(a) Explanation Given information: The boat travels along the path of unknown trajectory y = f ( x ) starting from the point ( 30 , 0 ) on a rope that is of 30 feet length. Formula: hyp 2 = ( adj ) 2 + ( opp ) 2 Calculation: Refer the Figure, the slope of the tangent to the path traced by the function f ( x ) is given by f ′ ( x ) . Consider the line joining the start and end points of path traced by the boat as the hypotenuse of the triangle. The value of hypotenuse is 30 ft and adjacent value is x . Calculate the height of the rope use the Pythagoras theorem as below. hyp 2 = ( adj ) 2 + ( opp ) 2 Substitute 30 ft for hyp and x for adj. 30 2 = ( x ) 2 + ( opp ) 2 900 − x 2 = opp 2 opp = 900 − x 2 Calculate the slope of the tangent line (b) To determine The equation f ′ ( x ) = − 900 − x 2 x for f ( x ) using the boundary condition f ( 30 ) = 0 .

University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)

3rd Edition

ISBN: 9780321999610

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

See similar textbooks

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Videos

Question

Chapter 8.3, Problem 58E

(a)

To determine

Show that the function f′(x)=−900−x2x that is based on the unknown path y=f(x) the skier will be pulled behind the boat.

(b)

To determine

The equation f′(x)=−900−x2x for f(x) using the boundary condition f(30)=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 57E

Chapter 8.4, Problem 1E

Students have asked these similar questions

Write the given third order linear equation as an equivalent system of first order equations with initial values. Use Y1 = Y, Y2 = y', and y3 = y". - - √ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t² \y(3) = 1, y′(3) = −2, y″(3) = −3 (8) - (888) - with initial values Y = If you don't get this in 3 tries, you can get a hint.

Question 2 1 pts Let A be the value of the triple integral SSS. (x³ y² z) dV where D is the region D bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0. Then the value of sin(3A) is -0.003 0.496 -0.408 -0.420 0.384 -0.162 0.367 0.364

Question 1 Let A be the value of the triple integral SSS₂ (x + 22) = 1 pts dV where D is the region in 0, y = 2, y = 2x, z = 0, and the first octant bounded by the planes x z = 1 + 2x + y. Then the value of cos(A/4) is -0.411 0.709 0.067 -0.841 0.578 -0.913 -0.908 -0.120

Chapter 8 Solutions

University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Show that the function f ′ ( x ) = − 900 − x 2 x that is based on the unknown path y = f ( x ) the skier will be pulled behind the boat.