Write three senteces about what your family members are doing right now. Use the present progressive.

Would it have been better for Sasha if the family had chosen to send him to prison? Explain your response.

In the following exercise, describe the family of planes represented by the equation, where c is any real number.

$$c y+z=0$$

Find in polar form the orthogonal trajectories of each of the following family of curves.

$r=k(1+\sin \theta)$.

Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen. $\int(x-1 / x) d x$

Use tener que to write a list of six things you and other family members have to do this week. ______________________________

The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem.

$$y = c _ { 1 } e ^ { 4 x } + c _ { 2 } e ^ { - x } , ( - \infty , \infty )$$

$$y ^ { \prime \prime } - 3 y ^ { \prime } - 4 y = 0 , y ( 0 ) = 1, y ^ { \prime } ( 0 ) = 2$$

A bank allows one person to have only one savings account insured to $100,000. However, a larger family may have accounts for each individual, and also accounts in the names of any 2 people, any 3 and so on. How many accounts are possible for a family of 2? Of 3? Of 5? Of n?

Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. What problems do you see with asking the following question of students? "Are you the first member of your family to seek higher education?"

Given that $y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x$ is a two-parameter family of solutions of $y^{\prime \prime}-2 y^{\prime}+2 y=0$ on the interval $(-\infty, \infty),$ determine whether a member of the family can be found that satisfies the conditions $y(0)=1, \quad y^{\prime}(0)=0$

Let F be a field, n a positive integer, and let V be the space of $n \times n$ matrices over F. If A is a fixed $n \times n$ matrix over F, let $T_{A}$ be the linear operator on V defined by $T_{A}(B)=A B-B A$. Consider the family of linear operators $T_A$ obtained by letting A vary over all diagonal matrices. Prove that the operators in that family are simultaneously diagonalizable.

Moiré pattern A moiré pattern is formed when two geometrically regular patterns are superimposed. Shown in the figure is a pattern obtained from the family of circles $x^2+y^2=n^2$ and the family of horizontal lines $y=m$ for integers $m$ and $n$.

Show that the points of intersection of the circle $x^2+y^2=n^2$ and the line $y=n-1$ lie on a parabola.

Given that $y=c_{1}+c_{2} \cos x+c_{3} \sin x$ is a three-parameter family of solutions of $y^{\prime \prime \prime}+y^{\prime}=0$ on the interval $(-\infty, \infty),$ find a member of the family satisfying the initial conditions $y(\pi)=0, y^{\prime}(\pi)=2,y^{\prime \prime}(\pi)=-1.$

Networking

• How effective are you at using a mentor?

• Are you a member of a professional organization?

• In which community, civic, or church groups are you participating?

• Whom have you added to your contact list in the last six weeks?