All Answers 358098 Answers

The angle NOP is NOT 30^o ; but if it is, then a point N is in between M and P.

∠OMP = 63.435^o ,      ∠MOP = 71.565^o ,    PM = 3

$${\mathtt{\,-\,}}{\frac{{\frac{{\frac{{\mathtt{16}}}{{\mathtt{40}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{15}}}{{\mathtt{40}}}}\right)}{{\mathtt{30}}}}}{{\mathtt{40}}}} = {\mathtt{\,-\,}}{\frac{\left({\mathtt{16}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{40}}\right)}{\left({\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{40}}{\mathtt{\,\times\,}}{\mathtt{30}}\right)}} = {\frac{{\mathtt{1}}}{{\mathtt{5}}}}$$

$${\mathtt{\,-\,}}{\frac{\left({\frac{{\mathtt{16}}}{{\mathtt{40}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{15}}}{{\mathtt{40}}}}\right)}{\left({\frac{{\mathtt{30}}}{{\mathtt{40}}}}\right)}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{5}}}} = -{\mathtt{0.2}}$$

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{8}}}} = {\frac{{\mathtt{7}}}{{\mathtt{24}}}} = {\mathtt{0.291\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{8}}}} = {\frac{{\mathtt{16}}}{{\mathtt{24}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{24}}}} = {\frac{{\mathtt{7}}}{{\mathtt{24}}}}$$

733.55    =>   9.5 %

    x         =>  100 %            $${\mathtt{x}} = {\frac{{\mathtt{733.55}}{\mathtt{\,\times\,}}{\mathtt{100}}}{{\mathtt{9.5}}}}$$   =  7 721.579

$${\frac{{\mathtt{733.55}}{\mathtt{\,\times\,}}{\mathtt{100}}}{{\mathtt{9.5}}}} = {\mathtt{7\,721.578\: \!947\: \!368\: \!421\: \!052\: \!6}}$$

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{6}} = {\mathtt{0}}$$

$${\mathtt{x}} = {\mathtt{0.5}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{{\mathtt{0.5}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}}}$$

$${\mathtt{x}} = {\mathtt{0.5}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{6.25}}}}$$               =>    x1 =  0.5 +2.5 = 3

                                            =>    x2  =  0.5 -2.5  = -2

 x² - x -6 = (x + 2)*(x - 3 )

(x+2)*(x-3) = 0                =>    x1 = -2      and   x2 = +3

yes it has.....new session started....its funny yours havent even started!

OK, Fiora........

OM^2 = PM^2 + OP^2 - 2(PM)(OP)sin 45

5  =  PM^2 + 8 - 2(PM)(2√2)(1/√2)

-3 = PM^2  - 4PM

PM^2 - 4PM + 3  = 0

(PM  - 1)(PM - 3)  = 0

PM = 1, 3

Is that correct ???

I see where I didn't take into account the SSA situation in my first answer!!!

Just take 733.55 and divide it by 0.095.

you got half of the anwsers,try it in another way,like using law of cosine

Here's (1)

sin MPO/OM  = sin PMO/ PO

sin(45)/√5 = sin PMO /[2√2]   

1/[√2 * √5] = sin PMO /[2√2]

1/√5 = sin PMO / 2.......therefore

sin^-1( 2/√5) = PMO  = about 63.43°

Then angle MOP = [180 - 45 - 63.43]° = about 71.57º

So

√5/sin 45  = PM/sin71.57

PM = √5sin71.57 / sin45  =   3

$${\mathtt{1\,869\,000\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{112\,140\,000\,000\,000}}$$

We don't need to worry about the "1" out front acting as a multiplier since 1 times anything is just that thing.........so.....

√(1-(719.31/89602783250817600))  = .99999.......

Thanks, fiora....I totally mis-read that one.....!!!!

Awesomeee's question is 21^2+22^2+...+40^2

not 1^2+2^2+3^2+4^2+....39^2+40^2

21^2+22^2+...+40^2=[(1^2+2^2+3^2+...39^2+40^2)-(1^2+2^2+...19^2+20^2)]/6

                                =$${\frac{\left[{\mathtt{40}}{\mathtt{\,\times\,}}\left({\mathtt{40}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}\left({\mathtt{81}}\right){\mathtt{\,-\,}}{\mathtt{20}}{\mathtt{\,\times\,}}\left({\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}{\mathtt{41}}\right]}{{\mathtt{6}}}} = {\mathtt{19\,720}}$$

We can multiply the numerator and denominator by 40 and we have:

(-16)(15)/30          notice that (15)/(30) = 1/2...so we have

(-16) (1/2)  =

-8

Very nice, TR....!!!!

Pemdas?

ohhhhhhhh i get it now

(please excuse my dear aunt sally=parenthesees, exponents, multiplication, division, addition, and subtraction)

even though i sort of got it right. Dang those decimal places always are so tiny to catch. Its like the sad tears of a jolly beetle!

Plaease excuse my dear aunt sally. I need to talk to her for not teaching me pemdas correctly.

Ok this problem requires serious thinking 

covernt all mixed number fractions into improper fractions

so, this is how anon words this situation:

4 4/9 / 1 1/5

We need to make the two fractions improper. Lets start with 4 4/9

9*4=36+4=40=40/9

1*5=5+1=6=6/5

this is division though, so now we do the recipicult, as some really picky math masters say, but if you dont care about all the math vocab, you can just say, flip the numbers 6 and 5 in reverse, so now its 5/6

get rid of division, and replace it with multiplication

making the new equation:

$$40/9 * 5/6$$

as you can see you can cross cancel 40 and 6, divide by 2

40/2=20

6/2=3

now its $$20/9 * 5/3$$

20*5=100

9*3=27

now the improper fraction is:

$${\frac{{\mathtt{100}}}{{\mathtt{27}}}}$$

Now divide 100 by 27 and lets see what we get 

you see, 27 can go into 100 3 times 

do this equation to figure out the remaining:

$${\mathtt{100}}{\mathtt{\,-\,}}\left({\mathtt{27}}{\mathtt{\,\times\,}}{\mathtt{3}}\right) = {\mathtt{19}}$$

Correct answer:

3 19/27 or 100/27

[ 3 + -2(3 + (-2)) - 3^2 ] /  [ -2 -3 + (-2)^2 ]  =

[3  -2(1) - 3^2] / [ -5 + 4]  =

[ 1  - 9] / [-1]  = 

[-8] / (- 1)   =   8/1   =   8

Here's one method.....but.....maybe not the fastest one !!!

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

The equation of the circle  is  x^2 + y^2   = 56.25

The chord of 12 cm in  length will have one of its endpoints at  (6,y₁)......and y₁ =

√[56.25 - 6^2] = √[56.25 -36 ]  = 4.5  { taking the positive value of the  root  }

And

The chord of 9 cm in  length will have one of its endpoints at  (4.5, y₂)......and y₂ =

√[56.25 - 4.5^2] = √[56.25 - 20.25 ]  = 6   {again, taking the positive value of the root}

So....the distance between the chords is  y₂ - y₁  = 6 - 4.5   = 1.5 cm

Here's a pic.....

Note that ED = 9, CB = 12 and  FG = 1.5

How to get rid of my annoying sister Piper?