ElectricPavlov

5 ' x 6 '   x   .75 '  = volume of water in ft³    (.75 ft is 9 inches)

the water will rise by 1 ft³     which will be    1 ft³  =  5' * 6' * x'       x = 1/30 ft = .4 inch

a second cube will raise the level by the same amount   .4 inch

adding all of those cubes raises the wate level to the top of the cubes    =  1 ft deep

The HEMISPHERICAL cap has a 'height'   equal to the radius = 20  cm

Surface area of a sphere = 4 pi r^2     <====== take 1/2 of this because it is a HEMI-sphere

h   will = 0     when the ball hits the ground

0 = -16t^2+32t+128     Use quadratic formula of factoring to solve for 't'    throw out the negative t value

Flipped around the y -axis       blue = f(-x)

Volume of a sphere    V = 4/3 pi r³        Calculate the volume of the LARGER sphere r = 6

                                                                  then subtract the volume of the smaller sphere  r = 3   

The blue graph is shifted UP by 3     so     y = f(x) +3

     AND it is shifted to the RIGHT by 2    so    y = f(x-2) + 3

sin 5.9 = h / x        and     sin 10.3 = h / (2.9-x)   

h / sin 5.9  = x         and       x = 2.9 -  h/ sin10.3      equate the two definitions of 'x' to calculate 'h'

h / (sin 5.9)  = 2.9 - h / (sin10.3)

h = .189 km = 189 m

The black line is y = f(x) = 4      Wherever the black line crosses the red graph, scan down to the x-axis to get the x value

Average speed = total distance / total time          total distance = 4

50 m/hr     =     4 m /  ( 2 m / 30 m/hr   +  2 m/ x m/hr)

4 / 50 - 2/30 = 2/x

x = 150 m/hr    for the final 2 miles <=====Pretty fast!          See what you find for the next two !

Once you have the equations for two lines, the point of intersection (a,b) satisfies both equations ....so if you equate the line equations

   you can solve for the point x, which is 'a'

2x-10 = -4x+36  

6x = 46

x = 46/6    = 'a'      now use this value in one of the equations to calculate y (which is the 'b' value) .....then add them together to answer your Q