web2.0calc
 

All Answers 358087 Answers

  Questions   
Sort: 
 #1
avatar
+5

That's 24.

Jan 2, 2015
 #1
avatar+4 
+5

sqrt(64)=8

Jan 2, 2015
 #3
avatar+330 
+11

Greetings Melody,

 

All your accolades are marvelous . . . and thank you.

 

In the past year, this forum has become an amazing, structured, learning environment, surviving troll invasions and the ubiquitous snark questions.

http://web2.0calc.com/questions/need-help-nowwwwww

(I note the still present and perpetual 2+2 now lately replaced by 10+9)

 

The most fascinating element on this forum is the social structure. I‘ve never seen this on any other math forum. Another fascinating component is the multiple answers to the same question. The different techniques truly bring out the art that is in maths. This is like listening to skilled musicians play the same composition – where at first it seems the same, but in reality it is very different.

 

Time constrains do prevent me from posting often, but not a week will pass before I peruse this forum and study the posts. These always improve my skill set for mathematics and continuously expand my understanding of physics and related sciences.

 

I’m sure, I speak for many, if not all, when I say “thank you” for your time and energy you put into this forum to make it truly great!

 

Sincerely, 

    David Q. D.

Jan 2, 2015
 #1
avatar+118723 
+10

$${\sqrt{{\frac{\left({\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}}}$$

 

Well the domain is all possible values of x so lets look at this.

you  cannot divide by 0 so x cannot be -2

You cannot find the square root of a neg number so

$$\frac{(-x+3)}{(x+2)}\ge0$$

now I want to get rid of the fraction but I need to know if I am multiplying by a neg or a positive

so instead of mult by (x+2) to get rid of the fraction I am going to multiply by  $${\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}^{{\mathtt{2}}}$$   because I know that is positive.

$$\\(x+2)^2\times\frac{(-x+3)}{(x+2)}\ge0 \times (x+2)^2\\\\
(x+2)(-x+3)\ge0 \\\\
-(x+2)(x-3)\ge0$$

 

Now if I let   

 

y=-(x+2)(x-3)

 

then the statement above will be true when y is positive.

Now I can see straight off that  y=-(x+2)(x-3)   is a concave down parabola

It is a parabola because the degree is 2 (the highest power of x is 2)

and it is concave down because the coefficient of x^2 is -1.  i.e the leading coefficient is negative.

Since it is concave down, y will be positive in the middle ,   not at the ends.

The roots  are  x=-2 and x=3

so     $$y\ge0$$     when        $$-2\le x\le 3$$

 

so what do we have here.

$$x\ne -2\qquad and \qquad -2\le x \le3$$

 

So the domain is      $$-2< x \le 3$$       this can also be written as    Domain (-2,3]

 

this is the graph - All makes perfect sense (to me anyway)

Feel free to ask questions  

Jan 2, 2015
 #202
avatar+118723 
0

Sat 3/1/15

1) Interesting domain question.

 http://web2.0calc.com/questions/what-is-the-domain-of-this-function-sqrt-x-3-x-2#rr1

2) Interesting trig.  Unit circle and exact values.   Melody

http://web2.0calc.com/questions/evaluate-each-expression-without-using-a-calculator-and-write-your-answers-in-radians

3) What are permutations and combinations ?      Melody

http://web2.0calc.com/questions/how-many-possible-combinations-are-there-for-a-deck-of-cards

4) A really good rates and volume question.        Melody

 http://web2.0calc.com/questions/help-with-problem_1#rr5

5) Physics    Thanks Alan

 http://web2.0calc.com/questions/two-5-kg-masses-are-attached-to-opposite-ends-of-a-long-massless-cord-which-passes-tautly-over-a-massless-frictionless-pulley-the-upper-mas

6) Some geometry.  Chris would like someone to check his answer but he thinks it is good.  Thanks Chris.

http://web2.0calc.com/questions/the-area-of-a-rhombus-is-250-and-one-of-the-angles-is-37-deg-27-what-is-the-length-of-each-side

7) All in fun :))    NotTheBestMathMaster, Melody, Nauseated, Alan and CPhil.

 http://web2.0calc.com/questions/how-many-times-would-a-mole-of-shoe-strings-16cm-long-stretch-from-earth-to-the-moon

8) Formula for triangular numbers  Thanks Alan and Chris  

 http://web2.0calc.com/questions/how-do-you-work-out-the-formula-nth-term-for-the-triangular-number-sequence

9) Parabola question, different from the norm - Thanks Alan

 http://web2.0calc.com/questions/the-vertex-of-the-parabola-is-on-the-line-y-20-the-y-intercept-is-15-and-3-is-a-zero-of

10) This is not a high level question but I liked it. (percantages)  :)

http://web2.0calc.com/questions/a-chemist-needs-a-solution-of-tannic-acid-70-pure-how-much-distilled-water-must-he-add-to-5-gallons-of-acid-which-was-90-pure-to-obtain-t

11) A couple of revision/learning sites suggested by Chris

http://web2.0calc.com/questions/so-i-am-currently-taking-solid-mensuration-in-college-i-am-having-a-hard-time-to-pick-up-and-learn-the-lessons-were-currently-at-quadrilat

12) Induction  Thanks Chris

http://web2.0calc.com/questions/math-induction

 

                ♫♪  ♪ ♫                                ♬ ♬ MELODY ♬ ♬                                 ♫♪  ♪ ♫

Jan 2, 2015
 #1
avatar+118723 
+5

$$x\times x = x^2$$

.
Jan 2, 2015
 #4
avatar+118723 
+10

-3cos²(-π/2)=0    also

 

I would like to try and explain something to you.

Look at this page  

http://www.mathsisfun.com/sine-cosine-tangent.html

There is an interactive unit circle at the bottom of the page.  You can choose radians or degrees.

Now the hypotenuse of the triangels is the radius of the cirlcle which is 1

The sine of the angle is given by the y value on the circumference of the unit circle

The cos of the angle is given by the x value on the circumference of the unit circle.

The tan of the angle is given by the y value over the x value on the circumference of the unit circle.

 

Play with it and really try to understand the concept.  It will help you enormously if you really understand this.

At pi/2 and at -pi/2 the x value is 0 so cos of these angles will be zero!  

Sine will be 1 and -1 respectively.  Tan will be undfined - you cannot divide by 0  :)

Jan 2, 2015

0 Online Users

Top Users

avatar+15127 asinus moderator
avatar+2125 Bosco
avatar+762 history
avatar+113 thatgirlaj
avatar+108 ikleyn
avatar+63 TheDeathlyHallows
avatar+23 Dragononweb2.0calc
avatar+4 fof.urmum
avatar+0 D R Muse
avatar+0 The_Slipster
avatar+0 joshtheminer27

Sticky Topics