ElectricPavlov

for f(2)   the piece    ax + 3    applies since  2 is > 0

           f(2) = a(2)+3 = 5

                    so   a  =1

for f(0)    the second piece applies because x = 0

                  f(0) = ab = 2       we know a = 1    so  b = 2

for f(-2)     the third piece applies since   -2 <0

                      f(-2) = bx+c = 0

                                 2 (-2) + c = 0       so c = 4                  I'll let you finish !

Set the pieces = 0 to see if they qualify

4x+1 = 0

  x = -1/4           this piece was for x <= 3    so   x = -1/4    is one answer

18-4x = 0

  x = 4 1/2          this piece was for x > 3       so   x = 4 1/2 is another answer     

                                -1/4 + 4 1/2 = __________ 

You're welcome ! 

cos^2 + sin^2 = 1

   (3/5)^2   + sin^2 = 1

        sin B = 4/5

Tan = sin/cos = 4/3

This has been asked many times......you can search to find the explanation   

+- 1 +- i        (four solutions )

The EXTERIOR angles   sum to 360 degrees    so they are 80  120   and 160 degrees

The EXTERIOR + corresponding INTERIOR  angle   sum to 180 degrees    so the smallest INTERIOR would be   180 -160 = 20 degrees

y is the height of the ball....    when y = 0   the ball is on the ground

0 = -16t^2 + 26t+ 105         Now use the Quadratic Formula   to find the 't' values  

                                   \(t = {-26 \pm \sqrt{26^2-4(-16)(105)} \over 2(-16)}\)          a = -16     b = 26    c = 105     (throw out the negative 't' value)

Simple internet search:

isotope = "each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element."

y = k / sqrt(x)

4 = k / (sqrt 2)           k, the proprtionality constant = 4 sqrt 2

16 = 4 sqrt 2    / sqrt x

4 sqrt 2 / 16 = sqrt x

16 * 2  / 256  = x

x = 1/8

Need some angle iformation to complete this ....