Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Let S=x,y|x2+y21,x0

If the density at each point in S is proportional to the point’s distance from the origin, find the mass of S.

Short Answer

Expert verified

Answer is π3kwhere k is the constant of proportionality.

Step by step solution

01

Step 1. Given information

S=x,y|x2+y21,x0

02

Step 2. Explanation

S=x,y|x2+y21,x0

m=01-1-x21-x2kx2+y2dydx=20101-x2kx2+y2dydx

Let x=rcosθ,y=rsinθ

m=2k0π/2r3301dθ=2k0π/213-03dθ=23k0π/2dθ=23k[θ]0π/2=23kπ2-0=π3k

k is the constant of proportionality.

Mass is 9 units.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free