1) A little sled weighs 2 Newtons. It is set in motion over a frictionless icy s
ID: 2257123 • Letter: 1
Question
1)
A little sled weighs 2 Newtons. It is set in motion over a frictionless icy surface by a toy
rocket motor with a weight of 1 Newton. After the fuel has been expended, the sled is
coasting at a speed of 2 meters per second. How much force did the rocket exert on the
sled?
And why?
a) 1 N
b) 4 N
c) 6 N
d) 12 N
e) There is no way to tell from the information given
2)
Describe the purpose of the
A little sled weighs 2 Newtons. It is set in motion over a frictionless icy surface by a toy rocket motor with a weight of 1 Newton. After the fuel has been expended, the sled is coasting at a speed of 2 meters per second. How much force did the rocket exert on the sled? Describe the purpose of the 'first and second derivative tests' List the steps taken to perform the test and explain the purpose of each step. Eight identical spheres of mercury coalesce to form a single larger sphere. Compared to the surface area of the eight smaller spheres, the surface area of the larger sphere isExplanation / Answer
1)
you get force by taking the ratio between change in momentum and time for which change took place.But in the question no information is given about the time.
hence, there is no way to tell the answer
answer is E
2)
The ?rst derivative of the function f(x), which we write as f'(x) or as df/dx, is the slope of the tangent line to the function at the point x.The first derivative tells us how whether a function is increasing or decreasing, and by how much it is increasing or decreasing. Positive slope tells us that, as x increases, f(x) also increases. Negative slope tells us that, as x increases, f(x) decreases. Zero slope does not tell us anything in particular: the function may be increasing, decreasing, or at a local maximum or a local minimum at that point.
The second derivative tells us if the first derivative is increasing or decreasing. If the second derivative is positive, then the first derivative is increasing, so that the slope of the tangent line to the function is increasing as x increases. We see this phenomenon graphically as the curve of the graph being concave up, that is, shaped like a parabola open upward. Likewise, if the second derivative is negative, then the first derivative is decreasing, so that the slope of the tangent line to the function is decreasing as x increases. Graphically, we see this as the curve of the graph being concave down, that is, shaped like a parabola open downward. At the points where the second derivative is zero, we do not learn anything about the shape of the graph: it may be concave up or concave down, or it may be changing from concave up to concave down or changing from concave down to concave up
3)
let v be the volume of each small shpere
surface area of each small sphere is proportional to the v^2/3
total area of 8 small spheres is 8*(v^2/3)
after they combine volume becomes 8v
surface area of the bigger sphere is proprotional to (8v)^2/3=4*(v^2/3)
hence the area has been reduced to half
answer is C
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