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If tan(x) + sec(x) = 22/7, what is tan(x)?

Hello Guest!

\(tan(x) + sec(x) = \frac{22}{7}\)

\(tan(x)\ \pm \sqrt{1+tan^2(x)}= \frac{22}{7}\)          \(tan(x)\ is\ u.\ \frac{22}{7}\ is\ \pi.\)  

\(u\pm\sqrt{1+u^2}=\pi\\ \pm\sqrt{1+u^2}=\pi-u\\ 1+u^2=\pi^2-2u\cdot \pi+u^2\\ \pi^2-2\pi u-1=0\)

\(2\pi u=\pi^2-1\\ u=\frac{\pi^2-1}{2\pi}= \frac{\pi}{2}-\frac{1}{2\pi}\)                           \(\pi \ is\ \frac{22}{7}\)

\(u=\frac{22}{14}-\frac{7}{2\cdot 22}= \frac{11}{7}-\frac{7}{44}=\frac{44\cdot 11-49}{7\cdot 44}=\frac{435}{308}=\color{blue}1.41233766234\)

\(tan(x)=1.41233766\)

  !

\(AD:AE=AB:AC\\ (8+6):12=8:AC\\ AC=\large \frac{12\cdot8}{8+6}\)

\(AC=6.\overline{857142}\)

  !

Use the volume formula of a sphere to get the volume of the pearl:
v = 4/3 pi r³ 

v = 4/3 pi (2.1)³

v = 4/3 pi (9.261)

v = 38.79238608

v = 38.8 mm³

I feel strongly offended that you are still on here. You are one obnoxious little assshole.  

We’ll see if you are the next to go in this purge cycle…….. 

Thanks, Hugo
I just logged in an hour ago and now I see this lol
my user is unknown

wut! how?!

ok, thanks Hugo!
ur the best

i think so!

Hi.

Logarithmic functions are the inverse of exponents, which means...

an exponent, say a^b, is b number of a's multiplied together.

On the other hand.

Log_a (b) is asking a to the what power is b?

So we are solving for x where a^x = b.

Thus, say, log. base 10(this is the "a") of 1000, is 10^x = 1000, x = 3.

Log₂ (8) = 3.

If you don't understand anything feel free to ask!

Hi,

I solves it to get x = 3/7, y = -1/7, z = 4/7.

Solve for x:
x^6 - 2 x^4 - x^2 + 2 = 0

The left hand side factors into a product with four terms:
(x - 1) (x + 1) (x^2 - 2) (x^2 + 1) = 0

Split into four equations:
x - 1 = 0 or x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Add 1 to both sides:
x = 1 or x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0

Subtract 1 from both sides:
x = 1 or x = -1 or x^2 - 2 = 0 or x^2 + 1 = 0

Add 2 to both sides:
x = 1 or x = -1 or x^2 = 2 or x^2 + 1 = 0

Take the square root of both sides:
x = 1 or x = -1 or x = sqrt(2) or x = -sqrt(2) or x^2 + 1 = 0

Subtract 1 from both sides:
x = 1 or x = -1 or x = sqrt(2) or x = -sqrt(2) or x^2 = -1

Take the square root of both sides:

 x = 1     or      x = -1      or      x = sqrt(2)      or      x = -sqrt(2) 

Well we know from Guest that total time was 5 hours

   total distance was 180 + 180 = 360 km

Avg speed =   360km/5hr = .........    km/hr

The 'a' s   cancel and you have     3x = 102   divide both sides by 3

                                                        x = 34