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Tan(Y) = 4/10

--->   Y  =  Tan^-1(4/10)

--->   Y  =  21.80°  or  0.38^r  (approximately)

(Assuming that the uppercase T in Tan means that you want only the principal value.) 

Assuming that the main operation is the division, we get:

6 to the second is 6² = 6 x 6 = 36

2 times 3 plus 4 is 2 x 3 + 4  =  6 + 4  =  10

36 divided by 10 is 3.6

However, just starting from the left to the right, using the order of operations, we get:

6² ÷ 2 x 3 + 4

=  36 ÷ 2 x 3 + 4

=  18 x 3 + 4

=  54 + 4

= 58

Hello Herr Massow:

Aside from the occasional malfunctions caused by the bloated subroutines of Apache, your site has allowed for a remarkable creation of semi-structured mathematics and sciences at all levels-- from the basic to the advanced. The ebb and flow of the social component gives this forum a cohesive structure that is not seen in any other maths or sciences forums. For want of a better description, it seems as if this site is a virtual form of abiogenesis. It’s truly amazing!

Looks like my attack against popcorn has been called truce, as we both desire our popcorn to be buttered.....

however, the soda wars isnt over yet, we must come up with a new creation thatll defeat every soda in the world, release Operation Fanta Doomsday!

*after many hours of drafting new plans

 me: this plan is terrible! Why you choose to do a Dr. Pepper 2.0 when the first one is already good? We need one thats not only good and original, but also one that can defeat Fanta and Coke

dr. Terror: mwahahaha

me: whats so funny?

dr.: i came up with a new one, one even better, cuz its not even soda! Its iced coffee! Must try it!

me: ok

me: this is a genius plan, great plan. 

Alex: this is the best plan ever. Nothing can defeat this amazing iced coffee with caramel

me: i already know the name

Dr. : what is it?

me: lets call it:

The Caramel Frapuccino!

*evil laughs everywhere

now this brings doom to Fanta fans, or fanboys if i may say, not only will it guarentee to throw fits, but also let everyone join the Frapuccino Army, and defeat Fanta and Pepsi once and for all!!!! Wait, lets pour Coke in it for extra Evil!!!!!

new name: Coke Frapuccino!!!!

Operation Coke/Coffee Begins

$$125^{\frac{2}{3}}\rightarrow(125^{\frac{1}{3}})^2\rightarrow5^2\rightarrow25$$

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More explanation is needed!

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The exclamation mark is the factorial sign.  So 21!, spoken as twenty-one factorial, means 21*20*19*...*3*2*1,

$$\frac{21!}{5!6!10!}=\frac{21*20*19*...*11*10*9*...*2*1}{5!*6!*10*9*...*2*1}=\frac{21*20*...*11}{5*4*...*2*1*6*5*...*2*1}\\\\=\frac{14079294028800}{120*720}=\frac{14079294028800}{86400}=162954792$$

.

Does this help:

.

ive never tasted Sierre Mist or Dr.Pepper........so ive only got Fanta or Mirinda as my pets......or 7up if i want a lemon like taste.......and popcorn...im not giving up...butter-pepper popcorns are just the best!!

determine whether the sequence is arithmetic and find the common difference if it is arithmetic and if it is find the 32nd term 3,18,33,48,...

$$\small{\text{
we have $a_1=3, ~a_2=18,~a_3=33,~a_4=48$
}}\\\\
\small{\text{
the differences are $a_2-a_1=18-3=\mathbf{15}, ~a_3-a_2=33-18=\mathbf{15},~a_4-a_3=48-33=\mathbf{15}$
}}\\
\small{\text{
the common difference $ \mathbf{d} $ is $\mathbf{15} $
the sequence is arithmetic
}}\\\\
\small{\text{
the terms are $ a_n=a_1+(n-1)\cdot d $
}}\\\\
\small{\text{
the 32nd term is:
}}
\small{\text{$
\begin{array}{rcl}
a_{32} &=& 3+(32-1)\cdot 15\\
a_{32} &=& 3+31\cdot 15\\
\mathbf{a_{32}} &\mathbf{=}& \mathbf{468}\\
\end{array}
$}}\\\\$$

i need to know how far a .50 cal round will go if fired at a 45 degree angle with a muzzle velocity of 2850fps

The initial vertical velocity will be 2850*sin(45)=1425*sqrt(2)  f/s

The initial horizontal velocity will be 2850*cos(45)=1425*sqrt(2)  f/s

Let the initial point be x=0,y=0

$$\\\ddot y=-32\;fps^2\\\\
\dot y=-32t+1425\sqrt2\;fps\\\\
y=-16t^2+1425\sqrt2t+0\;f\\\\
$Find t when y=0$\\\\
0=-16t^2+1425\sqrt2t\\\\
0=t(-16t+1425\sqrt2)\\\\
t=0\qquad or \qquad 16t=1425\sqrt2\\\\
t=0\qquad or \qquad t=\frac{1425\sqrt2}{16}sec\\\\\\$$

$$\\\ddot x=0\\\\
\dot x=1425\sqrt2\\\\
x=1425\sqrt2 \;t\;\;\; feet\\\\\\
When\;\;t=\frac{1425\sqrt2}{16}sec\\\\
x=1425\sqrt2 \times\frac{1425\sqrt2}{16} \;\;\; feet\\\\
x=\frac{1425^2*2 }{16} \;\;\; feet\\\\$$

$${\frac{{{\mathtt{1\,425}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{2}}}{{\mathtt{16}}}} = {\mathtt{253\,828.125}}$$

