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Patrick Educator

Patrick E.

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INSTANT ANSWER

Figure $30-54$ shows a rod of length $L=10.0 \mathrm{cm}$ that is forced to move at constant speed $v=5.00 \mathrm{m} / \mathrm{s}$ along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance $0.400 \Omega ;$ the rest of the loop has negligible resistance. A current $i=100 \mathrm{A}$ through the long straight wire at distance $a=10.0 \mathrm{mm}$ from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?

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INSTANT ANSWER

In Exercises $7-12$ , describe all solutions of $A \mathbf{x}=0$ in parametric vector form, where $A$ is row equivalent to the given matrix. $$ \left[\begin{array}{rrrr}{1} & {-2} & {-9} & {5} \\ {0} & {1} & {2} & {-6}\end{array}\right] $$

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INSTANT ANSWER

Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have the same number of men and women?

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ANSWERED

Christopher Nilsen verified

Numerade educator

Technetium-104 has a half-life of 18.0 min. How much of a 165.0 g sample remains after 90.0 minutes have passed?

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ANSWERED

Albert Tres verified

Numerade educator

The function $f$ graphed below is defined by a polynomial expression of degree $4.$ Use the graph to solve the exercises. (a) A function value $f(a)$ is a local maximum value of $f$ if $f(a)$ is the ______ value of $f$ on some open interval containing $a$ . From the graph of $f$ we see that there are two local maximum values of $f :$ One local maximum is ______ and it occurs when $x=2$; the other local maximum is ______ , and it occurs when $x=$ ______ . (b) A function value $f(a)$ is a local minimum value of $f$ if $f(a)$ is the ______ value of $f$ on some open interval containing $a .$ From the graph of $f$ we see that there is one local minimum value of $f .$ The local minimum value is ______ , and it occurs when $x=$ ______ .

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ANSWERED

Evelyn Cunningham verified

Numerade educator

The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table. (Table Can't Copy) What’s the probability that a) a man has both conditions? b) a man has high blood pressure? c) a man with high blood pressure has high cholesterol? d) a man has high blood pressure if it’s known that he has high cholesterol?

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INSTANT ANSWER

During the years 1998–2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential. a. What is the probability that the next earthquake occurs within the next three months? b. Given that six months has passed without an earthquake in Papua New Guinea, what is the probability that the next three months will be free of earthquakes? c. What is the probability of zero earthquakes occurring in 2014? d. What is the probability that at least two earthquakes will occur in 2014?

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ANSWERED

Umar Sohail Qureshi verified

Numerade educator

(III) A door 2.30 m high and 1.30 m wide has a mass of 13.0 kg. A hinge 0.40 m from the top and another hinge 0.40 m from the bottom each support half the door's weight (Fig. 9-69). Assume that the center of gravity is at the geometrical center of the door, and determine the horizontal and vertical force components exerted by each hinge on the door.

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INSTANT ANSWER

You have constructed a hair-spray-powered potato gun and want to find the muzzle speed $v_0$ of the potatoes, the speed they have as they leave the end of the gun barrel. You use the same amount of hair spray each time you fire the gun, and you have confirmed by repeated firings at the same height that the muzzle speed is approximately the same for each firing. You climb on a microwave relay tower (with permission, of course) to launch the potatoes horizontally from different heights above the ground. Your friend measures the height of the gun barrel above the ground and the range $R$ of each potato. You obtain the following data: Each of the values of $h$ and $R$ has some measurement error: The muzzle speed is not precisely the same each time, and the barrel isn't precisely horizontal. So you use all of the measurements to get the best estimate of $v_0$. No wind is blowing, so you decide to ignore air resistance. You use $g$ = 9.80 m/s$^2$ in your analysis. (a) Select a way to represent the data well as a straight line. (b) Use the slope of the best-fit line from part (a) to calculate the average value of $v_0$. (c) What would be the horizontal range of a potato that is fired from ground level at an angle of 30.0$^\circ$ above the horizontal? Use the value of $v_0$ that you calculated in part (b).

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INSTANT ANSWER

Suppose a 35-kW radio station emits EM waves uniformly in all directions. (a) How much energy per second crosses a area 1.0 km from the transmitting antenna? (b) What is the rms magnitude of the $\vec E$ field at this point, assuming the station is operating at full power? What is the rms volt- age induced in a 1.0-m-long vertical car antenna (c) 1.0 km away, (d) 50 km away?

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