The globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why?

Scientists working with a particle accelerator determine that an unknown particle has a speed of $1.35 \times 10^{8} \mathrm{m} / \mathrm{s}$ and a momentum of $2.52 \times 10^{-19} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$. From the curvature of the particle’s path in a magnetic field, they also deduce that it has a positive charge. Using this information, identify the particle.

Let {aₙ} and {bₙ} be sequences of real numbers. Show that

$$Δ(a_nb_n) = a_{n+1}(Δb_n) + b_n(Δa_n).$$

The bond energy for the $\mathrm { C } - \mathrm { H }$ bond is about 413 $\mathrm { kJ } / \mathrm { mol }$ in $\mathrm {CH} _ { 4 }$ but 380 $\mathrm { kJ } / \mathrm { mol }$ in $\mathrm { CHBr } _ { 3 }$. Although these values are relatively close in magnitude, they are different. Explain why they are different. Does the fact that the $\mathrm { C } - \mathrm { H }$ bond energy in $\mathrm {CHBr} _ { 3 }$ is lower make any sense? Why?

Consider the evaluation of

$$y[n]=x_1[n]*x_2[n]*x_3[n]$$

, where

$$x_1[n]=(0.5)^n u[n], x_2[n]=u[n+3]$$

, and

$$x_3[n]=δ[n]=δ[n=1].$$

(a) Evaluate the convolution x1[n]*x2[n]. (b) Convolve the result of part (a) with x3[n] in order to evaluate y[n]. (c) Evaluate the convolution x2[n]*x3[n]. (d) Convolve the resault of part (c) with x1[n] in order to evaluate y[n].

The energy required to dissociate the $\mathrm{Cl}_2$ molecule to $\mathrm{Cl}$ atoms is $239 \mathrm{~kJ} / \mathrm{mol} \mathrm{Cl}$. If the dissociation of a $\mathrm{Cl}_2$ molecule were accomplished by the absorption of a single photon whose energy was exactly the quantity required. what would be its wavelength (in meters)?

If a reaction takes place at an equal rate in both directions, it is in $___________________$ The amount of energy needed to break a bond is called the

Determine the values of v, b, r, k, and $\lambda$ for the balanced incomplete block design associated with the projective plane that arises from AP(F) for the following choices of F: (a) Z5 (b) Z7 (c) GF(8).

mercury(ii) bromide dissociation equation

What is the difference between dissociation and dissolution?

Use matrices A and B to show that the indicated laws hold for these matrices.

$$A=\begin{bmatrix} -1 & 2 & 3 &7 \\ 0 & -3 & -1 &4 \\ 9 & -1 & 0 &-2 \end{bmatrix} \qquad B =\begin{bmatrix} 4 & -1 & -3 & 0 \\ 5 & 0 & -1 & 1 \\ 1 & 11 & 8 & 2 \end{bmatrix}$$

$$A+\mathit{O}=A$$

Suppose that X has a Weibull distribution with β = 0.2 and δ = 100 hours. Determine the following: a. P(X < 10,000) b. P(X > 5000)

The addition table and part of the multiplication table for the ring $R=\{a, b, c, d\}$ are given in Figure. Use the distributive laws to complete the multiplication table.

+	a	b	c	d
a	a	b	c	d
b	b	c	d	a
c	c	d	a	b
d	d	a	b	c

*	a	b	c	d
a	a	a	a	a
b	a	c
c	a		a
d	a		a	c

Write dissociation equation for Mg(OH)$_2$.