Express the cosine of W as a ratio of the given side lengths. A)12/13
B)13/12
C)5/12
D)5/13

Option A) 12/13

Step-by-step explanation:

we know that

The cosine of angle U is equal to divide the adjacent side to angle U (UV) by the hypotenuse of the right triangle (UW)

so

cos(U) = (UV)/(UW)

substitute the given values

cos(U) = 12/13

12 /13

Step-by-step explanation:

I do it on usatestprep

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

it would take 7/10 of an hour too fill the pool.

step-by-step explanation: