We know that
[length of a circle]=2*pi*r
r=12 in
[length of a circle]=2*pi*12--------------> 24pi in
if 360° (full circle)--------------------> has a length of 24pi in
X-------------------------------------------> 8pi
X=8pi*360/24pi-----------> 120°
the answer is 120°
47x > = 209....with x being number of lawns mowed
x > = 209 / 47
x > = 4.45....so he would have to mow at least 4.45 lawns.....but if u cant mow part of the lawn and u have to mow the entire lawn, the it would be at least 5 full lawns

By taking <span>logarithmic of base 10
∴ </span><span>

∴ x log 4 = log 64
∴

∴ The correct choice is
</span><span>x = log base 10 of 64, all over log base 10 of 4</span>
Answer:

Step-by-step explanation:
The given quadratic form is of the form
.
Where
.Every quadratic form of this kind can be written as

Observe that
is a symmetric matrix. So
is orthogonally diagonalizable, that is to say,
where
is an orthogonal matrix and
is a diagonal matrix.
In our case we have:

The eigenvalues of
are
.
Every symmetric matriz is orthogonally diagonalizable. Applying the process of diagonalization by an orthogonal matrix we have that:


Now, we have to do the change of variables
to obtain

Which can be written as:
