2. While standing near a bus stop, a student hears a distant horn beeping. The frequency emitted by the horn is 440 Hz. The bus
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Statement :- We assume the orthagonal sequence in Hilbert space, now
, the Fourier coefficients are given by:
Then Bessel's inequality give us:
Proof :- We assume the following equation is true
So that, is projection of
onto the surface by the first
of the
. For any event,
Now, by Pythagoras theorem:
Now, we can deduce that from the above equation that;
For , we have
Hence, Proved
This question involves the concepts of the law of conservation of energy, potential energy, and kinetic energy.
The data shown by the bar graph is "valid".
According to the law of conservation of energy, the total energy of the system must remain constant at any given point. Hence, the sum of the kinetic energy and the potential energy of the roller coaster must be constant at any given time.
Considering the bottom of the first hill:
Total Energy at 1st Hill = Kinetic Energy + Potential Energy
From the data given in the bar graph:
Total Energy at 1st Hill = 2,500,000 J + 0 J (since at the bottom potential energy is zero due to zero height)
Total Energy at 1st Hill = 2,500,000 J
Now, considering the top of the second hill:
Total Energy at 2nd Hill = Kinetic Energy + Potential Energy
From the data given in the bar graph:
Total Energy at 2nd Hill = 1,000,000 J + 1,500,000 J
Total Energy at 2nd Hill = 2,500,000 J
Hence,
Total Energy at 1st Hill = Total Energy at 2nd Hill
Therefore, the given bar graph is "valid".
Learn more about the law of conservation of energy here:
brainly.com/question/20971995?referrer=searchResults
The attached picture explains the law of conservation of energy.
