Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
<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>
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain
Answer:
x = 10
Step-by-step explanation:
∵ Both angle ∠A and are corresponding angles.
∠A = ∠B
9x - 40 = 3x + 20
9x = 3x + 20 + 40
9x - 3x = 20 + 40
6x = 60
x = 60/6
x = 10
∴ x = [10]
When taking square roots, you can't take square roots of negative roots of negative numbers. So, what will work for the domain of u(x) is what makes u(x) zero or more. We can make an inequality for that.
u(x) ≥ 0.
9x + 27 ≥ 0 by squaring both sides
9x ≥ -27
x ≥ -3
So the domain of the function is when x ≥ -3 is true.
