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jon bukley

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One can use turbines to exploit the energy contained in ocean currents, just like one can do it for wind. If the maximum amount of power is $918.8 \mathrm{~kW}$, which can be extracted from an ocean current with a turbine of rotor diameter $25.5 \mathrm{~m}$, what is the speed of the ocean current? (Hint 1: The density of seawater is $1024 \mathrm{~kg} / \mathrm{m}^{3}$. Hint 2 . The Betz limit applies to any fluid, including seawater.).

One can use turbines to exploit the energy contained in ocean currents, just like one can do it for wind. If the maximum amount of power is $918.8 \mathrm{~kW}$, which can be extracted from an ocean current with a turbine of rotor diameter $25.5 \mathrm{~m}$, what is the speed of the ocean current? (Hint 1: The density of seawater is $1024 \mathrm{~kg} / \mathrm{m}^{3}$. Hint 2 . The Betz limit applies to any fluid, including seawater.).

University Physics with Modern Physics

A lighthouse stands 500 m off of a straigh shore, the focused beam of its light revolving four times each minute, As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore $200 \mathrm{m}$ from $P .$ What is the speed of the beam along the shore when it strikes the point $Q ?$ Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q .$ Neglect the height of the lighthouse. (IMAGE CANT COPY)

A lighthouse stands 500 m off of a straigh shore, the focused beam of its light revolving four times each minute, As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore $200 \mathrm{m}$ from $P .$ What is the speed of the beam along the shore when it strikes the point $Q ?$ Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q .$ Neglect the height of the lighthouse. (IMAGE CANT COPY)

Calculus for Scientists and Engineers: Early Transcendental

Derivatives

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A lighthouse stands 500 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore 200 m from $P$. What is the speed of the beam along the shore when it strikes the point $Q ?$ Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q$. Neglect the height of the lighthouse.

A lighthouse stands 500 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore 200 m from $P$. What is the speed of the beam along the shore when it strikes the point $Q ?$ Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q$. Neglect the height of the lighthouse.

Calculus Early Transcendentals

Derivatives

Related Rates
Revolving light beam A lighthouse stands 500 m off a straight shore, and the focused beam of its light revolves (at a constant rate) four times each minute. As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore 200 m from $P$. What is the speed of the beam along the shore when it strikes the point $Q$ ? Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q$. Neglect the height of the lighthouse. (FIGURE CANNOT COPY)

Revolving light beam A lighthouse stands 500 m off a straight shore, and the focused beam of its light revolves (at a constant rate) four times each minute. As shown in the figure, $P$ is the point on shore closest to the lighthouse and $Q$ is a point on the shore 200 m from $P$. What is the speed of the beam along the shore when it strikes the point $Q$ ? Describe how the speed of the beam along the shore varies with the distance between $P$ and $Q$. Neglect the height of the lighthouse. (FIGURE CANNOT COPY)

Calculus: Early Transcendentals

Derivatives

Related Rates

Questions asked

INSTANT ANSWER

\[ x e^{x}=1 \text { for } x \in \mathbb{R} \] (a)show that the equation has one solution between \( \frac{1}{3} \) and 1 (b)show that the equation does not have more than the one solution on the entire \( \mathbb{R} \) (c) call the answer from the equation \( k \), use Newtons method one time on a appropriately chosen function with starting value \( x_{0}=1 \) to find a approximate value \( x_{1} \) for \( k \)

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ANSWERED

William Semus verified

Numerade educator

a factory produces cylindrical cans without lids. The materials used in the curved part are three times more expensive than the bottom parts. The cans should have a volume of 1 dm^3. what height and radius should give the cheapest cans to produce?

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ANSWERED

Oswaldo Jiménez verified

Numerade educator

find the Taylor polynomial ( P_{2}(x) ) for ( sqrt{x} ) of order 2 about the point 16

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ANSWERED

Sam Stansfield verified

Numerade educator

let ( f ) be a function given by: [ f(x)left{egin{array}{cc} frac{ an ^{-1}(4 x)}{sin x+ln (x+1)} & ext { for } x in(-1,0) \ 2 & ext { for } x=0 end{array} ight. ] (a) determine if ( f ) is continious at 0 (b) determine if ( f ) is differientable at 0 (use the definition of the derivative) (c) determine if ( f ) has any vertical or horizontal asymptotes

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ANSWERED

Gregory Higby verified

Numerade educator

two sprinters start the 100 m race at the same moment and finish at the same time, so that they share the victory. Show that at least in one point under the race, except for at the start and end, had the same speed. Justify what mathematical sentence(es) you've used.

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ANSWERED

Zack A verified

Numerade educator

a)Find the largest interval ( I subset mathbb{R} ) that contains 0 so that the function ( f ) : ( I ightarrow mathbb{R} ) given by ( f(x)=2 e^{-2 x}-e^{-x}+1 ) that has an inverse function ( f^{-1} ) b) find the domain and range for ( f^{-1} ) c) find the derivative ( left(f^{-1} ight)^{prime}(2) )

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ANSWERED

William Mead verified

Numerade educator

A factory releases ( mathrm{N} ) kilograms/day of a toxic waste in a lake. Within a day ( 30 % ) of the substance disappears from the lake. Assume that there is no pollution in the water when the emission start. a) Let ( mathrm{y}(mathrm{t}) ) be the amount of substance in ( mathrm{kg} ) in the lake by the time ( mathrm{t} ), measured in days after the emissions start, and set ( u(t)=y(t)-frac{10}{3} N ) Justify that ( u ) fulfill the starting value problem. [ u^{prime}(t)=-frac{3}{10} u(t), u(0)=-frac{10}{3} N ] b) The government will not notice the waste if the amount of waste in the lake does not override ( 20 mathrm{~kg} ). How much can the factory maximum release each day, without overriding? (hint: solve the starting value problem for ( mathrm{u}(mathrm{t}) ) and find ( mathrm{y}(mathrm{t}) )

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ANSWERED

William Mead verified

Numerade educator

find the largest interval $I subset mathbb{R}$ that contain 0 so that the function $f:I ightarrow mathbb{R}$ given by $f(x)=2e^{-2x}-e^{-x}+1$ has an inverse function $f^{-1}$

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ANSWERED

Keondre Parker verified

Numerade educator

How can I show that the limit does not exist? lim x-->0 cos(1/x)

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INSTANT ANSWER

use the formal definition of a limit (epsilon-delta) to prove that a) lim x->-3 (x^2+x-2)=4 b) lim x->1 (2/(x-2)=-2)

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