Why were the Sixteenth, Seventeenth, and Nineteenth Amendments adopted?

Suppose you are standing a few feet away from a bonfire on a cold fall evening. Your face begins to feel hot. What is the mechanism that transfers heat from the fire to your face?

Tell how to combine the given equations to obtain an equation in which the coefficient of x is 0. What is the new coefficient of y?

$$\left. \begin{array} { c } { x + 3 y - 2 z = 5 } \\ { - x + y + 4 z = 6 } \end{array} \right.$$

Write code to declare and instantiate an object of the Random class (call the object reference variable rand). Then write a list of expressions using the nextInt method that generates random numbers in the following ranges, including the endpoints. a. 0 to 10, b. 0 to 500, c. 1 to 10, d. 1 to 500, e. 25 to 50, f. -10 to 15.

Simplify

$$24 - 12 \div 2 ^ { 2 }$$

Pete Repeat was recursively evaluating this expression, starting with 2.

$$-0.2 \cdot \square-4$$

a. Check his first two stages and describe what, if anything, he did wrong.

$$-0.2 \cdot 2-4=0.4-4=-3.6$$

$$-0.2 \cdot-3.6-4=-0.72-4=-4.72$$

b. Redo Pete's first two stages and do two more. c. Now do three recursions starting with $-1$ d. Do you think this expression has an attractor value? Explain.

Prove each fundamental identity without using any of the other fundamental identities.
$1+\cot ^{2} \theta=\csc ^{2} \theta$

A page with dimensions of $8 \frac{1}{2}$ inches by 11 inches has a border of uniform width x surrounding the printed matter of the page. Find the area of the printed page for borders of widths 1 inch, 1.2 inches, and 1.5 inches.

Use an inequality symbol to write each statement. t is between -3 and 5.

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula.Then use the formula for

$$a _ { n } \ to \ find \ a _ { 20 }$$

the 20th term of the sequence.

$$a _ { 1 } = - 20 , d = - 4$$

Which nondimensional parameter in the nondimensionalized Navier-Stokes equation is eliminated by use of modified pressure instead of actual pressure? Explain.

Kristiana and Gregorio request that they be put on the same team so they cant easily share their different ways of thinking. Together, they are trying to algebraically evaluate $\lim _{x \rightarrow 1} \frac{x-1}{\sqrt{x}-1}$. a. What happens when they try to evaluate the limit by substituting x = 1 into the expression? What does this mean in terms of the value of the limit? b. The $\lim _{x \rightarrow 1} \frac{x-1}{\sqrt{x}-1}$ is a limit in an indeterminate form. In mathematics, an expression is said to be in an indeterminate form if it is not well-defined or precisely determined. What other limits in indeterminate forms have you encountered? c. Gregorio wants to factor and simplify to evaluate the limit. Kristiana is puzzled with his thinking once again. "How can you factor that?" "Well, isn't the numerator a difference of squares?" he replies. How can the numerator be factored by thinking about x - 1 as a difference of squares? How does this help you evaluate the limit? d. What happens to the graph of $y=\frac{x-1}{\sqrt{x-1}}$ at x = 1? e. Write your own limit problem in which factoring can be used as a way to evaluate the limit.

Use graphical evidence and known area facts to find $\int_{0}^{2}\left(-\sqrt{4-x^{2}}\right) d x$.

Determine whether the given vector is in the span of

$$\begin{equation*}\begin{Bmatrix}\begin{bmatrix}1.2\\-0.1\\2.3\\3.1\\-1.1\\-1.9\end{bmatrix},\begin{bmatrix}3.4\\-1.7\\0.0\\2.4\\1.7\\2.6\end{bmatrix},\begin{bmatrix} -3.1\\0.0\\2.5\\1.6\\-3.2\\1.7\end{bmatrix},\begin{bmatrix}7.7\\-1.8\\-0.2\\3.9\\3.8\\-1.0\end{bmatrix}\end{Bmatrix}\end{equation*}$$

$$\begin{equation*}\begin{bmatrix}1.0\\-1.5\\-4.6\\-3.8\\3.9\\6.4\end{bmatrix}\end{equation*}$$