(a) Do you think drinking the potion is a courageous or a foolish act? Explain. (b) How has Juliet changed during the play? Explain.

The graph of the height of a small projectile as a function of time, modeled by the equation, y = a(x - h)^2 + k, contains the vertex (2,67) and the points (0,3) and (4,3). You can find the particular equation of this graph by substituting (2,67) for (h,k) in the equation and then finding the value of a by substituting the coordinates of one of the other points for x and y. What is the particular equation?

Use Stokes’ theorem to evaluate the line integral $\oint_{C} A \cdot \mathrm{d} r$, where A = −yi + xj and C is the boundary of the ellipse $x^{2} / a^{2}+y^{2} / b^{2}=1$, z = 0.

Find a linear system in the unknowns x1, x2, x3, . . ., that corresponds to the given augmented matrix. (a) [0 3 -1 -1 -1, 5 2 0 -3 -6]

Rationalize the denominator of each expression and simplify. $\frac { 5 + 2 \sqrt { 3 } } { 7 + 4 \sqrt { 3 } }$

If

$$46 _ { x } = 101010_{t w o}$$

, find the base x.

Estimate the sum of

$$7 \frac { 1 } { 5 }$$

and

$$3 \frac { 7 } { 8 }$$

by rounding both numbers to the nearest whole number before adding.

Find $\mathbf { u } \cdot \mathbf { v }.$ $\mathbf { u } = - 2 \mathbf { i } , \mathbf { v } = 5 \mathbf { j }$

Is it more difficult to do a sit-up with your hands stretched in front of you or with them behind your head? Explain.

Which is your preferred method for solving linear systems? Explain why. Give two advantages and two disadvantages of the method you prefer.

Find an equation for the ellipse that satisfies the given conditions. Foci:

$$F ( 0 , \pm \sqrt { 10 } )$$

, vertices:

$$( 0 , \pm 7 )$$

Two objects are made from the same material. They have different masses and temperatures. If the two are placed in contact, which object will experience the greater temperature change? Explain.

$$\begin{array} { l } { \text { If } \phi \text { and } \gamma \text { are isomorphisms from the cyclic group } \langle a \rangle \text { to some } } \\ { \text { group and } \phi ( a ) = \gamma ( a ) , \text { prove that } \phi = \gamma } \end{array}$$

(a) What is Friar Lawrence's plan for Juliet? (b) Why do you think Juliet trusts the Friar?