Really easy question 10pts.....pic below..
2 answers:
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Answer:
Step-by-step explanation:
Let us assume that we have n different dots on a paper. We are to connect pairwise by a line. We have to find out how many lines can be formed.
Let us prove by induction.
If there is one dot then we have no line = 1(1-1) =0
Thus n(n-1) is true for 1 dot
Let us assume that for n dots we have n(n-1) lines
Add one more point now total points are n+1.
Already the existing n points are connected by a line.
So the extra point has to be connected to each of n point
i.e. n lines should be added from the new point to the n points and again n lines from the points to the new point(Assuming lines are different if initial and final point are different)
So 2n lines would be added
So total number of lines for n+1 points
Thus true for n+1 if true for n. Already true for n =1
So proved by induction for all natural numbers n.
Answer:
Final potential energy = 24 Joule
The velocity with which object must be thrown = m/s
Step-by-step explanation:
<u>Given:</u>
Mass of object, m = 0.30 Kg
Height of object, h = 8 m
Acceleration due to gravity, g = 10
a) Formula for Potential Energy:
Where m is the mass of object
g is acceleration due to gravity and
h is the height of object
Putting the values of m, g and h
b) Formula for initial and final velocity:
where v is the final velocity
u is the initial velocity with which the object is thrown
g is acceleration due to gravity and
h is the height obtained by object
here v = 0 at the height 8 m because it will come to rest at the point it attains the maximum height.
h = 8m
g = -10 (negative because the object's velocity is decreasing)
Putting the values to find 'u':