hectictar

\(\frac{\sin C}{20}=\frac{\sin 65^{\circ}}{19}\)

Multiply both sides of the equation by 20.

\(\sin C=20\,*\,\frac{\sin 65^{\circ}}{19} \\~\\ \sin C = \frac{20\sin 65^{\circ}}{19}\)

Take the arcsin of both sides of the equation.

\( C = \arcsin(\frac{20\sin 65^{\circ}}{19})\)

So...putting this into a calculator gives us

\(C\approx72.556^{\circ}\)

Hey..I think I can make up one that only requires basic trig and algebra knowledge 

Once upon a time there was a boy named Chris. He liked to eat potato chips and watch football on TV. One day, Chris decided that he needed a place to store all his potato chips. So, he set out to make a gigantic silo to hold all the chips.

The bottom was to be shaped like a cylinder, and the top shaped like a cone. The entire thing, from the lowest point to the highest point, was to be 100 feet tall.

The diameter of the cylinder, as well as the cone at the top, will be 30 feet. The angle formed inside the silo by the wall of the cylinder and the wall of the cone will be 110º.

What is volume of the silo?

Here's roughly how it looked like:  

Yep! There is a " ! " button right next to the " log " button.
Or, you can just type an exclamation point after the number you want "factorialized" (?) 

On this calculator, you can type them in like this:

numerator / denominator

For example...

To do:   \(\frac45\)

Type: 4/5

If the numerator or denominator contains another operation, make sure to put parenthesees around it.

Also, on the right end of the input bar, you can click "input helpers" and select "fractions."

OOOH ! I got one...it requires more than just logarithm knowledge though!

Be warned! I spent a VERY LONG time on this and never got the answer 

But....you asked for it....here it is:

3log(x - 2) = log(2x) - 3

In order to make   x² + 14x   a perfect square trinomial, add (14/2)²

x² + 14x + (14/2)²

x² + 14x + 7²

x² + 14x + 49

Now it can be factored like this

(x + 7)(x + 7)

(x + 7)²

And whatever you do to one side of the equation, do the same thing to the other side.

So we had to add 49 to both sides. This video might help explain it more:

We can multiply this out like this...

-3(x - 2)² + 4

(-3)(x - 2)(x - 2) + 4

(-3)(x² - 2x - 2x + 4) + 4

(-3)(x² - 4x + 4) + 4

-3x² + 12x - 12 + 4

-3x² + 12x - 8

Here's one way to do it.

We can get the equation of this parabola in vertex form.

y = -1/4 x² + 4x - 19

Multiply through by -4 .

-4y = x² - 16x + 76

Subtract 76 from both sides of the equation.

-4y - 76 = x² - 16x

Add (16/2)² , or 64, to both sides of the equation.

-4y - 76 + 64 = x² - 16x + 64

Now we can factor the right side.

-4y - 12 = (x - 8)²

Divide both sides by -4.

(y + 3) = (-1/4) (x - 8)²

Now we can see that the vertex of the parabola is the point (8 , -3 )

We want to get the equation of the circle into this form:

(x - h)² + (y - k)² = r²          , where (h, k) is the center and r is the radius.

x² + y² + 14x + 10y - 7 = 0

Subtract 7 from both sides of the equation and rearrange the left side.

x² + 14x   +   y² + 10y   =   7

Add (14/2)² , or 49,   and   (10/2)² , or 25, to both sides of the equation.

x² + 14x + 49   +   y² + 10y + 25   =   7 + 49 + 25

Now we can factor both parts like this

(x + 7)²   +   (y + 5)²   =  81

Now that it is in that form, we can see that the center of the circle is (-7 , -5)