Question

A boat is travelling due south at a speed of 53 miles per hour. If the boat started off 29 miles directly west of the city of Johnstown, how fast (in radians per hour) is the angle opposite the southward path changing when the boat has travelled 23miles? (Do not include units in your answer, and round to the nearest hundredth.)

Provide your answer below:

Step 1

Let us suppose the distance of the boat towards south is y. Let the angle of the boat from the Johnstown be Ɵ. The distance in the west direction covered is 29 miles. To clear the picture, lets draw it.

Step 2

Use tan Ɵ and form a function Ɵ that depends on y as follows.

Step 3

The speed of the boat in the south direction is 53 miles per hour which is nothing but dy/dt=53. Differentiate it with res...

Tagged in

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...

Q: Calculate the area, in square units, bounded above by f(x)=−2x2 −x−21 and below by g(x)=−x2 −12x+9.

A: Click to see the answer

Q: Help please.

A: The given function is (tan-1x)2.

Q: Solve for complex x. e^(x^2+4x)=8

A: Solve the equation e^(x^2+4x) = 8 for complex x as follows.

Q: How do you set up the line integral for y=x(6-x) boundary?

A: The vector field is given by,

Q: Please help

A: Since f(x0,y0) is minimum of f(x,y). Then g(0) is minimum of g(t). That means g(0)<g(t) for t any...

Q: Calculus Question

A: Let's call the given integral as I. Further let's make the substitution: x2 + 1 = zHence, 2xdx = dzP...

Q: A theorem states that one local extremum implies an absolute extremum. Verify that the following fu...

A: The given function is,

Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and...

A: The equation of the plane is

Sorry about that. What wasn’t helpful?