Answer:
The two objects will collide with the same position vector for all three components at exactly t = 4 s
Explanation:
For two particles starting out at the same time to collide, their position Vector's at the time of collision must be exactly the same.
So, at the collision point, position vector of object 1 is equated to that of object 2.
r₁ = (t², 13t-36, t²)
r₂ = (7t-12, t², 5t-4)
At he point of collision
t² = 7t - 12
t² - 7t + 12 = 0
t² - 4t - 3t + 12 = 0
t(t - 4) - 3(t - 4) = 0
t = 3s or t = 4s
13t - 36 = t²
t² - 13t + 36 = 0
t² - 4t - 9t + 36 = 0
t(t - 4) - 9(t - 4) = 0
t = 9s or 4s
t² = 5t - 4
t² - 5t + 4 = 0
t² - 4t - t + 4 = 0
t(t - 4) - 1(t - 4) = 0
t = 1s or t = 4s
The three components intersect at other times, but at t = 4s, they all intersect at the same time! Meaning that, at this point the two objects are at the same place with the same position vector at that time.
Choice-a is a very rubbery, imprecise, ambiguous, slippery statement. But it's probably less wrong than any of the other choices on the list.
Answer:
1280 mg
Explanation:
Radioactive decay is a phenomenon that occurs when a certain isotope of an element, said to be radioactive, decays, turning into a lighter nucleus and emitting radiation + energy in the process.
The radioactive decay of this isotope of polonium is described by the equation
where
is the amount of polonium left after time t
is the amount of polonium t time t = 0
is the half-life of the polonium, in days (it is the time it takes for the initial element to halve its amount)
IN this problem, we know that:
After t = 560 days, the amount of polonium left is 
. Therefore, we can re-arrange the equation, substituting t = 560 d, and solve for to find the initial amount of polonium:
Crafting, reusing
Good luck!
