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
Answer:
a) x = 40 t
, y = 39 t
, z = 6 + 32 t - 16 t
², b) x = 80 feet
, y = 78 feet
, the ball came into the field
Explanation:
a) This is a projectile launch exercise, where in the x and y axes there is no acceleration and in the z axis the acceleration of the acceleration of gravity, let's write the equations of motion in each axis
Since the cast is in the center of the field, let's place the coordinate system
x₀ = 0
y₀ = 0
z₀ = 6 feet
x-axis (towards end zone, GOAL zone)
x = xo + v₀ₓ t
x = 40 t
y-axis (field width)
y = y₀ +
t
y = 39 t
z axis (vertical)
z = z₀ + v_{oz} t - ½ g t²
z = 6 + 32 t - ½ 32 t²
z = 6 + 32 t - 16 t
²
b) The player catches the ball at the same height as it came out, so we can find the time it takes to arrive
z = 6
6 = 6 + 32 t - 16 t²
(t - 2)t = 0
t=0 s
t= 2 s
The ball position
x = 40 2
x = 80 feet
y = 39 2
y = 78 feet
the dimensions of the field from the coordinate system (center of the field) are
x_total = 150 feet
y _total = 80 feet
so we can see that the ball came into the field
Answer:
one for physical is that your muscles will seize up or cramp when you try to move. one for mental is that if your always sitting down you will most likely become stressed or get depression
Explanation
the reason your muscles cramp is from lack of exercise form sitting they get used to that position and want to stay that way. then theres the deprestion ive had it it aint fun nor is stress ive had that too
The exact location of the 'subtropical-jet stream' is located at the North phase of 30 Degrees and the reason behind this is due to the variation of air which lies on the region of mid-altitude and warmer equatorial air. the correct answer would be Cool and Warm air masses meeting near the equator.