All Answers 356000 Answers

it is 4 dots by 4 dots (sorry for not specifying)

ology does mean 'study of' but based on these examples alone I think it could just as easily mean 'relating to'.

Hence I am a mathematician and not a linguist.

Yes that looks right.

And h is the height above ground that the plane is flying

FP =  h units

Thanks for the clarification!

The center of a circle lies on the line y=6x+2 and is tangent to the x-axis at (-2,0)

Heureka beat me to it   

What is the greatest positive integer n such that 3 to the power of n is a factor of 200!. (that exclamation mark is a factorial by the way)

Here is a neat little way to do it. See if you can work out why it works.  

3,9,27,81  are all powers of 3

How many multiples af 81 are there      2

How many multiples af 27 are there     7

How many multiples af 9 are there     22

How many multiples af 3 are there     66

2+7+22+66 = 97

What is the greatest positive integer n such that 3 to the power of n is a factor of 200!

\(\begin{array}{|rcll|} \hline n &=& \lfloor \dfrac{200}{3}\rfloor + \lfloor \dfrac{200}{3^2}\rfloor+\lfloor \dfrac{200}{3^3}\rfloor+\lfloor \dfrac{200}{3^4}\rfloor \\\\ n &=& 66+ 22+7+2 \\ \mathbf{n} &=& \mathbf{97} \\ \hline \end{array}\)

What you have to do is factor the top and then cancel.

Not quite,

Let the point where the plane is be P      

F is the point on the ground directly below.

Obviously you must assume that the ground is flat so  A,B,C, and F all are in the same plane

This also means that  angles  PFA,   PFB,  PFC  are all 90 degrees.  

This is becasue PF is vertical and AF, BF, and CF are all lines on the horizontal ground.

also,

r, s and t are  ground distances to F   (which is directly below the plane.)

Reason for edit.

I have to edit becasue of display errors, I think this happens when I use the less  than sign to donote angles ...

thanks!

200! =  2^197 * 3^97 * 5^49 * 7^32 * 11^19 * 13^16 * 17^11 * 19^10 * 23^8 * 29^6 * 31^6 * 37^5 * 41^4 * 43^4 * 47^4 * 53^3 * 59^3 * 61^3 * 67^2 * 71^2 * 73^2 * 79^2 * 83^2 * 89^2 * 97^2 * 101 * 103 * 107 * 109 * 113 * 127 * 131 * 137 * 139 * 149 * 151 * 157 * 163 * 167 * 173 * 179 * 181 * 191 * 193 * 197 * 199

As you can see, n = 3^97

1A

2A (i think)

This is mostly a math forum, so we're not the best at english but i did study greek and latin so ill give it a go.

It think 1 and 2 are both C

That's beautiful.....let's say....made my week!

Just one point...can you confirm that I got my geometry right as follows:

The graph of \(y=ax^2 + bx + c\) is given below, where \(a\), \(b\), and \(c\) are integers. Find \(a\).

You get three Points from the picture above:

• Point 1 ( Vertex ): \(P_1 (-1,-2)\)
• Point 2 : \(P_2(0,-1)\)
• Point 3 ( symmetric to Point 2) : \(P_3(-2,-1)\)

\(\begin{array}{|lrcll|} \hline & y &=& ax^2 + bx + c \\ \hline P_2(0,-1): & -1 &=& a*0+b*0 + c \\ & \mathbf{c} &=& \mathbf{-1} \\ \hline P_1(-1,-2): & -2 &=& a*(-1)^2+b*(-1) -1\\ & -2 &=& a -b -1 \\ & b &=& a + 1 \\ & \mathbf{b} &=& \mathbf{a+1} \\ \hline P_3(-2,-1): & -1 &=& a*(-2)^2+b*(-2) -1 \\ & -1 &=& 4a -2b -1 \\ & 4a-2b &=& 0 \quad | \quad :2 \\ & 2a-b &=& 0 \quad | \quad b=a+1 \\ & 2a-(a+1) &=& 0 \\ & 2a-a-1 &=& 0 \\ & a-1 &=& 0 \\ & \mathbf{a} &=& \mathbf{1} \quad | \quad b= a+1=1+1=2 \\ \hline \end{array} \)

\(y=x^2+2x-1\)

hey this is an aops question

-1,-2 is the vertex, so you can make it into the vertex form

y = a(x+1)^2 - 2

then plug in 0,-1

-1 = a - 2

a = 3

a linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. the value of the function at 0 is 3

Eine lineare Funktion h modelliert eine Beziehung, in der die abhängige Variable um 1 Einheit pro 5 Einheiten abnimmt. Der Wert der Funktion bei 0 ist 3.

Hello Guest!

\(\large h(x)=-\frac{1}{5}x+3\)

  !

Simplify   4(3x^2 y^4)^3/(2x^3y^5)^4

Hello Guest!

\( 4(3x^2 y^4)^3/(2x^3y^5)^4 \)

\(=\large \frac{4(27x^6y^{12})}{16x^{12}y^{20}}\)

\(=\large \frac{27}{4x^6y^8}\)

  !

Hence,

General equation of a circle is in this form: (x-h)^2+(y-k)^2=r^2

The question gave you just few information that you need to complete it by completing the square (I.e collect the x's in one barract and y's in other barract and numbers on the other side of the equation. 

If you still don't know what to do here you can find the answer:

Just complete the square by diving the no infront the variable (With degree of 1) by 2 then square it

eg. 2x , 2/2=1 , then square 1 which is 1

by doing that in the question we get: 

(x-1/3)^2+(y-3/2)^2= -2+1/9+9/4 = 13/36

A is correct.

Hey Sv can you give a small reason as to how you got the answer. it will be much appreciated.

135 times in all.

 is the answer.

No that is not an answer. 

Words and numbers without explanation are not answers.

At least they are not answers for anyone who is trying to learn anything.