All Answers 358090 Answers

You can add that step below your other work; it is correct.

To make the calculations easier, for now, replace "sin(2θ)" with x:

Then we have:     x² - 5x - 1  =  0

Using the quadratic formula:  x  =  [5 + √(25 + 4)] / 2  ≈  5.1926    

                                   or     x  =  [5 - √(25 + 4)] / 2  ≈  -0.19258

Since x = sin(2θ):       sin(2θ)  =  5.1926     or     sin(2θ)  =  -0.19258

     --->                           2θ  =  sin^-1(5.1928)     or     2θ  =  sin^-1(-0.19528)

     --->                             θ  =  sin^-1(5.1928) / 2     or   θ  =  sin^-1(-0.19528) / 2

Since sin does not have a value larger than 1, θ  =  sin^-1(5.1928) / 2  is an impossibility.

For  θ  =  sin^-1(-0.19528) / 2,  

      θ equals either 275.55°  or  354.4° (and all multiples of 180°, larger and smaller).

Oh no, the buddy system, the one thing that can make or break a field trip

someone call the panic patrol!!!

Hmmmm, although youre taking religion and maths the wrong way, this is hillarious

btw, im not completely protestant

im half protestant, half science

No one yet has dared to try out this bad boy problem, and today, im here to do it

So, what is 120.8/1593.50 you ask?

$${\frac{{\mathtt{120.8}}}{{\mathtt{1\,593.5}}}} = {\mathtt{0.075\: \!807\: \!969\: \!877\: \!63}}$$

5+2P=10-2P

im assuming here that 5+2P is 10, so we can use that for our find what equals P situation

(besides, its easier for me 5+2P than 10-2P)

$${\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{P}} = {\mathtt{10}}$$

We can subtract 5-5 and 10-5, equaling:

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{P}} = {\mathtt{5}}$$

We divide 2 on both 2P and 5, and P=2.5

overall answer: $${\mathtt{P}} = {\mathtt{2.5}}$$

What if i magically disappeared before i turn old?

when i get to paradise, i can just drink all the coke i want, and eat all the holy fuddruckers burgers i want, and magically win every single eating challenge, and that sounds way better than hating the taste

(i am a christian protestant btw, so dont get confused with other religious paradises)

7up? Its really good, but....

#SPRITEFTW

fanta is pretty decent, i can relate to that

You can factor it as:

$$(x-\frac{1}{2})(x-4m+\frac{1}{2})=0$$

so  

$$\\ x=\frac{1}{2}\\ or\\x=4m-\frac{1}{2}$$

.

I tried the other two questions but still dont understand where to start because the equation doesnt look the same as the first question. What do i do? The square root and divison between the x's terrifies me :(

Sorry, it is in German!

standard deviation = Standardabweichung

Please try it!

1.) Mittelwert

2.) Varianz

3.) Standardabweichung

Hello Melody,

both links are the same. I will delete one !

Gruß radix !

Zero

it will be zero

Maybe maybe maybe but wen you guys will be like 70 then you will protest against it......coke is the worst for our bones......that's why I avoid black drinks........kids like taste......old people won't like taste....( soon you'll be one) ^^

I'm telling you maths humour is the best........looks like worlds new comedian is passing time on a maths forum....^_^

@@ End of Day Wrap  Sun 12/7/15   Sydney, Australia Time   8:25pm  ♪ ♫

Hi everyone,

It was another quiet day but there were still some good questions and our answerers were keen to help :)

Today answer credits go to TitaniumRome, CPhill, Geno3141, Radix and Alan.  Thank you :)

Thanks Geno :)

Thanks Radix,

Did you mean both those links to be the same?

I added this little applet to the reference material thread. :)

3. if the parallel sides of trapezium are 25cm and 11cm, while its non- parallel sides are 15cm and 13 cm . find the area of the trapezium... 

I am let the long parallel side 25cm be the bottom.

15+13=28  Only 3cm more than 25cm.  

So it is obvious to me that the two angles at the bottom MUST both be acute angles.

Here is the trapezium.

Now I am going to cut the two triangles of the end and push them up together so that I have a triangle with side lengths   14cm on the bottom and 15cm and 13cm on the other two sides

The height of the triangle is also the height of the trapezium.

Here is a pic

Using pythagoras's theorem

$$\\15^2=(14-x)^2+h^2\\
225=196+x^2-28x+h^2\\
29=x^2-28x+h^2\qquad(1)\\\\
169=x^2+h^2\qquad (2)\\
(2)-(1)\\
140=28x\\
x=5\\
so\\
169=25+h^2\\
144=h^2\\
h=12cm\\\\
$Area of trapezium $ = \frac{(25+11)}{2}\times 12=216cm^2$$

48/2 * (9+3) = 24 * 12 = 288        I think this is right !

$${\frac{{\mathtt{48}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}\left({\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right) = {\mathtt{288}}$$

48 : (2*(9+3)) = 48 : (2*12) = 48 : 24 = 2

$${\frac{{\mathtt{48}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)\right)}} = {\mathtt{2}}$$

Gruß radix !

Fanta is probably the best fizzy orange drink.

But coke will never get boring.

Good morning Anonymous,

2000 / 13 degrees = $${\frac{{\mathtt{2\,000}}}{{\mathtt{13}}}} = {\mathtt{153.846\: \!153\: \!846\: \!153\: \!846\: \!2}}$$   degrees

=  $${\frac{{\mathtt{2\,000}}{\mathtt{\,\times\,}}{\mathtt{60}}}{{\mathtt{13}}}} = {\mathtt{9\,230.769\: \!230\: \!769\: \!230\: \!769\: \!2}}$$   minutes

+ 24 minutes  =>    $${\frac{{\mathtt{2\,000}}{\mathtt{\,\times\,}}{\mathtt{60}}}{{\mathtt{13}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{24}} = {\mathtt{9\,254.769\: \!230\: \!769\: \!230\: \!769\: \!2}}$$   minutes

=   $${\frac{\left({\frac{{\mathtt{2\,000}}{\mathtt{\,\times\,}}{\mathtt{60}}}{{\mathtt{13}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{24}}\right)}{{\mathtt{60}}}} = {\mathtt{154.246\: \!153\: \!846\: \!153\: \!846\: \!2}}$$    degrees

Gruß radix !

2. if p = 2-a, then find the value of a^3 + 6ap + p^3 -8 

$$\\a^3 + 6ap + p^3 -8 \\
= (6ap+p^3)-(8-a^3)\\
=p(6a+p^2)-(2-a)(4+2a+a^2)\\
$sub\;\; 2-a for p$\\
=p(6a+p^2)-p(4+2a+a^2)\\
$ factor out the p$\\
=p(6a+p^2-4-2a-a^2)\\
=p(p^2-a^2+4a-4)\\
=p((2-a)^2-a^2+4a-4)\\
=p(4+a^2-4a-a^2+4a-4)\\
=p(0)\\
=0$$

i don't kow