Find the area of the circles given the circumference. Give your answers in terms of $\pi .$ $C = 8 \pi$

Find the eigenvalues of the matrix. For the eigenvalue, find an eigenvalue. Sketch the Gershgorin circles, and then locate the eigenvalues in these circles.

$$\left( \begin{array}{rrrr}{-2} & {1} & {0} & {0} \\ {1} & {0} & {0} & {1} \\ {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0}\end{array}\right)$$

To test if the graph of a polar equation may be symmetric with respect to the polar axis, replace $\theta$ by _____.

Explain the origin of universities in Europe.

Provide one benefit of subsidies to the Indian leather businesses and European farmers.

Determine the constant speed of satellite S so that it circles the earth with an orbit of radius r = 15 Mm.

What were the causes and results of European revolutions in 1830 and 1848?

Indicate the best answer by writing the appropriate letter.

A cone has radius 5 and height 12. A cylinder with radius 10 has the same volume as the cone. What is the cylinder's height? a. 1 b. 2 c. 3 d. 4

An ideal $I$ in $R\left[x_{1}, \ldots, x_{n}\right]$ is called a homogeneous ideal if whenever $p \in I$ then each homogeneous component of $p$ is also in $I$ . Prove that an ideal is a homogenecus ideal if and only if it may be generated by homogeneous polynomials, [Use inducticn on degrees to show the "if" implication. The following exercise shows that some care must be taken when working with polynomials over noncommutative rings $R$ (the ring operations in $R[x]$ are defined in the same way as for commutative rings $R,$ in perticular when considering polynomials as functions.

Using the poem from the discussion before, answer the following questions:

(a) What image does the speaker use to characterize his neighbor as he repairs the wall?

(b) What is the meaning of the "darkness" in which the man walks?

Use integration to compute the volume of a right circular cone generated by revolving the ordinate set of a linear function f(x)=cx over the interval $0 \leq x \leq b$. Show that the result is one-third the area of the base times the altitude of the cone.

If the graph of an equation is symmetric with respect to the origin and -4 is an x-intercept of this graph, name another x-intercept.

Quand il sera en Europe

aller a Bruxelles

Draw a cone with a surface area that is between 100 and 150 square units.