the circle has a diameter of 12, thus its radius is half that, or 6.
Write an expression to represent: 8 less than the product of 3 and a number.
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We are given polynomial: .
We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and why the binomial (x + 1) IS NOT a factor of this polynomial expression.
Let us set first factor equal to 0 and solve for x.
x+2=0
x=-2.
Plugging x=-2 in given polynomial, we get
<em>Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.</em>
Now, let us check second factor x+1=0
x=-1.
Plugging x=-1 in given polynomial, we get
=-5+8+7-6.
= -4.
<em>Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.</em>
Stokes' theorem says the integral of the curl of over a surface
with boundary
is equal to the integral of
along the boundary. In other words, the flux of the curl of the vector field is equal to the circulation of the field, such that
We have
Parameterize the ellipse by
with and
.
Take the normal vector to to be
Then the flux of the curl is