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
Whats the question exactly?
Answer:
For the first one its about 25 feet
Explanation:
Answer:
F₂= 210 pounds
Explanation:
Conceptual analysis
Hooke's law
Hooke's law establishes that the elongation (x) of a spring is directly proportional to the magnitude of force (F) applied to it, provided that said spring is not permanently deformed:
F= K*x Formula (1)
Where;
F is the magnitude of the force applied to the spring in Newtons (Pounds)
K is the elastic spring constant, which relates force and elongation. The higher its value, the more work it will cost to stretch the spring. (Pounds/inch)
x the elongation of the spring (inch)
Data
The data given is incorrect because if we apply them the answer would be illogical.
The correct data are as follows:
F₁ =80 pounds
x₁= 8 inches
x₂= 21 inches
Problem development
We replace data in formula 1 to calculate K :
F₁= K*x₁
K=( F₁) / (x₁)
K=( 80) / (8) = 10 pounds/ inche
We apply The formula 1 to calculate F₂
F₂= K*x₂
F₂= (10)*(21)
F₂= 210 pounds
Answer:
go to the link quizzlet it will give you tha answer
Explanation: