A bicycle wheel with radius 0.3m rotates from rest to 3 rev/s in 5 s. What is the magnitude and direction of the total acceleration vector at the edge of the wheel at 1.0 s?

What is (a) the angular speed and (b) the linear speed of a point on Earth's surface at latitude 30° N. Take the radius of the Earth to be 6309 km. (c) At what latitude would your linear speed be 10 m/s?

For each function, (a) apply the leading-term test, (b) determine the zeros and state the multiplicity of any repeated zeros, (c) find a few additional points, and than (d) graph the function. $f(x)=-x(x-3)(x 2)^{3}$

In Exercise given below, find a polynomial function with real coefficients and of least possible degree having the given zeros. Let the leading coefficient be 1.

$$-2+\sqrt{5},-2-\sqrt{5},-2,1$$

For Exercise given below, find a polynomial function P(x) of least possible degree, having real coefficients, with the given zeros. Let the leading coefficient be 1.

$1+\sqrt{2}, 1-\sqrt{2}$, and 3

Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

$$p ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 3 x - 4 x ^ { 3 } + 6 x ^ { 4 } - 1$$

Solve for x in the equation 5x - 2x + x = 15. Show all steps leading to your solution. The answer should be 3$\frac{3}{4}$ or 3.75. The answer is provided so that you can check.

Decide whether the function is a polynomial function. If so, write it in standard form and stat its degree, type, and leading coefficient.

$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + 2 x ^ { 3 } - 4 x ^ { 4 } - \sqrt { 3 }$$

Let $a_n$ be the leading coefficient.

(a) Find the complete factored form of a polynomial with real coefficients $f(x)$ that satisfy the conditions.

(b) Express $f(x)$ in expanded form.

Degree $3 ; a_n=-2 ; \quad$ zeros $1-i$ and $3$

For the following exercise, determine whether the function is a polynomial function. For those functions that are polynomial functions, identify a. the leading coefficient, b. the constant term, and c. the degree.

$$g(x)=-4 x^5-3 x^2+x-\sqrt{7}$$

Let G be a connected planar graph of order n having e=3n-6 edges. Prove that, in any planar representation of G, each region is bounded by exactly is edge-curves.

What is the least possible degree of a polynomial with rational coefficients, leading coefficient 1, constant term 5, and zeros at $\sqrt{2}$ and $\sqrt{3} ?$ Show that such a polynomial has a rational zero and indicate this zero.

For the sentence below, draw an arrow from each underlined pronoun to its antecedent.

Leading Ryan to the display case, Katie said, “$\underline{\text{These}}$ are the watches I described to $\underline{\text{you}}$ earlier.”

Describe two ways to express the edge length of a cube with a volume shown.