At time $t = 0$, a 3.0 kilogram particle with velocity ${\hat{v}} = (5.0\ \text{~m/s}){\hat{i}}\ -\ (6.0\ \text{~m/s}){\hat{j}}$ is at $x = 3.0\text{~m}, y = 8.0\text{~m}$. It is pulled by a $7.0 \text{~N}$ force in the negative x direction. About the origin, what is the particle’s angular momentum?

At time $t = 0$, a 3.0 kilogram particle with velocity ${\hat{v}} = (5.0\ \text{~m/s}){\hat{i}}\ -\ (6.0\ \text{~m/s}){\hat{j}}$ is at $x = 3.0\text{~m}, y = 8.0\text{~m}$. It is pulled by a $7.0 \text{~N}$ force in the negative x direction. About the origin, what is rate at which the angular momentum is changing?

A particle is acted on by two torques about the origin:

$$\vec { \tau } _ { 1 }$$

has a magnitude of

$$2.0 \mathrm { N } \cdot \mathrm { m }$$

and is directed in the positive direction of the x axis, and

$$\vec { \tau } _ { 2 }$$

has a magnitude of

$$3.0 \mathrm { N } \cdot \mathrm { m }$$

and is directed in the negative direction of the y axis. In unit-vector notation, find

$$d \vec { \ell } / d t$$

, where

$$\vec { \ell }$$

is the angular momentum of the particle about the origin.

Circle the letter of each simple sugar. a. glucose b. sucrose c. fructose d. starch

A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.4 m/s². (a) If the tension in the cord is 89 N, what is the lamp’s mass? (b) What is the cord’s tension when the elevator ascends with an upward acceleration of 2.4 m/s²?

Rationalize the following lattice energy values:

$$\begin{matrix} \text{Compound} & & \text{Lattice Energy (kJ/mol)}\\ \hline \\ \begin{array} { l } { \text { CaSe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Se } } \\ { \text { CaTe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Te } } \end{array} & & \begin{array} { l } { - 2862 } \\ { - 2130 } \\ { - 2721 } \\ { - 2095 } \end{array} \end{matrix}$$

Simplify: 4.315 ÷ 5

Use elimination to solve the system of equation. 8x + 3y = -7, 7x + 2y = -3

When graphed, which of the following polynomial functions is symmetric about the origin?

$$A. f(x) = -x^3 + 2x + 5$$

$$B. f(x) = x^3 + 8x$$

$$C. f(x) = -7x^2 + 5$$

$$D. f(x) = 5x^3 + 3x^2 – 7x + 1.$$

find Pk+1 for the given Pk. Pk=3/(k+2)(k+3)

The acceleration of a particle traveling along a straight line is $a=(8-2 s) \mathrm{m} / \mathrm{s}^2$, where $s$ is in meters. If $v=0$ at $s=0$, determine the velocity of the particle at $s=2 \mathrm{~m}$, and the position of the particle when the velocity is maximum.

A small block with mass 0.0400 kg is moving in the xy -plane. The net force on the block is described by the potential-energy function $U ( x , y ) = \left( 5.80 J / m ^ { 2 } \right) x ^ { 2 } - \left( 3.60 J / m ^ { 3 } \right) y ^ { 3 }$. What are the magnitude and direction of the acceleration of the block when it is at the point (x = 0.300 m, y = 0.600 m)?

Marilyn earns $150 per month delivering newspapers plus$7 an hour babysitting. If she wants to earn at least $300 this month, how many hours will she have to babysit?

Two cars $A$ and $B$, each having a mass of $1.6 \mathrm{Mg}$, collide on the icy pavement of an intersection. The direction of motion of each car after collision is measured from snow tracks as shown. If the driver in car $A$ states that he was going $50 \mathrm{~km} / \mathrm{h}$ just before collision and that after collision he applied the brakes, so that his car skidded $4 \mathrm{~m}$ before stopping, determine the approximate speed of car $B$ just before collision. Assume that the coefficient of kinetic friction between the car wheels and the pavement is $\mu_k=0.15$. Note: The line of impact has not been defined; furthermore, this information is not needed for solution.