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a = 34.

180 - (180 -36-39) = ......

Use sin law to find the sidelengths      120/sin120 = RSide/sin35 = LSide/sin25

Then area = 1/2 ab sin (angle between ab)

ZX = sqrt(32)

angle(ZXY) = 105-45

YZ = sin(ZXY) * sqrt(32)

0.0015926535897932+(22/7-pi) = 0.0028571428571428187      =  1/350

Your explanation is a bullshit reason, because you have access to the AoPS help forum AND extra online access to your teacher if you are in an AoPS brick & mortar school.

Nibberlat, you explained everything except why you removed your question? 

It’s very covenant that 12 minutes after Geno answers your question, a guest posts,

“Please don't post AoPS problems. Is this from Algebra B?”  

Then 3 minutes later you delete your question.   

Do you really think we are that stupid?

Put the question back, so others can learn from it.

This question has been answered multiple times already...(your classmates probably asked it?)

Use the law of cosines to find angles B and C.

 ∠ B = 53.13°           ∠ C = 67.38°

x / tan(B) + x + x / tan(C) = 14   

x ≈ 6.461      

Use the law of sines to find a.

So, we can say that 6/sin(58)=a/sin(109). You should be able to solve this with a calculator. 
 

For c, do the same thing, but instead, say 6/sin(58)=c/sin(13)

:)

Not exactly, but you are getting closer! Let's think about it case by case. 
 

So, you are right that there is one chief, so that is 10.

Now, don't go ahead and choose the officers first! First, choose your two supporting chiefs. So that is 9C2.

Next, we choose our officers. It is not 5C2, since 1) we do not have 5 left (9-2=?) and 2) you need 4 officers, not 2 officers.

Can you go from here?

:)

The Pythagorean Theorem:  [ sqrt(N) ]² + 11²  =  17²

                                                           N + 121  =  289

                                                                      N  =  168

Step 1)  Place the equation into graphing form:  2x² + 2y² + 10x - 6y - 18  =  0

                     divide by 2:                                             x² + y² + 5x - 3y - 9  =  0

                     rearrange:                                         x² + 5x       + y² - 3y       =  9

                     complete the square:             x² + 5x + 25/4  +  y² - 3y + 9/4  =  9 + 25/4 + 9/4

                     simplify:                                                 (x + 5/2)² + (y - 3/2)²  =  35/2

Step 2)  Find the radius:  sqrt(35/2)

Step 3)  Find the area:  Area  =  pi ·[ sqrt(35/2) ]²  =  pi · 35/2

Area  6 x 8  + 3 x8  +  3x8  + 3x8    +  1/2 (3+6) x 2.6 x 2  mi²

Volume  1/2 (3+6) x 2.6   x8    mi³         You are left to do the calculations.....

Oh ok! I see, thank you!

When the ball hits the ground,  h will = 0

0 = -16t^2 + 28t + 144      Use quadratic formula to find t    .... throw out negative t values

a = -16    b = 28    c = 144

\(t = {-28 \pm \sqrt{28^2-4(-16)(144)} \over 2(-16)}\)

We have 10 choices for the first chief, no doubt about that 

then 9 choices for the supporting chief A

ASSUMING A officers are inferior to b, we have 8C2 ways

Then 6 for support B

then 5C2 for b officer?

Really? that's it?

ok, thanks! I was having a hard time factoring out x+9y but now I get it. 

The distance formula:  Distance  =  sqrt( (x₂ - x₁)² + (y₂ - y₁)² )

--->                  sqrt( (4 - x)² + (7 - 21)² )  =  10 · sqrt(2)

squaring both sides:  (4 - x)² + (7 - 21)²  =  200

                                  16 - 8x + x² + 196  =  200

                                             x² - 8x + 12  =  0

                                             (x - 6)(x - 2)  =  0

Either  x = 6  or  x = 2.

You'll need to finish ...

To expand upon Guest's answer:

sec(x) + tan(x)  =  5/2     --->     1 / cos(x)  +  sin(x) / cos(x)  =  5/2

Multiplying each side by  2·cos(x)   --->         2( 1 + sin(x) )  =  5( cos(x) )

Squaring both sides:                      4( 1 + 2sin(x) + sin²(x) )  =  25cos²(x)

Since  cos²(x) = 1 - sin²(x):                4 + 8sin(x) + 4sin²(x)  =  25 - 25sin²(x)

Rewriting:                                        29sin²(x) + 8sin(x) - 21  =  0

Quadratic formula:                                                      sin(x)  =  [ -8 +/- sqrt(2500) ] / 58

Choosing the positive answer:                                    sin(x)  =  42/58

Taking the opposite side as 42 and the hypotenuse as 58, 

by the Pythagorean formula, the adjacent side will be 40,

which means that the value of tangent is 42 / 40  =  1.05.

There are several ways to approach this; I'm going to rationalize the denominator of each term first.

[ 1 / (1 + 2i) ] · [ (1 - 2i) / (1 - 2i) ]  =  (1 - 2i) / 5

[ 3 / (1 - i) ] · [ (1 + i) / (1 + i) ]  =  3(1 + i) / 2

[ (3 -2i) / (1 + 3i) ] · [ (1 - 3i) / (1 - 3i) ]  =  (-3 - 11i) / 10

[ 1 / (1 + 2i) + 3 / (1 - i) ]  =  [ (1 - 2i) / 5 + 3(1 + i) / 2 ]  =  (17 + 11i) / 10

[ (17 + 11i) / 10 ] · [ (-3 - 11i) / 10 ]  =  (70 - 220i) / 100  =  7/10 - (11/5)i

I believe that the answer is 1.05.