Given pa=7 in. and cb=11 in. what is ca ?

The answer is 11 inches.

The length of CA is 11 in.  

Step-by-step explanation:

We need to find the length of CA of provided figure

Given:- AP = PB  , CB = 11 in. and ∠CPB =90°

In triangle ΔAPC and ΔBPC

CP =CP ( common )

Since, AP = PB

⇒ PB = 7 in.

In ΔBPC

By pythagoras ( since ΔBPC is right angle at ∠P )

(prependicular)² + (base)² = (hypoteneous)²

                     (CP)² + (PB)²  = (CB)²

                      (CP)² + (7)²  = (11)²

                       (CP)² + 49  = 121

Subtract both the sides by 49, in above

                (CP)² + 49 - 49  = 121 - 49

                               (CP)²   = 72

                                 CP = √72

In ΔAPC

By pythagoras ( since ΔAPC is right angle at ∠P )

(prependicular)² + (base)² = (hypoteneous)²

                     (CP)² + (PA)²  = (CA)²

                      (√72)² + (7)²  = (CA)²

                           72  + 49  = (CA)²

                                    121  = (CA)²

                                   √121 = CA

                                        11 = CA

Therefore, The length of CA is 11 in.

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.

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

~just a girl in love with shawn mendes