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\(\text{Each of your new points is derived as }\\ (x^\prime_k,y^\prime_k) = \begin{pmatrix}\frac 1 2 &0 \\0 &2\end{pmatrix}\begin{pmatrix}x_k\\y_k\end{pmatrix}\)

\(\text{This results in an overall transformation matrix of }\\ \begin{pmatrix} \frac 1 2 &0 &0 &0 &0 &0\\ 0 &2 &0 &0 &0 &0 \\ 0 &0 &\frac 1 2 &0 &0 &0\\ 0 &0 &0 &2 &0 &0 \\ 0 &0 &0 &0 &\frac 1 2 &0 \\ 0 &0 &0 &0 &0 &2 \end{pmatrix}\)

\(\text{The determinant of this matrix is simply the product of the diagonal terms and equals }1\\ \text{Thus the transformation will leave the original area unchanged}\)

Let C  = (0,0)     A  = (0,4)  and  B = (7,0)  F = ( 3,0)   E = (0,2)

The area of triangle ABC  = (1/2) ( 4) (7)  = 14

And the area of triangle ACF  = (1/2)(3)(4)  = 6

Now...

The line through  AF has a slope  of (-4/3)

And the equation of this line is  y = -(4/3)x + 4      (1)

The line through EB has a  slope of (-2/7)

And the equation of this line is  y = -(2/7)x + 2    (2)

Find the x intersection of   (1) and (2)

-(4/3)x + 4 =   -(2/7)x + 2

2 = -(2/7)x + (4/3)x

2= (22/21)x

21/11= x

And the  y coordinate of their intersection  = -(2/7)(21/11) + 2  = 16/11

Call this intersction point G = ( 21/11. 16/11)

So.....the height of triangle  DFB  = 16/11    and the  area of triangle  DFB  = (1/2)(4) (16/11)=  32/11

So....area of  triangle ADB  =  

Area of tiangle ABC  - Area of triangle ACF  - Area of triangle  DFB  =

14 - 6 - 32/11 =

8 - 32/11 = 

(88 - 32) /11 =

56 / 11   units^2

\(\text{One key part is that for }k\geq 2,~\{\zeta(k)\}=\zeta(k)-1\)

\(\text{That applies to all of the terms of the series we are to compute}\)

\(\text{What you do is this....}\\ \text{Consider the sum of the fractional parts of the zeta functions for all integers 2 and larger}\\ \text{Write out horizontally some of the terms of some of each series in the sum, for a few terms, i.e. }\\ \{\zeta(2)\} = \zeta(2)-1 = (1/2)^2 + (1/3)^2 + (1/4)^2 + \dots\\ \{\zeta(3)\} = \zeta(3)-1 = (1/2)^3 + (1/3)^3 + (1/4)^3 + \dots\\ \{\zeta(4)\} = \zeta(4)-1 = (1/2)^4 + (1/3)^4 + (1/4)^4 + \dots\\ \vdots\)

\(\text{Now consider the sums vertically for each term}\\ \sum \limits_{k=2}^\infty (1/2)^k = \dfrac 1 2\\ \vdots\\ \sum \limits_{k=2}^\infty~(1/n)^k = \dfrac{1}{n(n-1)}\)

\(\text{And then you take the sum over these simplified terms}\\ \sum \limits_{n=2}^\infty \dfrac{1}{n(n-1)} = 1\)

\(\text{I leave it to you to modify this whole thing slightly to just sum the odd terms}\\ \text{greater than 2, as is asked for in the problem}\\ \text{You'll find the odd terms } > 2 \text{ sum to }\dfrac 1 4\\ \text{and the even terms }\geq 2 \text{ sum to }\dfrac 3 4\)

What are you trying to ask here? This doesnt make any sense.

A z-score of 0 is 0 s.d. from the mean...so it eqauls the mean of 95

A z-score of -1 is one standard deviation below the mean   so   -3.9 below the mean ....and below the other golfer.     3.9 mph

I agree, if you dont let them get the answer on thier own, life will be harder for them whether its in a higher grade.

It simply does not help

z score =  [ raw score - mean ] / std deviation

So...for the fiirst

[ raw score - 95 ] / 3.9  = 0       multiply throughh by 3.9

 raw score- 95  = 0

Raw score = 95    =   95 mph

For the second, we have

[ raw score - 95 ] / 3.9  = -1    multiply through by 3.9

raw score - 95 =  -3.9     add 95 to  both sides

raw score =  91.1    =   91.1 mph

So....the difference in speeds  is

95  - 91.1  = 

 3.9  mph

The volume of the pyramid is (1/3) (base area) height

The base area =    AB * BC  = 8 * 4  =  32

We can find the length of  the base diagonal AC  as

√ [ AB^2 + BC^2 ]=   √ [ 8^2 + 4^2 ] = √ [ 64 + 16 ] = √80  = 4√5

And  half of this distance is   2√5 =  √20

So...the height  =  √[ PA^2 - (√200^2 ] =  √ [ 6^2 -  20  ]  =  √ [ 36 - 20 ]  = √ 16  =  4

So....the volume of the  pyramid is

(1/3)(32)(4) =

(1/3) 128   =

128 / 3  units^3   =    42 + 2/3   units^3

BUT u could say 1E42. Since decimal places wont be irregular

Love, Gabe

Then again, you dont have a geometry teacher

But, he will accept an answer like that im sure.

Using a positive z-score table reveals  z = 2.8  is a score better than 99.74% of other players !

2.8 x 4  + 17 = 28.2 pts total    for Sarah....

But not only is it that were not looking for a CIRCUMFRENCE in the first place.

The radius of the sphere will be 9 inches

And this will be the length of the  "long" diagonal drawn from the bottom vertex of the small cube to the oppositie top vertex

And we can find the edge length , e, of this cube as

e^2 + 2e^2  = 9^2

3e^2  = 81

e^2  = 27

e = √27

So...the volume of the smaller cube  is  

e^3  = (√27)^3 =  

27√27 =

81√3  in^3

Well its not wrong my math teacher would accept an answer like that.

Too lazy to put answer. 

99999999999999999999999999999999999999999999999999999999999999999999 squared

Am i the only one that noticed that on the top of the picture there is the tabs and the one he is currently in is an exam? That seems a little fishy. Is Little nick using this site to cheat on an exam?

Hey guest, just letting u know u shouldnt tell them what the answer is.  If you just answer the question but dont explain how, you are just giving them a free answer without them doing any work. If you see my answer above, i told them how to solve, but not the answer.  Its like helping the cheater. If you check out the link below, Melody and a few others found some people that were using Web2Calc as a place to get free answers without doing any work. Dont be the guy that just goes around to every question and just writes the answer in. Its helping cheaters. If younwish to answer, write how to solve it, but not the answer. Let them have the chance to figure it out on their own.

As an edit yes this problem is very simple but still you shouldnt just give them the answers.

https://web2.0calc.com/questions/raziel305-is-using-this-as-a-cheat-site

This is the problem