Let x and y be differentiable functions of t and let s = x 2 + y

Question:

Let x and y be differentiable functions of t and let s = √x² + y² be the distance between the points (x, 0) and (0, y) in the xy-plane.

a. How is ds/dt related to dx/dt if y is constant?

b. How is ds/dt related to dx/dt and dy>dt if neither x nor y is constant?

c. How is dx/dt related to dy/dt if s is constant?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

See More Books

Question Posted: Apr 19, 2023 11:03 AM

See More Questions

Describe market equilibrium using relevant graphs and discuss market surplus and market shortage.?
Write a Java program to compute the sum of the first 100 prime numbers Sample Output: Sum of the first 100 prime numbers: 24133
Let X and Y be jointly distributed on the portion of the Cartesian plane between the curves y = x and y = x2. Let the joint density of X, Y be fX,Y(x, y) =8y/3x in this regions, and fX,Y (x, y) = 0...
In each of the homeowners forms, OA) the property coverage is the same OB) the liability coverage varies OC) both the property and liability coverage are the same OD) the property coverage varies
Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither...
A debt of $12 500 with interest at 7% compounded semi-annually is repaid by payments of $1900 made at the end of every three months. Construct an amortization schedule showing the total paid and the...
Consider the gasoline mileage data in Table B.3. Delete eight observations (chosen at random) from the data and develop an appropriate regression model. Use this model to predict the eight withheld...
How is the cost of ending inventory calculated in a process costing system?
Lev and Gu are surprised that the structure and content of corporate annual reports have not changed between 1 9 0 2 and 2 0 1 2 . Why would one expect the accounting system to change over time? 2 -...
Assume that the Special Contract Division of Smith experienced the following transactions during the year ended December 31, 2020. i (Click the icon to view the transactions.) Requirements 1. Prepare...
Find the linearization of (x) = x + 1 + sin x at x = 0. How is it related to the individual linearizations of x + 1 and sin x at x = 0?
Find the derivatives of the function. r = 2 sin
How do you think one can balance the duty of confidentiality with the duty to be honest to opposing parties and courts?
What will be the moment of inertia of a homogeneous triangular board of mass m with side lengths a and b when rotated about the axis passing through side a? mb mb mb mb (a) (b) 2mb 3 (c) (e) 3 12 2 6...
10. A ray of light falls on a horizontal plane mirror as shown. 40 In order to reflect the light ray vertically upwards, the plane mirror should be rotated by A. 20 B. 25 C. 40 D. 50
You are at a funhouse at Hershey Park. The ride you are on is a huge spinning platform.Suppose you move towards the outside edge of the spinning platform. What would happen to the angular momentum of...
A tennis ball is tossed straight up into the air. In addition to the force of gravity, the tennis ball is subject to a frictional force due to air friction. The time the tennis ball takes to reach...
The capacitor in the circuit is charged to 20 V at the time the switch is closed. (Figure 1) Figure 20 V C 1 0 12 x 10 i 20 1 of 1 80 www Part A If the capacitor ruptures when its terminal voltage...
1. Evaluate the five general valuation rules discussed at the beginning of the case. Is it useful to have those different valuation methods? Explain. 2. Why are the impairment rules for goodwill...
You are the newly appointed tax practitioner to complete Emilys tax return and have downloaded the prefill report for Emilys tax return (hint, you can read what a prefill report is here (Links to an...
At what numbers is the following function t differentiable? Give a formula for g and sketch the graphs of g and g. 2x if x < 0 if 0 < x < 2 g(x) = {2x x if x > 2
Find the limit or show that it does not exist. lim tan-(In x)
Show that f is continuous on (-, ). |sin x if x < /4 [ sin f(x) = cos x if x > /4 %3D >T/4
Materials handling Machine maintenance Setups $ 2 4 1 , 6 8 0 Inspections $ 1 3 3 , 9 2 0 Overhead Costs Activity - cost driver 9 8 , 0 0 0 orders 2 0 , 0 0 0 maintenance hours 4 5 , 6 0 0 setups 2 1...
It is not necessary for non-profit organizations like schools and churches to develop vision and mission statements. Explain with your understanding.
what is difference between using right outer join, left outer join, inner join. example : select *from course right outer join prereq on course.course_id = prereq.course_id; select *from course left...

Let x and y be differentiable functions of t and let s = x 2 + y

Question:

Step by Step Answer:

a If y is constant it means that y does not change with respect to t Therefore dydt 0 In this case s ...View the full answer

Thomas Calculus Early Transcendentals

Students also viewed these Mathematics questions