Melody

Hi TR,

Congratulations on hitting the "Top Users Board"    You will have to answer lots of questions to retain ,and advance your position.   I am sure you will give it your best shot.  Thank you for protecting Camelot and your Queen so valiantly :)   

$$7x+4>18\\ 7x>14\\ x>2$$

cos(theta)=-1/2 and tan(theta)=sq3 find csc

Cos is neg and tan is pos so theta is in the 3rd quad.

Now put this aside for now and look for the 1st quad equivalent angle.

Draw a right angled triangle and call one of the acute angles theta.

The adjacent side is 1, the hypotenuse is 2, Using pythagoras's theorum you can determing that the third side is sqrt(3)

so tan (theta)=sqrt(3)

cos(theta)=1/2

cosec(theta)=1/sin2(theta)=hyp/opp = 2/sqrt(3) = (2sqrt3)/3

But theta it is in the 3rd quad so  sine and cosec are negative

cosec(theta)= - (2sqrt3)/3             (as an aside, theta is 240 degrees)

sec(1.24) to radian

The question does not really makes sense

sec(1.24) is a ratio not an angle so how can you express it in radians?

You probably mean that 1.24 is an angle in radians

Set your calc to radians and then just enter it

1/cos(1.24) = 3.0788

2^x - 6 + 2 ^( 3-x) = 0

$$2^x - 6 + 2 ^{3-x}= 0\\ 2^x - 6 + \frac{2 ^3}{2^x}= 0\\\\ (2^{x})^2 - 6*2^x + 8= 0\\\\ let\;\;y=2^x\\\\ y^2-6y+8=0\\\\ (y-2)(y-4)=0\\\\ y=2 or 4\\\\ 2^x=2\;\;or\;\;2^x=4\\\\ x=1\;\;or\;\;x=2 $$

Thanks Andre  :)

Can we see who is logged on ?

I am glad that you are back Alan.   :D

We have missed you and no one could answer these questions :(

You are on a calculator site !!

I have found the natural log of 200,000 (12.20607264553). How do I work backwards from the natural log to get 200,000?

$${ln}{\left({\mathtt{200\,000}}\right)} = {\mathtt{12.206\: \!072\: \!645\: \!530\: \!173\: \!7}}$$

$${{\mathtt{e}}}^{{ln}{\left({\mathtt{200\,000}}\right)}} = {\mathtt{199\,999.999\: \!999\: \!999\: \!9}}$$

 which IS    200,000

If you appraoch zere from the positive side it will approach infinity

BUT

If you approach zero from the negative side it will approach negative infinity.

so if you by zero the answer it NOT infinity.  It is undefined :))