Numerade

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Pritesh Ranjan

Numerade educator

Show that the energy associated with a conducting sphere of radius $R$ and charge $Q$ surrounded by a vacuum is $U=$ $k_{e} Q^{2} / 2 R .$

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Lorie Mcfee

Numerade educator

The following table gives the percent of the US population living in urban areas as a function of year. $$\begin{array}{c|c|c|c|c|c}\hline \text { Year } & 1800 & 1830 & 1860 & 1890 & 1920 \\\hline \text { Percent } & 6.0 & 9.0 & 19.8 & 35.1 & 51.2 \\\hline \text { Year } & 1950 & 1980 & 1990 & 2000 & 2005 \\\hline \text { Percent } & 64.0 & 73.7 & 75.2 & 79.0 & 79.0 \\\hline\end{array}$$ (a) Find the average rate of change of the percent of the population living in urban areas between 1890 and 1990 (b) Estimate the rate at which this percent is increasing at the year 1990 (c) Estimate the rate of change of this function for the year 1830 and explain what it is telling you.

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Babita Kumari

Numerade educator

In Exercises $13-24,$ determine whether the equation represents $y$ as a function of $x .$ $$ y=\sqrt{x^{2}-1} $$

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INSTANT ANSWER

In Exercises 1 and $2,$ use the graph to estimate the slope of the tangent line to $y=x^{n}$ at the point $(1,1)$ . vErify your answer analytically. To print an enlarged copy of the graph, go to the website www.mathgraphs.com. $$ y=x^{-1 / 2} \quad \text { (b) } y=x^{-1} $$

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Umar Sohail Qureshi

Numerade educator

The portion of truss shown represents the upper part of a power transmission line tower. For the given loading, determine the force in each of the members located above $H J$. State whether each member is in tension or compression.

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Prabhat Tyagi

Numerade educator

Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s. (b) What is unreasonable about the range you found? (c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer. (d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon.

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INSTANT ANSWER

32. Support the hypothesis that signaling pathways appeared early in evolution and are well-conserved using the yeast mating factor as an example. a. Signaling in yeast uses the R T K pathway and is evolutionarily conserved, like insulin signaling in humans. b. Signaling in yeast uses G-protein coupled receptors for signaling and is evolutionarily conserved, like insulin signaling in humans. c. Signaling in yeast uses an endocrine pathway and is evolutionarily conserved, like insulin signaling in humans. d. Mating factor in yeast uses an auto crine signaling pathway and is evolutionarily conserved.

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Bryan Valdivia

Numerade educator

What evidence would you use to support this statement: Ancient people thought that disease was transmitted by things they could not see.

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Prabhat Tyagi

Numerade educator

(a) A concave spherical mirror forms an inverted image 4.00 times larger than the object. Assuming the distance between object and image is 0.600 $\mathrm{m}$ , find the focal length of the mirror. (b) What If? Suppose the mirror is convex. The distance between the image and the object is the same as in part (a), but the image is 0.500 the size of the object. Determine the focal length of the mirror.

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Leon Druch

Numerade educator

Ideally, the sampling frame in a sample survey should list every individual in the population, but in practice, this is often difficult. Suppose that a sample of households in a community is selected at random from the telephone directory. Explain how this sampling method results in under coverage that could lead to bias.

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Samuel M.