ls it possible for an object to have an acceleration when the velocity of the object is constant? When the speed of the object is constant? In each case, give your reasoning.

Find the absolute maximum and minimum values of the following functions on the given region R. $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 2 y + 1 ; R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 4 \right\}$

Let $M=\langle v,u\rangle$ be the modular group of order $16$ described previously. Prove that $\langle v^4\rangle$ is normal in $M$ and use the Lattice Isomorphism Theorem to draw the lattice of subgroups of $M/\langle v^4\rangle$. Which group of order $8$ has the same lattice as this quotient? Use generators and relations for $M/\langle v^4\rangle$ to decide the isomorphism type of this group.

Draw a plane intersecting a cube to get the cross section indicated. pentagon

Is each given binomial a factor of the given polynomial? If so, write the polynomial as a product of two factors

$$polynomial: P(x) = 4x^4 - 9x^3 - 7x^2 - 2x + 25; binomial: x + 4$$

Match the term below with its correct definition. social norms A. the tendency to slack off when part of a group B. group decision-making process in which the group makes decisions in accordance with what the majority wants C. the strengthening of a group member's attitudes D. unspoken, unwritten rules E. one who speculates, or forms a theory F. the tendency for people to take greater risks as part of a group G. the concept that people often perform better when other people are watching H. the standards people share I. concern about the opinion of others

For

$$y = x ^ { 2 } - 2 x - 15$$

find the: a. i. y-intercept ii. x-intercepts iii. equation of the axis of symmetry iv. coordinates of the vertex b. Hence sketch the graph showing all of the above features.

The Gotham City Maternity Ward contains 2 beds. Admissions are made only at the beginning of the day. Each day, there is a .5 probability that a potential admission will arrive. A patient can be admitted only if there is an open bed at the beginning of the day. Half of all patients are discharged after one day, and all patients that have stayed one day are discharged at the end of their second day. a. What is the fraction of days where all beds are utilized? b. On the average, what percentage of the beds are utilized?

A particle moves horizontally to the right. For $n \in Z+,$ the distance the particle travels in the (n + l)st second is equal to twice the distance it travels during the nth second. If $\mathrm{xn}, \mathrm{n} \geq 0,$ denotes the position of the particle at the start of the (n + 1)st second, find and solve a recurrence relation for xn, where x0 = 1 and x1 = 5.

Graph the surface and the tangent plane at the given point. (Choose the domain and viewpoint so that you get a good view of both the surface and the tangent plane.) Then zoom in until the surface and the tangent plane become indistinguishable. z=x^2+xy+3y^2, (1,1,5)

Determine whether each statement is always, sometimes, or never true. Justify your answer. If x > 0 and

$$y\ge 0,$$

then xy > 0.

Suppose you have a 9.00-V battery, a $2.00 - \mu \mathrm { F }$ capacitor, and a $7.40 - \mu \mathrm { F }$ capacitor. (a) Find the charge and energy stored if the capacitors are connected to the battery in series. (b) Do the same for a parallel connection.

Your friend says she can always find a common denominator for two rational expressions by finding the product of the denominators. Will your friend's method always give you the LCD? Explain.

Describe the steps for solving a rational equation that is not a proportion.