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Rachel Wilson

Rachel W.

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Linda Hand verified

Numerade educator

Maximizing the curvature of a helix In Example $5,$ we found the curvature of the helix $\mathbf{r}(t)=(a \cos t) \mathbf{i}+(a \sin t) \mathbf{j}+b t \mathbf{k}$ $(a, b \geq 0)$ to be $\kappa=a /\left(a^{2}+b^{2}\right) .$ What is the largest value $\kappa$ can have for a given value of $b ?$ Give reasons for your answer.

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Training Rats The following data are based on information from the Regis University Psychology Department. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day $1,$ a group of three rats was given a reward of one food pellet each time they ran a maze. A second group of three rats was given a reward of five food pellets each time they ran the maze. On day $2,$ the groups were reversed, so the first group now got five food pellets for running the maze and the second group got only one pellet for running the same maze. The average times in seconds for each rat to run the maze 30 times are shown in the following table.Do these data indicate that rats receiving larger rewards tend to run the maze in less time? Use a $5 \%$ level of significance.

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Tracy Tourville verified

Numerade educator

Determine the chemical formula of each compound and use it to calculate the mass percent composition of each constituent element. a. potassium chromate b. lead(II) phosphate c. cobalt(II) bromide

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Juan Nicolás verified

Numerade educator

Explain how an increase in your nominal income and a decrease in your real income might occur simultaneously. Who loses from inflation? Who loses from unemployment? If you had to choose between $(a)$ full employment with a 6 percent annual rate of inflation and $(b)$ price stability with an 8 percent unemployment rate, which would you choose? Why?

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Explain how each of the following policies redistributes income across generations. Is the redistribution from young to old or from old to young? a. an increase in the budget deficit b. more generous subsidies for education loans c. greater investments in highways and bridges d. an increase in Social Security benefits

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Eduard Sanchez verified

Numerade educator

You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20 m/s to the right and an acceleration of 8.40 m/s$^2$ to the left. How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?

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a. If the open-tube manometer in Exercise 45 contains a non volatile silicone oil (density $=1.30 \mathrm{g} / \mathrm{cm}^{3}$ ) instead of mercury (density $=13.6 \mathrm{g} / \mathrm{cm}^{3} ),$ what are the pressures in the flask as shown in parts a and $\mathrm{b}$ in torr, atmospheres, and pascals? b. What advantage would there be in using a less dense fluid than mercury in a manometer used to measure relatively small differences in pressure?

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Darshan Maheshwari verified

Numerade educator

Find the derivative of the function. Simplify where possible. $ y = \cos^{-1} (\sin^{-1} t) $

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Albert Tres verified

Numerade educator

Bungee Jumping Luisa goes bungee jumping from a 500 -ft-high bridge. The graph shows Luisa's height $h(t)$ (in ft) after $t$ seconds. (a) Describe in words what the graph indicates about Luisa's bungee jump. (b) Suppose Luisa goes bungee jumping from a 400 -ft-high bridge. Sketch a new graph that shows Luisa's height $H(t)$ after $t$ seconds. (c) What transformation must be performed on the function $h$ to obtain the function $H ?$ Express the function $H$ in terms of $h .$

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Vishal Gupta verified

Numerade educator

A generator connected to an RLC circuit has an rms voltage of150 $\mathrm{V}$ and an rms current of 39 $\mathrm{mA}$ . If the resistance in the circuit is 3.3 $\mathrm{k} \Omega$ and the capacitive reactance is $6.6 \mathrm{k} \Omega,$ what is the inductive reactance of the circuit?

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