Circle the word or words modified by the adverb in italics. On the blank, write $v$ if the adverb modifies a verb. Write $adj$. if the adverb modifies an adjective. Write $adv$. if the adverb modifies another adverb.\ _____Tuyen was completely calm when we jumped out and yelled “Happy Birthday!”

Convert $\text{F}111_{\text {sixteen }}$ to binary.

Compare the average reaction rate measured over an initial, short time interval to one measured over a long time interval.

The purpose of this exercise is to develop a formula for the monthly payment P that is required to repay a loan of A dollars in n monthly installments, with the interest on the unpaid balance equal to a monthly rate r. Let $A_k=$ amount still owed after paying k installments. Then interest for the (k+1) st month is $r A_k$, and the principal paid off in the (k+1) st payment is $P-r A_k$. Thus,

$$A_{k+1}=A_k-\left(P-r A_k\right)=(1+r) A_k-P .$$

a. Use the equation above and the fact that $A_0=A$ to find $A_1, A_2$, and $A_3$ in terms of A, r, and P.

b. Generalizing from $A_1, A_2$, and $A_3$, you get $A_n=(1+r)^n A-\left[(1+r)^{n-1}+(1+r)^{n-2}+\cdots+(1+r)+1\right] P$.

Since the bracketed quantity above is a geometric series, show that the equation can be rewritten

$$A_n=(1+r)^n A-\left[\frac{(1+r)^n-1}{r}\right] P .$$

c. Since $A_n=0$ (why?), use the last equation in part (b) to show that

$$P=\frac{A r(1+r)^n}{(1+r)^n-1} \text {. }$$

Compute the nun1ber of (a) five-digit binary numbers.

Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $\$ 14,000 /$ day to operate, and it yields $50 \mathrm{oz}$ of gold and $3000 \mathrm{oz}$ of silver per day. The Horseshoe Mine costs $\$ 16,000 /$ day to operate, and it yields $75 \mathrm{oz}$ of gold and 1000 ounces of silver per day. Company management has set a target of at least $650 \mathrm{oz}$ of gold and 18,000 oz of silver.

a. How many days should each mine be operated so that the target can be met at a minimum cost?

b. Find the range of values that the Saddle Mine's daily operating cost can assume without changing the optimal solution.

c. Find the range of values that the requirement for gold can assume.

d. Find the shadow price for the requirement for gold.

Complete the following conversations that you overhear in school.
A: ¿Qué hay... la mochila? B: Hay muchos libros.

Evaluate the series.

$$\sum _ { k = 1 } ^ { 20 } k ^ { 2 }$$

Use the $\epsilon=\delta$ definition of limit to verify the limit statements given.

$$\lim _{(x, y) \rightarrow(0,0)}\left(x+y^{2}\right)=0$$

Write as an algebraic expression.

Suppose $w$ was Lisa's weight last year. Lisa lost $7$ pounds this year. Write an expression for Lisa's weight this year.

A particle P is in uniform circular motion, centered on the origin of an $x y$ coordinate system. At what values of $\theta$ is the vertical component $r_y$ of the position vector greatest in magnitude?

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

$$f\left(x_1, x_2\right)=x_1^2+x_2^2, \quad x_1+x_2=1$$

Use the Ratio Test to determine whether each series converges or diverges or state that it provides no information. $\sum_{k=1}^{\infty} \frac{(2 k) !}{5^{k} 3^{k-1}}$

Briefly explain the importance of each of the following. culture