Prove for all n\inN
2n= (\stackrel{n}{0})+(\stackrel{n}{1})+...+(\stackrel{n}{n})
So I used mathematical induction
base case: n=0 so 20=1 and (\stackrel{0}{0})=1
induction step: Let n\inN be given, assume as induction hypothesis that 2n=...
Yes I meant minus on the bottom
the 7 is from how far away the cicle is from the begin on the rectangle
sorry I don't have the picture but the shapes are on a coordinate system and inside the rectangle (that goes from (-6,0) to (7,0) ) the circle lies at (1,0) to (5,0).
Homework Statement
A uniform flat plate of metal with a circular hole, where it is a rectangle starting from -6 to 7 from the length, and the height is -3 to 3.
The circle has a radius of 2, and it starts at 1 to 5.
Calculate the x-coordinate of the center of
mass xcm of the metal plate...
Homework Statement
An m2 = 1.2 kg can of soup is thrown upward with a velocity of v2 = 4.6 m/s. It is immediately struck from the side by an m1 = 0.63 kg rock traveling at v1 = 7.9 m/s.
The rock ricochets off at an angle of α = 65◦ with a velocity of v3 = 5.5 m/s.
(a)What is the angle of...
Homework Statement
A 4.39 g particle is moving at 4.15 m/s toward a stationary 9.64 g particle.
(a)With what speed does the heavier particle approach the center of mass of the two particles?
Answer in units of m/s.
(b) What is the magnitude of the momentum of the lighter particle...
would it be
1/2kx2=mgh
h=kx2/2mg
well i tried and did 1400(.19)2/(2*2.3*9.8)
h=1.12112m
then sin33=o/h
h=o/sin30
h=2.05846
2.05846-.19 m=1.8684m
which is 186.84 cm which is wrong
well I reread the problem and it says when it is uncompressed so .57 m
I misused 2.05846-.57=1.48846
which is...
Homework Statement
A spring with a spring-constant 2.5 N/cm is compressed 35 cm and released. The 4 kg mass skids down the frictional incline of height 37 cm and inclined at a 20◦ angle. The acceleration of gravity is 9.8 m/s2 . The path is frictionless except for a distance of 0.5 m along the...