Let pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. let d2: p3→p1 be the function that sends a polynomial to its second derivative. that is, d2(p(x))=p′′(x) for all polynomials p(x)∈p3. is d2 a linear transformation?

Yes. A trasformation is linear if:

The (second) derivative satisfies both these request: in fact, a generic element in p3 is . Let's prove that, for any real number , .

We have:

On the other hand,

The proof of the second point is the same: write the derivative of the sum, and the sum of the derivaties. You'll see that they are the same polynomial.

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi

answer: i think you should do the math and pay attention in class : )

step-by-step explanation:

that is truly what   think but if i get the answer i will