Please help with this problem!
Planet Pemdas is a perfect sphere that does not rotate. If a rocket flies in a path following the circumference of Pemdas, and maintains a constant altitude of 25,000 feet above the surface for one orbit, how many more feet than the planet's circumference is the path of the rocket? Express the answer to the nearest thousand feet.
radius increasses by 25000 solve for dimater then solve for circumference i think
circumf of planet = 2pi(r)
circumf of path of rocket = 2pi(r+25000)
= 2p(r) + 2pi(25000)
so the increase is 2pi(25000)
(I am sure the people of Pemdas would not use a medieval unit of measurement as the "foot")
Thank you SO much!!!
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To calculate how many more feet than the planet's circumference the path of the rocket is, we need to find the length of the path and then compare it to the circumference.
Let's start by finding the circumference of Planet Pemdas. The formula to calculate the circumference of a sphere is:
C = 2πr
Where C is the circumference and r is the radius. Since we don't know the radius directly, but we know the altitude above the surface, we can find the radius by adding the altitude to the radius of the planet.
Let's assume the radius of Planet Pemdas is 'r' (unknown).
So the radius of Planet Pemdas including the altitude is r + 25,000 feet.
Therefore, the circumference of Planet Pemdas is:
C = 2π(r + 25,000)
Next, we need to calculate the length of the path of the rocket. We know that it flies at a constant altitude of 25,000 feet above the surface. Therefore, the length of the path of the rocket is equal to the circumference of Planet Pemdas plus twice the altitude:
Path = C + 2(25,000)
Now, we can substitute the value of C we found earlier into the equation:
Path = 2π(r + 25,000) + 2(25,000)
Finally, we can simplify and calculate the length of the path by substituting the value of π (pi ≈ 3.14) and rounding to the nearest thousand feet:
Path = 2(3.14)(r + 25,000) + 2(25,000)
Now you can substitute the value of the radius 'r' into the equation to find the exact number of feet the path of the rocket differs from the planet's circumference.