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4. How well does the potential energy stored in the spring agree with the kinetic energy gained by the cart? Discuss fully!

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2. Given a pipe with an initial pressure (p1), an initial cross-sectional area of 0.2 m², and an initial velocity of 5 m/s, then constricting to an area of 0.05 m² at 10m higher, determine: volume flow rate, speed at the constriction point (p2), and pressure difference.

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Which of the following is the meaning of the chromosome theory of inheritance as related to Mendel's principles? 1) Natural selection acts on certain chromosome arrays rather than on genes 2) Mendelian genes are at specific loci on the chromosome and in turn segregate during meiosis 3) Homologous chromosomes give rise to some genes and crossover chromosomes to other genes 4) No more than a single pair of chromosomes can be found in a healthy normal cell 5) Individuals inherit particular chromosomes attached to genes

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There are three different substances with the formula C2H4O. Draw them.

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Charge in an LRC circuit obeys the same differential equation as a damped harmonic oscillator, \begin{equation} \dot{q} + \frac{1}{\tau}\dot{q} + \omega_0^2 q = 0. \end{equation} When applying this in Physics 1C, you can just immediately write down the general solution, \begin{equation} q(t) = Ae^{-t/(2\tau)}\cos(\omega t + \phi), \end{equation} where $A$ and $\phi$ are integration constants, and the damped frequency $\omega$ is a bit less than the undamped frequency $\omega_0$, \begin{equation} \omega = \omega_0\sqrt{1 - 1/(2\omega_0\tau)^2}. \end{equation} In this problem, you will see one way to quickly derive the general solution. Plug the trial solution \begin{equation} q(t) = e^{\gamma t} \end{equation} into Eq. 1, and then solve the resulting quadratic equation for $\gamma_{\pm}$.

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3. The Starship Enterprise uses Dylithium Crystals in a matter/anti-mater, quantum intermix, 11th dimensional string-tuner/singularity-controller employing gravitron particles to heat water for coffee and tea. In order to keep the crew properly caffeinated, it operates at a stress of $\sigma$ = 16,000 psi with the corresponding steady-state creep rates found to be: \begin{tabular}{cc} Temperature \\ (F) & Steady State Creep Rate \\ & (in./in./hr.) \\ \hline 900 & $2.6 \times 10^{-5}$ \\ 1,000 & $1.27 \times 10^{-3}$ \\ 1,100 & $4.10 \times 10^{-2}$ \\ 1,200 & $8.5 \times 10^{-1}$ \\ \end{tabular} Find the activation energy, $\Delta H$, for the crystals at 16,000 psi in order to keep the crew happy and avoid a reversal of the current expansion of the universe, thus leading to the \"Big Crunch,\" and the end of all space-time (definitely very bad).

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How do inflation and unemployment relate to the interest rate? What is the relationship between wage growth and inflation?

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The yield strength of a copper alloy is 50 MPa. A 20-gram diamond is placed on it, with a pyramid-shaped tip against the copper surface. The diamond will : A) be damaged B) leave a dent of about 63.2 microns in copper C) leave a dent of about 36.5 microns in copper D) not damage the copper at all Please kindly answer and provide explanation or working. Thank you.

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Consider this scenario: The population of a city increased steadily over a six-year span. The following ordered pairs show the population and the year over the six-year span (year, population) for specific recorded years. (2000,3600), (2001,3900), (2003,4600), (2006,6000) A. Use linear regression to determine a function y, where the population depends on the year to three decimal places of accuracy. B. Identify the slope and explain what it means in the context of the problem C. Identify the correlation coefficient and explain what it tells you about the relationship

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\overline{AB} is dilated by a scale factor of $\frac{1}{4}$ to form \overline{A'B'}. \overline{A'B'} measures 9. What is the measure of \overline{AB}?

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