ElectricPavlov

1 /5   of 35   =   7 preferred GG

Note that     sin^2 + cos^2 =1 

                              1 - sin^2 = cos ^2

sin / sqrt (cos^2) = sin/cos = tan

e = 7a

then

e-s  = 36    and   a+s = 36        where 's'  is 'some'

e = 36+s              a = 36 -s       sub these into the red equation

36+s = 7 ( 36-s)

s = 27

Let's use conservation of momentum   

32.5 * 388  = 7.42 * m_c

m_c =  1699.46 ~~1700 kg

F = G  m1 m2 / r²       and m1 = m2

F * r²  /G   =  m²               F = 85   N      r = .036 m      G = 6.67430 x 10^-11   N m² / kg²

85 * (.036)²  / (6.67430 x 10^-11)    = m²     <====== NOTE:    m^{2    ,}    Also 'm' will have  kg  units

You should be able to take it from here !

Use Law of Cosines

52² + 67² - 2 (52)(67)cos(60) = (AB)²         I'll let you finish with the calculations ! 

Sphere volume = 4/3 pi r^3

      6.08 x 10^25 = 4/3 pi r^3

cubrt (6.08 x 10^25   * 3/4 / pi)  = r   = 2.439 x 10⁸ cm

..... but the question says the vertex is   2, 3    NOT    -2, 3

We want how many apples  's' picked ...so if possible put everything in terms of 's'

s = k+10        k = s-10

k = j+10         s-10 = j+10    so  j = s-20   

s    + s-10    + s-20 = 156

s = 62 pounds

The focus is always 'inside' the parabola curve    vertex 2,3     focus  0,3   is LEFT the vertex so the parabola opens leftward.