Answer:
Explanation:
Let x ft be used to make square and 2-x ft be used to make equilateral triangle.
each side of square = x/4
area of square = ( x /4 )²
Each side of triangle
= (2-x) /3
Area of triangle = 1/2 (2-x)²/9 sin 60
= √3 / 36 x (2-x)²
Total area
A = ( x /4 )² +√3 / 36 (2-x)²
For maximum area
dA/dx = 0
1/16( 2x ) -√3 / 36 x2(2-x) = 0
x / 8 - √3(2-x)/ 18 = 0
x / 8 - √3/9 + √3/18 x = 0
x ( 1/8 + √3/18 ) = √3/9
x(.125 +.096 ) = .192
x = .868 ft
the answer is a: galaxies. galaxy clusters are groups of galaxies that like to hang out together out there in space. the milky way's own galaxy cluster is called the local group.
Answer:
a) 
b) 
c) 
d) 
Explanation:
Given:
- mass of the astronaut,
- vertical displacement of the astronaut,
- acceleration of the astronaut while the lift,
a)
<u>Now the force of lift by the helicopter:</u>
Here the lift force is the resultant of the force of gravity being overcome by the force of helicopter.
where:
force by the helicopter
force of gravity
b)
The gravitational force on the astronaut:
d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero, 
using equation of motion:
c)
Hence the kinetic energy:
Potential energy U = 174J = m*g*Δh
m mass
g = 9.81 m/s²
Δh = 5.1 - 5.1cos32° = 0.77
Solve for m.
A theory cannot become a law because it explains what is observes and does not describe it.
