The region determined by the intersection of the circles $x^2+y^2=4$ and $(x-2)^2+(y-2)^2=4$

An elderly sailor is shipwrecked on a desert island, but manages to save his eyeglasses. The lens for one eye has a power of +1.20 diopters, and the other lens has a power of +9.00 diopters. What is the magnifying power of the telescope he can construct with these lenses?

In Exercise, evaluate the integrals by hand, and check your answers with a CAS if you have one.

$$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { e ^ { x } } }$$

Multiply to expand each binomial Write your final answer so that the powers of a are in descending order.
a. $(a+b)^{0}$ b. $(a+b)^{1}$ c. $(a+b)^{2}$ d. $(a+b)^{3}$ e. $(a+b)^{4}$

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The normalized wavefunctions for a particle confined to move on a circle are $\psi ( \phi ) = ( 1 / 2 \pi ) ^ { 1 / 2 } \mathrm { e } ^ { - \mathrm { i } m \phi }$, where $m = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$ and $0 \leq \phi \leq 2 \pi$. Determine $\langle \phi \rangle$.

State the name of the property illustrated. √3·7=7·√3

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

$$( 2 , - 1 ) ; y = - \frac { 3 } { 2 } x + 6$$

Let R be the set of all real numbers and define a relation R on

$$\mathbf { R } \times \mathbf { R }$$

as follows: For all (a, b) and (c, d) in

$$\mathbf { R } \times \mathbf { R }$$

,

$$( a , b ) R ( c , d ) \Leftrightarrow$$

either a<c or both a=c and

$$b \leq d$$

Is R a partial order relation? Prove or give a counterexample.

For $y=x^{3}$, describe how the graph to the left of the y-axis compares to the graph to the right of the y-axis. Show that for $f(x)=x^{3}$, we have f(-x)=-f(x). In general, if you have the graph of y=f(x) to the right of the y-axis and f(-x)=-f(x) for all x, describe how to graph y=f(x) to the left of the y-axis.

Find each absolute value.
|1|

For the given constant c and functions f(x) and g(x), answer the following: (a) Is the limit $\lim _ { x \rightarrow c } \frac { f ( x ) } { g ( x ) }$ of the form 0/0? (b) Find $\lim _ { x \rightarrow c } \frac { f ( x ) } { g ( x ) }.$ c = 3, $f ( x ) = x ^ { 2 } - 3 x , g ( x ) = \sqrt { x + 1 } - 2$

Convert the given time period to years, in reduced fraction form, assuming a 360-day year [this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a year]. 90 days.

Why is mercury a more suitable substance to use in a barometer than water?