Perform the indicated operation. Write your answer in scientific notation. $\left( 5.1 \times 10 ^ { 8 } \right) \times \left( 3.2 \times 10 ^ { 5 } \right)$

$D$ denotes the unit disc. Let $\phi: \partial D\to \mathbb{R}$ be continuous and let $T$ be a solution on $D$ to $\nabla^2 T = 0$, continuous on $D$ and $T = \phi$ on $\partial D$.
a) Show that such a solution, if it exists, must be unique. (b) Suppose that $T (x, y)$ represents a temperature function that is independent of time, with $\phi$ representing the temperature of a circular plate at its boundary. Can you give a physical interpretation of the principle stated in part (a)?

In this unit, you have learned that reactions take place all around you. You should now be able to look at some everyday chemical changes and see them in a new way. (a) Choose two common chemical changes and explain how you understood them before you knew about chemical reactions. (b) Explain how you understand the same two chemical changes now.

Many substitution reactions involve an initial electrostatic attraction between reactants. Show where this attraction arises in the formation of an amide from an amine and an ester.

Simplify the expression. 20. -2/3(12c - 9) + 14c

Find the value of ab/bc when a =6, b = 0.9, c = 5.

Andy Is buying a new laptop computer. The store Is offering a 15% discount on the model he wants. Andy also has a certificate from the manufacturer good for $120 off his next computer purchase. Andy wants to know whether he will pay less if the certificate amount is deducted before or after the discount is applied.
Will Andy pay less if the certificate amount is deducted before or after the discount is applied? Explain.

During the basketball season, Morgan made 3 times as many 2-point baskets as she made 3-point baskets and free throws combined. If she made 14 free throws and eight 3-point baskets, how many 2-point baskets did she make? Write and simplify an expression to solve the problem.

Determine whether the relation is a function.

$$\begin{matrix} \text{Input, x} & \quad & \text{Output, y}\\ & \quad & \text{0}\\ \text{1.4} & \stackrel { \nearrow } { \searrow } & \text{1}\\ \text{1.6} & \stackrel { \nearrow } { \searrow } & \text{2}\\ \end{matrix}$$

Change the verb into the future tense, keeping the same person, number, and voice. Translate both forms: mittitur

Solve the inequality.

$$8 a - 7 \leq 2 ( 3 a - 1 )$$

find a polynomial of degree n that has the given zero(s). (There are many correct answers.) Zero x = -2, 4, 7 Degree n = 3

Find the vertex, axis of symmetry, and directrix of the parabola. $x = -2y^2$

Suppose you are doing a presentation for your class about the daily growth of a bean plant over the course of a month. Would you use a chart, a table, or a graph to help explain your results to your class? Explain your answer.