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Sliva
18 days ago
6

Two row boats start at the same location, and start traveling apart along straight lines which meet at an angle of π3. Boat A is

traveling at a rate of 5 miles per hour directly east, and boat B is traveling at a rate of 10 miles per hour going both north and east. How fast is the distance between the rowboats increasing 3 hours into the journey?
Mathematics
1 answer:
tester [8.8K]18 days ago
5 0

Answer:

  5√3 miles per hour

Step-by-step explanation:

During their journey, the eastward velocity component of rowboat B matches that of rowboat A:

  (10 mph)(cos(π/3)) = 5 mph

Meanwhile, the northward velocity component for rowboat B is...

  (10 mph)(sin(π/3)) = 5√3 mph

As rowboat A consistently travels at a right angle to the direction between the boats, it doesn't affect their relative speed. Rowboat B remains directly north of rowboat A, so its northward speed represents their relative speed.

The rate at which the distance between the rowboats is increasing is 5√3 mph, approximately 8.66 mph.

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The tangent plane equation for the hyperboloid

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We have

The ellipsoid's equation is

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

The equation for the tangent plane at the point \left(x_0,y_0,z_0\right)

\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1  (Given)

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\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1

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\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0

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