Answer:
4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Subtract 8y from both sides.
Step 3: Subtract 18 from both sides.
Step 4: Divide both sides by -9.
y=4
Answer:250 N
Step-by-step explanation:
Given
mass of skater on left side 
mass of skater on right side 
If the skater on the left experience a force of 
If they push against each other then they must experience an equal force according to newtons third law
Thus 
Thus skater on right experience
force
Answer:
The length of the base in feet is 8 ft.
Step-by-step explanation:
The volume V of the rectangular prism is given by
V = l × w × h
But Area, A = l × w
∴ V = A × h
Where A is the base area and h is the height
From the question
A = 56 ft.² and V = 840 ft.³
∴ 840 ft.³ = 56 ft.² × h
840 ft.³ / 56 ft.² = h
15 ft. = h
∴ h = 15 ft.
Hence, the height of the rectangular prism is 15 ft.
Also, from the question
the sum of the length and the width of the base is equal to the height
i.e l + w = h
where l is the length of the base and w is the width of the base
Then, l + w = 15 ------ (1)
Also, A = l × w
Then, 56 = l × w ------- (2)
From equation (1)
l + w = 15
Then, w = 15 - l ------- (3)
Substitute this into equation (2)
56 = l × w
56 = l × (15-l)
56 = 15l - l²
Then,
l²- 15l + 56 = 0
l² -8l -7l + 56 = 0
l(l - 8) -7(l - 8) = 0
(l - 7)(l - 8) = 0
l - 7 = 0 OR l - 8 = 0
∴ l = 7 OR l = 8
Substitute the values of l into equation (3)
w = 15 - l
when l = 7
w = 15 - 7
w = 8
and when l = 8
w = 15 - 8
w = 7
From the question, the length of the base is longer than the width
∴ l = 8 and w = 7
Hence, the length of the base in feet is 8 ft.
<span>The 3rd astronaut would catch the 2nd astronaut and throw the 2nd astronaut towards the 1st and the game would end there.
The key thing to remember is conservation of momentum. Since all of the astronauts have the same mass and strength, I will be introducing a unit called "A" which represents the maximum momentum that one astronaut can produce while throwing another. So here's the game of catch, throw by throw.
Before the game begins, I will assume all three astronauts are stationary and have 0 momentum. So
Astronaut 1 = 0 A (Stationary, next to astronaut 2)
Astronaut 2 = 0 A (Stationary, next to astronaut 1)
Astronaut 3 = 0 A (Stationary)
1st astronaut grabs the 2nd astronaut and throws him towards the 3rd.
Since every action has an equal and opposite reaction, what will happen is the 1st astronaut will be sent moving backwards with a momentum of -1/2A and the 2nd astronaut will be heading towards the 3rd with a momentum of +1/A. So we're left with
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/2 A (Moving to the right)
Astronaut 3 = 0 A (Stationary)
Now the 3rd astronaut catches the 2nd who was thrown at him. Both of them continue moving in the same direction as the 2nd astronaut was just prior to being caught, but at a reduced velocity, giving
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/4 A (Moving to the right, slowly)
Astronaut 3 = +1/4 A (Moving to the right, slowly)
Finally, Astronaut 3 throws astronaut 2 back towards Astronaut 1, giving
Astronaut 1 = -1/2 A (Moving to the left)
Astronaut 2 = +1/4 A -1/2A = -1/4A (Moving to the left, slowly)
Astronaut 3 = +1/4 A +1/2A = +3/4A (Moving to the right, rapidly)
So what you're left with is Astronaut 1 moving to the left faster than Astronaut 2, so those two astronauts will never catch each other. Meanwhile, Astronaut 3 is moving to the right and getting further and further away from the other 2 astronauts. So none of the astronauts will ever be able to catch or throw anyone ever again.</span>