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To find the height of Delicate Arch in Arches National Park in Utah, a surveyor levels a theodolite with the bottom of the arch. From there, she measures the angle of elevation to the top of the arch omegle (link, that didn't even work, removed)

She then measures the distance from where she stands to a point directly under the arch. Her results are shown in the diagram.

What is the height of the arch?

PERIMETER:

We know all the measurements, we just need to know the line above the 12m. We see that the small figure poking out has a width of 3m. So 12m - 3m = 9m. 3m + 9m + 9m + 12m + 5m = 38m

AREA:

If the figure had no piece cut out, then the answer is 12 x 9 = 108m². The piece that is cut out is basically 9m x 4m = 36m².

108-36 = 72

Area = 72m²

Perimeter = 38m

How about proofreading your question....

  C (9, 2)  =  36 outcomes

Only  1  possibility   ⇒    1  and  4

Probabilty  =   1  /  36

Vol  of cube  =  side^3  =  30^3     (1)

Vol  of sphere =  4/3  pi * (15)^3   (2)

Vol not  occupied by the sphere =  (1)  - (2)  = 

30^3  - (4/3)pi (15)^3  =  

(27000 - 4500pi) cm^3  

h(t) = -16t^2+ 64t + 17

put in t = 1  and calculate the height at 1 second

Highest point occurs a t t = -b/2a    where b = 64   and a = -16    use this value of 't' in the equation to calculate the highest point

When the rock hits the ground h = 0

    sooooo    0 = -16t^2 + 64 t + 17          use Quadratic Formula to find 't' values   (throw out the negative 't' value)

                            quadratic formula   a = -16     b = 64     c = 17

$t = {-b \pm \sqrt{b^2-4ac} \over 2a}$             plug and play !

I see what EP means......pick your poison  ( carefully)

I think the English language has got us cornered....

I think it says      A square is a rectangle   but it (square ) is not a rhombus

Chris thinks it says        A   square is a rectangle but a rhombus is not a rectangle.

Pick you interpretive answer !  

Yah...no kidding !   Kinda Escher-like  !     Makes my mind all pretzel-up !

area =  l x w

        =   4 1/8 x 2 =  8 1/4   ft ²

Find the area of the triangular sides......then multiply be the 'thickness' of 15 ft

cos (8.95/2)   * 35 = 'height' = 34.8933 ft

base = 2 *  35 * sin (8.95/2) = 5.462 ft

volume = THICKNESS * area =    15       *   1/2  5.462 * 34.8933 =  1429.32 ft³

LOL!!!!......the  second near-to-impossible figure.....here's  the first :

Rectangle -  a quadrilateral having 4  right angles

Thus....a square is a rectangle.....but a rhombus is not

.....again   ....   haha    

Wow....what a skewed-not-to-scale looking drawing..... if that angle is really 45 ^o  then the lower right angle is also 45^o

   the hypotenuse of the 3-4 triangle is 5

sin45 = opposite/hypotenuse = x / 5

sqrt 2/ 2 = x/5

x = 5 sqrt(2) / 2     or  5/2  sqrt 2

-7pi/6  =  5pi/6

tan (5pi/6)  =  -1/sqrt (3) =  - sqrt (3) / 3

csc (pi/4)  =  sqrt (2)

cos (17 pi / 3)  =   cos (5pi / 3)  =  1/2

I think this is false..... a square is a rhombus

" A rhombus with right angles is a square"    from     various.....

2sqrt (7) =  sqrt (28)

r =  sqrt  [ 5^2  + (sqrt (28))^2 ]  = sqrt  [ 25 + 28 ]  =  sqrt (53)

This is an angle in  Q2.....the cos  is  negative here....so.....

cos B  =  -5 / sqrt (53)  =  -5sqrt (53) / 53

The bottom triangle's base is 3 ft and its height is 2.6 ft.

Using the formula for the area of a triangle, $\frac{bh}{2}$, we get 3.9 square feet.

Now for the rest of the triangles

All 3 of the other triangles have the same base and height. The base is 3 and the height is 4.

Using the formula for the area of a triangle, we get 6 square feet. There's 3 of these triangles, so we multiply 6 by 3, getting 18.

Now we add 3.9 and 18

So the answer is 21.9 square feet

True.....

Btw, try to do these AOPS problems by yourself before posting them here, it helps you learn

Please let me know if this agrees with any 'correct' answer you may be given.

I like to learn and improve my understanding here as well.

I put 'correct' in quotations because I would want to see the logic behind it before I would necessarily accept an alternate solution as the better or correct one.

See my answer, here  :

https://web2.0calc.com/questions/ep-melody-cphil-please-come

There are 2pi radians in a full rev

  2pi R/ 3 R/ min =   2/3 pi minutes per rev    = 2.0944 min per rev

Period is   2/3 pi       2pi/x = 2/3 pi     x = 3

soooo     sin 3t   

   he starts at 3 o'clock position which is 1/2 way between low and high points....so there is no phase shift

Amplitude = 44                 44 sin 3t    = height above center

Height above ground  IS shifted by 44 feet up from center         44 sin (3t) + 44  would be height above ground   ( at time = 0 he is 44 ft above ground)

Thx, CPFB!!!!!

Glad we could "un-stump" you......