CPhill

OK........we have .246 degrees

To find the number of minutes, multiply this by 60 = 14.76 minutes

This says we have 14 minutes and another .76 minutes. And since there are 60 seconds in a minute, we have .76 * 60 = 45.6 seconds

So....

.246 degrees  = 0 degrees 14 minutes 45.6 seconds

EF is the hypoteneuse and we're trying to find the side adjacent to angle E, i.e., DE

So, we can use the cosine for this....we have

cos(68) = DE/11   mutiply both sides by 11

11* cos (68) = DE = about 4.12

----------------------------------------------------------------------------------------------------------------------------

The second one is just like the first...we know the hypoteneuse XY and we're trying to find the adjacnt side to angle Y, i.e., ZY

So we have

cos (15) = ZY / 14

14 * cos (15) = ZY = about  13.52

Thanks for those kind words......I'll recommend that Melody use your answer in her "Daily Wrap"....

Ln uses base "e" ≈ 2.718 .......this number occurs naturally in many "growth" and "decay" situations

Log uses 10 as the base

I didn't run the numbers 7UP, but it looks good....well done !!!

If the diameter of the photo is 18, then the radius  = 9

And the area of the circle is

A = pi * r^2   =  pi * (9)^2  = 81* pi

And the area of the frame is just (20)^2 = 400

So, the ratio of the area of the photo to the area of the frame is just .... [ 81 * pi ] : 400

sin^2(0) = sin(0) * sin(0) = 0 * 0 = 0

The general form is

y = a ( x -  h)^2 + k     where (h, k) is the vertex  and (x, y) is the y intercept

Since we know the y intercept is a point (0, b), we can plug this into the "formula" to find "a"

Example......suppose we have a parabola whose vertex lies at (2, -2) with a y intercept of (0, 0)

Then we have

0 = a (0 - 2)^2  - 2   add 2 to both sides

2 = a(-2)^2

2 = a(4)    divide both sides by 4

2/4 = 1/2 = a

So...our equation is  y = (1/2)(x - h)^2 + k  =  

y = (1/2)(x - 2)^2 - 2

The arc length, S, is given by

S = rΘ  where Θ is in radian measure

An alternative formula is

S = (Θ / 360) * 2 * pi * r    where Θ is in degrees

Using the Pythagorean Theorem, we have

Hypoteneuse = √[(6.1)^2 + (9.3)^2 ] = √123.7 = about 11.12 units