You want to photograph a circular diffraction pattern whose central maximum has a diameter of $d=0.90~\text{cm}$. You have a helium-neon laser (l$\lambda=633~\text{nm}$) and a $d_p=0.13~\text{mm}$ diameter pinhole. How far behind the pinhole should you place the viewing screen?

Assume that there is a region with cylindrical symmetry in which the conductivity is given by $\sigma=1.5 e^{-150 \rho} \mathrm{kS} / \mathrm{m}.$ An electric field of $30 a_{z} V/ m$ is present. (a) Find J. (b) Find the total current crossing the surface $\rho<\rho_{0},$ z = 0, all $\phi.$ (c) Make use of Ampere’s circuital law to find H.

For the following, find the indicated term of each binomial without fully expanding the binomial.

The fourth term of $(3 x-2 y)^5$

Suppose a set A has 2,048 subsets. How many distinct objects are contained in A?

How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?

Find $M_x, M_y$, and $(\bar{x}, \bar{y})$ for the laminas of uniform density $\rho$ bounded by the graphs of the equations.

$y=x^{2 / 3}$, y=0, x=8

In what ways do you think the progressive belief in using experts played a role in shaping Roosevelt's reforms? Refer to details from the text.

Write a situation in which order is not important when 3 of 8 objects are being selected.

Find $M_x, M_y$, and $(\bar{x}, \bar{y})$ for the laminas of uniform density $\rho$ bounded by the graphs of the equations.

$x=4-y^2$, x=0

Water is poured into a conical tank at the rate of $3 \mathrm{~m}^3$ per minute. The tank stands with the point downward. Determine how fast the water level in the tank is rising when the depth is $2 \mathrm{~m}$ and the radius of the water surface is $1.5 \mathrm{~m}$.

If a rock is thrown upward on the planet Mars with a velocity of $10 \mathrm{~m} / \mathrm{s}$, its height in meters $t$ seconds later is given by $y=10 t-1.86 t^2$. Estimate the instantaneous velocity when $t=1$.

Los chicos estan haciendo muchas cosas. Escoge la forma correcta del presente progresivo. (Choose the correct form of the present progressive.)

An estimate of the minimum velocity required for a round flat stone to skip when it hits the water is given by (Lyderic Bocquet, "The Physics of Stone Skipping," Am. J. Phys., vol. 71, no. 2, February 2003)

$$V = \frac { \sqrt { \frac { 16 M g } { \pi C \rho _ { w } d ^ { 2 } } } } { \sqrt { 1 - \frac { 8 M \tan ^ { 2 } \beta } { \pi d ^ { 3 } C \rho _ { w } \sin \theta } } }$$

where $M$ and $d$ are the stone mass and diameter, $\rho _ { w }$ is the water density, $C$ is a coefficient, $\theta$ is the tilt angle of the stone, $\beta$ is the incidence angle, and $g = 9.81 \mathrm { m } / \mathrm { s } ^ { 2 } .$ Determine $d$ if $V = 0.8 \mathrm { m } / \mathrm { s } .$ (Assume that $M = 0.1 \mathrm { kg } , C = 1$ , $\rho _ { w } = 1000 \mathrm { kg } / \mathrm { m } ^ { 3 } ,$ and $\beta = \theta = 10 ^ { \circ } .$ ).

Completely factor this binomial. The binomial is prime if, say so, Use the answers from earlier Exercises

$$49 m^2-100 p^2$$