Rom

This is a right triangle with hypotenuse equal to the length of the ladder, 50 feet, and one leg equal to 33.6 feet.

By the Pythagorean theorem we have

$$50^2=(33.6)^2+h^2$$

$${{\mathtt{50}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\left({\mathtt{33.6}}\right)}^{{\mathtt{2}}} = {\mathtt{1\,371.04}}$$

$${\mathtt{h}} = {\sqrt{{\mathtt{1\,371.04}}}} = {\mathtt{h}} = {\mathtt{37.027\: \!557\: \!305\: \!336\: \!791\: \!6}}$$

so about 37.03 feet up the side of the house.

$$80=2 \sqrt{5s}$$

$$40=\sqrt{5s}$$

$$1600=5s$$

$$s=320$$

Here's another way to do this....it's a "trick" I used to use when I tutored...

Take the points and "reverse" them.....we have (2, -1) and (3, 3)

Line them up like this and draw a line under them

(2 , -1)

(3 ,   3)

______      Now just "subtract" the "underneath" things from the things "overhead" - individually - like this

 (2 , -1)

(-3 ,  - 3)

_______

-1  ,  -4

Now.......put the thing in the first column "over" the thing in the second column   (-1) / (-4)  = 1 / 4 and Voila!!.......there's the "slope" 

 

Let's take a look at this.

given (x1,y1), (x2,y2)

CPhil flips the coordinates to create (y1,x1) and (y2,x2) then subtracts to obtain

(y1-y2,x1-x2) and then creates (y1-y2)/(x1-x2)=(y2-y1)/(x2-x1) which is the usual slope formula.

It's Bona Fide!

$$5 - e^{2x}=-15$$

$$20=e^{2x}$$

$$\ln(20)=2x$$

$$x=\dfrac {\ln(20)} 2$$

$${\frac{{ln}{\left({\mathtt{20}}\right)}}{{\mathtt{2}}}} = {\mathtt{1.497\: \!866\: \!136\: \!776\: \!995\: \!5}}$$

commission = 5.25% * sales = 0.0525 * sales

65.42 = 0.0525 * sales

sales = 65.42 / 0.0525 = $1246.10

(-2.9 + 4.4)a + (6.8 - 7.3) = 3.9a - 2.9

$$radians = \pi \dfrac {degrees} {180}$$

$$x^{-a} = \dfrac 1 {x^a}$$

other than that I'm not sure what you are asking.

The word is equation

No

it equals

3² x 4903 x 1054177223806713372655216164815924278402046003316696308730997973143754\
147290028619127229262829292630108573784479937781952803