways to choose the number.  For the second, there 2 choices, and then there is only 1 choice.  So there are 3*2*1 = 6 ways that the numbers can be chosen.  Doing this for the other attributes, we get 6*6*24*6 ways.  But the order of cards doesn't matter in a set, so we divide by 3!: 6*6*24*6/3! = 864.  So there are 864 sets for part (c).

(d) The cards can have the same number, color, shape, or shading.  If all the colors are the same, then there are 6*24*6/3! = 144 sets.  If all the numbers are the same, then there are 144 sets.  We get the same number for shape and shading, so there are 4*144 = 576 sets for part (d).

(e) We need to choose two of the attributes.  There are C(4,2) = 6 ways of choosing two attributes.  For each of these two attributes, there are 3 options.  For the other two attributes, there are 3 ways of assigning the choices, so there are 6*3*3*3*3 = 486 sets for part (e)

(f) First we choose which attributes are the same.  There are C(4,3) = 4 ways of choosing which attributes are the same.  There are then 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute, so there are 4*36*4 = 576 sets for part (f).

2/3 * 3/4* 4/5x=100

2/5x=100

x=250

4/3*3/5*3/4x=3/5x

3/5x=150

answer is 150

The formula for a cylinder is V = π*r^2*h

Plug in the numbers we know and we'll get 2700π = π(30)^2*h

Then just solve!

2700π = π(30)^2*h

2700π = 900π*h

2700/900 = 3

2700π = 900π * 3

2700π = 2700π

h = 3 meters

I graphed it!  There are 5 solutions.  LOL

Let \(AE= x \) and \(CE = y\)

From \(\triangle AEC\), we have the equation: \(x^2 + y^2 = 81\)

Using the Pythagorean Theorem on \(\triangle CAD\) and \(\triangle DAB\), we find that \(DB = 12 \sqrt {2} \)

Also, from \(\triangle BEC\), we have the equation: \((x+7)^2 + y^2 = (12 \sqrt 2)^2\)

Now we just need to solve the system for x and y. 

Can you take it from here?

First prism

Other leg length  =  sqrt (10^2 - 6^2)   =sqrt (64)  = 8

Volume of this  prism =  base area * height =  (1/2) (6 * 8)  * x =  24x

Second prism

Other leg length = sqrt (10^2 - 50)  =sqrt (50)

Volume of this prism (1/2) (sqrt 50)^2 * ( x - 2 ) =   25 ( x - 2)

And we know that

.75 (24x)  = 25 ( x - 2)

18x = 25x - 50                rearrange as

25x - 18x  =  50

7x = 50

x =  50 /  7

thanks! 

No problem, nerdiest  !!!

I agree with your answer.....good job  !!!

yes it is! :)

[ 36563 -  25952 ]  /  2.5   = 4244.4   mph  !!!!!

{That's one  fast vehicle !!!! }

noice.

(2/3)x + (3/5)y =  12

- 3x    + (5/2)y =  6

Multiply the first equation through by   15    and the  second  through by 2

10x + 9y =  180

-6x  + 5y  =  12

Multiply  the first equation  through by  6   and the second through by 10

60x  + 54y  =  1080

-60x + 50y  =    120          add these

104y  =  1200

y  = 1200  /  104  =  150 / 13

And

-6x + 5(150/13)  = 12

-6x =  12 - 750/13

-6x = ( 156 - 750) / 13

x = (156 - 750) / (-6 *13)   = 99 / 13

144/625 is the awnser 

CPhill, did I steal your question... if I did, I'm sorry, but I want to see your explanation!