How does the U.S. Constitution balance individual rights and the need to uphold the authority of government?

Prove that if w = f (z) is analytic at $z _ { 0 }$ and $f ^ { \prime } \left( z _ { 0 } \right) \neq 0$, then $z = f ^ { - 1 } ( w )$ is analytic at $w _ { 0 } = f \left( z _ { 0 } \right)$, and $\frac { d f ^ { - 1 } } { d w } ( w ) = \frac { 1 } { \frac { d f } { d z } ( z ) }$ for $w = w _ { 0 } , z = z _ { 0 }$.

How important do you feel individual rights are in the United States? Are there times when individual rights are more important than the greater public good? Why or why not?

Find the coordinates of the reflection of each point across the line y = -5. (x, y)

Solve the given problem. Express $4^{2} \times 64(\text { a })$ as a power of 4 and $(b)$ as a power of 2.

What accounted for Ghana’s financial success?

Express each polynomial function In the form f(x)=(x-k)q(x)+r for the given value of k. $f(x)=4 x^{4}-3 x^{3}-20 x^{2}-x$; k=3

What is a rational function?

A triangle has an area of 100 square units. Its vertices are (0, 0), (20, 0), and (x, y). Write an equation involving a determinant that you can use to find the coordinates of the unknown vertex.

Which inequality has 5 in its solution set?

$$F. \ 5 - 2 x \geq 3$$

$$G. \ 3 x - 4 \geq 8$$

$$H. \ 8 - 3 x > - 7$$

$$I. \ 4 - 2 x < - 6$$

Define referred pain, and provide an example.

A rocket sled having an initial speed of 160 mi/h is slowed by a channel of water. Assume that, during the braking process, the acceleration a is given by

$$\begin{gather*} a(v) = −\mu v^2, \end{gather*}$$

where v is the velocity and \mu is a constant. (a) As in Example 4 in the text, use the relation

$$\begin{gather*} \dfrac{dv}{dt} = v \dfrac{dv}{dx} \end{gather*}$$

to write the equation of motion in terms of v and x. (b) If it requires a distance of 2200 ft to slow the sled to 16 mi/h, determine the value of $\mu$. (c) Find the time t required to slow the sled to 16 mi/h.

Simplify each expression.

$$\frac { b ^ { 3 } c ^ { 2 } } { b ^ { 3 } c }$$

What types of memory are volatile? Non- volatile?