Is $\ce{BrCl3}$ polar molecule?

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 2000$ deposit in an account with an $\mathrm{APR}$ of $3.1 \%$

Let X be some arbitrary set, and P(X) the set of all subsets of X. In the previous Example we proved that if X has n elements, then P(X) has $2^n$ elements; we are here allowing the possibility that $X$ (and hence $P(X)$ ) has infinitely many elements. Define operations on $P(X)$ as follows, where $a, b \in P(X)$ :

$$a+b=(a \cup b) \backslash(a \cap b) \text { and } a b=a \cap b .$$

(Addition here is often called the symmetric difference of the two sets $a, b$.) Prove that $P(X)$ is a commutative ring. $(P(X)$ is called the power set for the set $X$.)

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers.

$$- 5 r + 6 \leq - 5 ( r + 2 )$$

Determine all real solutions to the equation. $a^2-40=0$

Solve the equation for $x$, where $x$ represents a real number

$$5 x=-3$$

Find all the real square roots of the following number.

-64

Give a complete graph of the below polar equation. Also, identify the type of polar graph.

$$r^2=4 \cos 2 \theta$$

In earlier Figure , suppose a new flow E is added that takes a path from R1 to R2 to R6. How does the max-min bandwidth allocation change for the five flows?

Find the polar equation of the line tangent to the polar curve $r=4 \cos \theta$ at the origin. Explain why the slope of this line is undefined.

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold.

All rational functions.

For the given pair of polar coordinates. Give two other pairs of polar coordinates for the point.

$$\left(1,45^{\circ}\right)$$

Show that $x^2=x \sin x+\cos x$ for exactly two real values of $x$.

Let $x>0$ and $n>1$ be real numbers. Prove that $(1+x)^n>1+n x$