A steam Rankine cycle operates the condenser at $1\ \text{psia}$ and the boiler at $2500\ \text{psia}$, while the temperature at the inlet of the turbine is $800\degree \text{F}$. The turbine's isentropic efficiency is $90\%$, the pump losses are negligible, and the cycle is sized to produce $1000\ \text{kW}$ of power. Calculate the mass flow rate through the boiler, power produced by the turbine, the rate of heat supply in the boiler, and thermal efficiency.

Solve for v in the following differential equation, subject to the stated initial condition.

$$2 d v / d t-v=3 u(t), \quad v(0)=-6$$

Desmond creates and administers a test of the personality trait of neuroticism to a group of ninth graders. He finds that students in the sample tend to get drastically different scores on the test each time they take it, suggesting that his test is particularly lacking in ________.

Determine the location and order of the zeros. (sin z-1)³

Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.

$$e^{z-i}+2/z-i-8/(z-i)^3$$

State three examples of a static load application and three examples of a dynamic load application.

A circuit is described by

$$4 \frac{d v}{d t}+v=10$$

If $v(0)=2$, find $v(t)$ for $t \geq 0$.

Sketch the following function:

$$z(t)=\cos 4 t \delta(t-1)$$

A negative correlation coefficient indicates that as scores on one variable ______, scores on the other variable __________.

(a) Explain why the interval of definition of the explicit solution

$$y = - \sqrt{25-x^2}$$

of the initial-value problem

$$\frac { d y } { d x } = - \frac { x } { y } , \quad y ( 4 ) = - 3$$

is the open interval $(-5, 5)$. (b) Can any solution of the differential equation cross the $x$-axis? Do you think that $x^2+ y^2 = 1$ is an implicit solution of the initial-value problem $dy/dx = -x/y, y(1) = 0$?

Margo is studying people's moods during stressful laboratory situation. Wanting to be nice, she smiles at each participants who enters the experimental condition (where they will be stressed) and remains neutral toward participants in the control group. Surprisingly, she finds that participants in the stressful condition report being in a better moods at the end of the experiment, compared to the participants in the control group. Margo's professor is not so surprised, however, because she realizes the outcomes are plagued by ________.

During a night's sleep, when do REM periods tend to get longer and occur closer together?

Integrate z²/(z²-1) by Cauchy’s formula counterclockwise around the circle. |z+i|=1.4

In his dreams, Andy is a child crawling through a dark tunnel looking for something he has lost. Hearing about this, a psychologist remarks, "Andy ahs broken up with his lover and is working through the emotional loss." Which theory of dreams does the psychologist likely subscribe to?