253828 feet  

$${\frac{{\mathtt{253\,828}}}{{\mathtt{5\,280}}}} = {\mathtt{48.073\: \!484\: \!848\: \!484\: \!848\: \!5}}$$

48 miles.    Mmmm Now that sounds like a stretch.   

In the diagram, DAB = CBA = 90 degrees, EC = 5cm and ED = 10cm. The point F is the reflection of C in the line AB, and DF intersects AB at E. Given that the area of Traingle CED is 12.5 cm squared, and angle DEC =30 degrees, what is the length of CD?

read"the point F is the reflection of C in the line AB, and DF intersects AB at E."

the point F is the reflection of C in the line AB mean point F in the line AB;DF intersects AB at E mean point e is also in line AB (this is not important to this question tho)

"EC = 5cm and ED = 10cm.angle DEC =30"

CD^2=DE^2+CE^2-2DE*CE*cos(angle DEC)

CD^2=100cm^2+25cm^2-100cm*sqrt(3)/2

$${{\mathtt{CD}}}^{{\mathtt{2}}} = \left({\mathtt{125}}{\mathtt{\,-\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{{\mathtt{cm}}}^{{\mathtt{2}}}$$

$${\mathtt{CD}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}}{\mathtt{\,\times\,}}{\mathtt{cm}}$$ 

$${\mathtt{CD}} = {\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}} \Rightarrow {\mathtt{CD}} = {\mathtt{6.196\: \!568\: \!374\: \!637\: \!379\: \!5}}$$ cm

This is an AP

the common diff is -2.5

Tn=a+(n-1)d

Tn=4+(n-1)*-2.5

Tn=4+-2.5(n-1)

Tn=4-2.5n+2.5

Tn=6.5 - 2.5n

you have a=1

and

x as a function of a       OR             a as a function of x             ( It makes no difference which)

I suppose since the first one has the subject a it is probably a little nicer if the second on also has a subject of a but either way is correct.  That is what I think anyway. :)

So, as long as you state your restrictions, your answer is fine Sabi :)

Who is Mark?   

Is he the dead guy?  You would think he would have paid his own debts before he got knocked off, would't you?  How thoughtless of him!

"The who knocked off the insured mark". Sorry but you lost me.

1/2 + x/6=18/x

6x(1/2 + x/6)=6x*(18/x)

3x+x^2=108

x^2+3x-108=0

(x+12)(x-9)=0

x=-12 or x= 9

Try to make sense of this post

$$\\\frac{\sqrt{10}}{10}+\frac{1}{\sqrt{10}}\\\\
=\frac{\sqrt{10}}{10}+\frac{1*\sqrt{10}}{\sqrt{10}*\sqrt{10}}\\\\
=\frac{\sqrt{10}}{10}+\frac{\sqrt{10}}{10}\\\\
=\frac{2\sqrt{10}}{10}\\\\
=\frac{\sqrt{10}}{5}\\\\$$

ok I think I understand you

Eddie gets 300+(400/3) dollars   and   joe and John both get (400/3) dollars

The extra 300 that Eddie gets it 3/7 of the total so that should attract 3/7 of the debt

$${\frac{{\mathtt{3}}}{{\mathtt{7}}}}{\mathtt{\,\times\,}}{\mathtt{300}} = {\frac{{\mathtt{900}}}{{\mathtt{7}}}} = {\mathtt{128.571\: \!428\: \!571\: \!428\: \!571\: \!4}}$$    that is $128.57

The rest of the debt is divided equally 3 ways        

rest of debt =    $${\mathtt{300}}{\mathtt{\,-\,}}{\mathtt{128.57}} = {\mathtt{171.43}}$$

$${\frac{{\mathtt{171.43}}}{{\mathtt{3}}}} = {\mathtt{57.143\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

So Eddie pays    $${\mathtt{128.57}}{\mathtt{\,\small\textbf+\,}}{\mathtt{57.14}} = {\mathtt{185.71}}$$   dollars

John and Joe pay   $57.14

check:   $${\mathtt{185.71}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{57.14}} = {\mathtt{299.99}}$$       

There you go ...   someone better cough up the extra 1 cent :)

There are lots, wqhat do you want me to choose from?

You cannot post pics unless you are a member.   :/

Great answer DarkbBlaze347  

There is no graph - you have to be a member to post pictures.