The small block of mass m slides along the radial slot of the disk while the disk rotates in the horizontal plane about its center O. The block is released from rest $\dot{r}$relative to the disk and moves outward with an increasing velocity for the torque M that must be applied to the disk to maintain a constant angular velocity $\omega$ of the disk.

The lines $y=2 x+3$ and $y=a x+5$ are parallel if a = _____.

The integral represents the volume of a solid. Sketch the region and axis of revolution that produce the solid. $\int_{0}^{1} 2 \pi x\left(x-x^{2}\right) d x$

Identify the term that best fits the following description - identification of an object or event that has been previously encountered

Four lines are represented by the equations below. $\ell: y=-x+1 \quad m: y=-x+7 \quad n: y=2 x+1 \quad p: y=2 x+7$ Graph the four lines in the coordinate plane.

Which of the following most accurately describes the epicardium?

A) Encircles the heart with complex layers of fibers

B) Houses nerves to the heart and coronary blood vessels

C) Comprised of bands of cardiac muscle fibers

D) Contains the branches responsible for the heart s conduction system

Consider a concentric shaft, fixed axially and rotated inside the sleeve. Let the inner and outer cylinders have radii

$$r_i$$

and

$$r_0$$

, respectively, with total sleeve length L. Let the rotational rate be Ω (rad/s) and the applied torque be M. Using these parameters, derive a theoretical relation for the viscosity μ of the fluid between the cylinders.

_____ open water area of a lake or pond that is well lit and dominated by plankton.

The power output (in watts) of a certain brand of wind turbine generators is estimated to be

$$P=f(R, V)=0.772 R^2 V^3$$

where $R$ is the radius (in meters) of a rotor blade and $V$ is the wind speed (in meters per second). Estimate the power output of a model of these generators if its radius is $30 \mathrm{~m}$ and the wind speed is $16 \mathrm{~m} / \mathrm{s}$.

Imagine instead that you choose to take payments spread over 20 years, starting with $1,500,000 in year 1 and growing by 5 percent each year. a. How much money would you receive in year 2? In year 5? b. Write an equation to show how much money you receive in any given year. c. How much money will you have received after 20 years? Be ready to explain your thinking to the class.

Find the moment of inertia about the z-axis of the solid cone $\sqrt{x^2 + y^2} \leqslant z \leqslant h$. Assume that the solid has constant density $k$.

Design a wormgear set for the below specifications to produce the desired velocity ratio when transmitting the given torque at the output shaft for the given output rotational speed:

$$\begin{array}{ccc} \boldsymbol{V} \boldsymbol{R} & \begin{array}{c} \text { Torque } \\ (\mathbf{lb} \cdot \mathrm{in}) \end{array} & \begin{array}{c} \text { Output speed } \\ (\mathbf{r p m}) \end{array} \\ \hline 40 & 4200 & 45 \end{array}$$

A torque of $650\ \mathrm{Nm}$ rotates a shaft of diameter $0.25 \mathrm{~m}$ with $\omega=50\ \mathrm{rad} / \mathrm{s}$. What are the shaft surface speed and the transmitted power?

At the start of 2000, the U.S. money supply (M1) was $1,148 billion, distributed as follows: Currency totaling$523 billion, traveler's checks totaling $8 billion, and checking deposits totaling$616 billion. Let's say the Fed made the decision to raise the reserve requirement from 10% to 11% in order to decrease the amount of money in circulation. How much of a change in the money supply would the change in the reserve requirement have caused, assuming that all banks were initially lent up (had no extra reserves) and currency held outside of banks remained constant?