Find the second Taylor polynomial of $x(x+1)^{3 / 2}$ at x=0.

What were the motives behind European exploration in the 1400s? Explain

Let A be an n × n symmetric negative definite matrix. Show that the leading principal submatrices of A are negative definite.

Determine whether the graph of the function is symmetric about the y-axis, the origin, or neither.

$$y = e ^ { - x ^ { 2 } }$$

Care is needed in plotting and interpreting points in three-dimensional space. When plotting points, it is helpful to show the "path" to the point as indicated in the diagram.

a. Plot and draw the paths to points P(-2, 3, 4) and Q(2, 3, 4) on a copy of the three-dimensional coordinate system shown.

b. What should appear to be true about the plot of the two points in Part a?

c. On a copy of a three-dimensional coordinate system, plot and label each of the following points.

• A(0, 2, 3)
• B(3, 2, 4)
• C(3, -2, -4)
• D(-5, 3, 5)
• E(-4, -7, -2)

d. Describe in general how you would plot a point A(a, b, c).

Define budgetary slack. Why might managers try to build slack into their budgets?

$\odot Q$ and $\odot R$ both have a radius of $3 \mathrm{cm} .$ Therefore the circles are ____________. (concentric or congruent)

If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled? F. The x-intercept becomes four times as great. G. The x-intercept becomes twice as great. H. The x-intercept becomes one-fourth as great. J. The x-intercept remains the same.

For this item, draw a cone with a height of 12 cm and a radius of 5 cm. Find the volume.

Quand il sera en Europe

faire du ski

Now suppose that instead of paying a dividend Good Values (from the previous problem) plans to repurchase $10,000 worth of stock.

a. What will be the stock price before and after the repurchase? b. Suppose an investor who holds 200 shares sells 20 of her shares back to the firm. If there are no taxes on dividends or capital gains, show that she should be indifferent between the repurchase and the dividend. c. Show that if dividends are taxed at 30% and capital gains are not taxed, the value of the firm is higher if it pursues the share repurchase instead of the dividend.

The points (2,3),(6,3),(6,-1), and (2,-1) are corners of a square. Find the equations of the inscribed and circumscribed circles.

What did natives of the Caribbean likely teach to European colonists?

If a supersonic jet flies at Mach 3.2, what will be the cone angle (to the nearest degree)?