Three point charges lie along a straight line, where $q_{1}=6.00 \mu \mathrm{C},$ $q_{2}=1.50 \mu \mathrm{C},$ and $q_{3}=-2.00 \mu \mathrm{C}$. The separation distances are $d_{1}=3.00 \mathrm{cm}$ and $d_{2}=2.00 \mathrm{cm}$. Calculate the magnitude and direction of the net electric force on (a) $q_{1},$ (b) $q_{2}$, and (c) $q_{3}$.

Three-point charges are arranged as we discussed earlier. Find
(a) the magnitude and
(b) the direction of the electric force on the particle at the origin.

Find the norms of A and B and the inner product of A and B, and note that the Schwarz inequality is satisfied: (a) $A = (3+i, 1, 2 − i,−5i, i + 1), \ B = (2i, 4 − 3i,1 + i, 3i, 1);$ (b) $A = (2, 2i − 3,1 + i, 5i, i − 2), \ B = (5i − 2, 1,3 + i, 2i, 4).$

Two charges, $q_{1}$ and $q_{2},$ are located at the origin and at (0.50 m, 0), respectively. Where on the x-axis must a third charge, $q_{3},$ of arbitrary sign be placed to be in electrostatic equilibrium if (a) $q_{1}$ and $q_{2}$ are like charges of equal magnitude, (b) $q_{1}$ and $q_{2}$ are unlike charges of equal magnitude, and (c) $q_{1}=+3.0\ \mu \mathrm{C}$ and $q_{2}=-7.0\ \mu \mathrm{C} ?$

Two charges $Q _ { 1 } ( + 2.00 \mu \mathrm { C } ) \text { and } Q _ { 2 } ( + 2.00 \mu \mathrm { C } )$ are placed symmetrically along the x-axis at $x = \pm 3.00 \mathrm { cm }$. Consider a charge $Q _ { 3 }$ of charge $+ 4.00 \mu \mathrm { C }$ and mass 10.0 mg moving along the y-axis. If $Q _ { 3 }$ starts from rest at y = 2.00 cm, what is its speed when it reaches y = 4.00 cm?

A point charge

$$q _ { 1 } = + 5.0 \mu C$$

is fixed in place at x=0, and a point charge

$$q _ { 2 } = - 3.0 \mu \mathrm { C }$$

is fixed at x=-20.0 cm. Where can we place a point charge

$$q _ { 3 } = - 8.0 \mu C$$

so that the net electric force on

$$q_1$$

due to

$$q_2$$

and

$$q_3$$

is zero?

Your friends rely on you for help with various things. Write out your responses to the questions your friends ask you. You may answer in the affirmative or negative. Follow the model. Modelo: ¿Quieres hablar conmigo sobre la fiesta? No, te hable anoche. ¿Tengo que traer algo a la fiesta para ti?

find all horizontal and vertical asymptotes. $f(x)=\frac{x}{x^{2}+4}$

Find the amplitude, period, frequency, and velocity amplitude for the motion of a particle whose distance s from the origin is the given function. $s=3 \sin (2 t+\pi / 8)+3 \sin (2 t-\pi / 8)$

For each of these five separate cases, identify the principle(s) of internal control that is violated. Recommend what the business should do to ensure adherence to principles of internal control. 1. Chi Han records all incoming customer cash receipts for her employer and posts the customer payments to their respective accounts. 2. At Tico Company, Julia and Trevor alternate lunch hours. Julia is the petty cash custodian, but if someone needs petty cash when she is at lunch, Trevor fills in as custodian. 3. Nori Nozumi posts all patient charges and payments at the Hopeville Medical Clinic. Each night Nori backs up the computerized accounting system to a drive and stores it in a locked file at her desk. 4. Ben Shales prides himself on hiring quality workers who require little supervision. As office manager, Ben gives his employees full discretion over their tasks and for years has seen no reason to perform independent reviews of their work. 5. Carla Farah’s manager has told her to reduce costs. Carla decides to raise the deductible on the plant’s property insurance from $5,000 to$10,000. This cuts the property insurance premium in half. In a related move, she decides that bonding the plant’s employees is a waste of money because the company has not experienced any losses due to employee theft. Carla saves the entire amount of the bonding insurance premium by dropping the bonding insurance.

Which of the following functions will have a graph with an axis of symmetry at x = 1 and an intercept at the origin?

A) $f(x) = 5(x + 1)^2- 5$

B) $f(x) = (x - 1)^2 - 2$

C) $f(x) = -(x + 1)^2+ 2$

D) $f(x) = 4(x - 1)^2 - 4$

E) $f(x) = -1/2(x - 1)^2 + 2$

Write an equation for each conic section. Parabola with vertex at the origin; through the point $(\sqrt{10},-5)$; opens down

Find a polynomial junction f(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. 3+2i, -1, and 2

A 1000 W carbon-dioxide laser emits light with a wavelength of 10 $\mu \mathrm{m}$ into a 3.0-mm-diameter laser beam. What force does the laser beam exert on a completely absorbing target?