Question

Electric charge is distributed over the rectangle 1 sxs 3,0 Sys 2 so that the charge density at (x, y) is o(x, y) = 2xy + y? (measured in coulombs per square meter). Find the total charge on the rectangle. Need Help? Read It Watch It Talk to a Tutor -/1 points VI SCALCET8 15.3.035. My Notes Ask Your Teach A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3 Need Help? Read It Watch It Talk to a Tutor -/1 points V SCALCET8 15.2.026. My Notes Ask Your Teach Find the volume of the given solid. Enclosed by the paraboloid z = x2 + y2 + 1 and the planes x = 0, y = 0, Z = 0, and x + y = 4

Answer 1

Electric Charge Гахуу? ) ауам — J, Los ag) » - 84 8) — (2 + 8)) - 2 1 - 14 2 -8 - 19 3 , орні для со • 21 1. 333 с

Date let us assume y varies from Since height varies linearly we have, hly-aytb south to north from south to north, 0 h (-10) = -10 atb - n(10) = abib Since halw=2 So, 2 = - loath Abrh (10) 71 - So, I h (20) = 7 = loatb - Add eah 1 + ② oble - loa+b+ loath = 9 2 b = 9 1h 9 put the value of bin eqh 6 7 - 10q+ 10 a=

hly) = 1 + 2 Now, volume - Is hy da par to 1 g + 2 dA = 422 1 1 1 r sind + 9 ) rardo =S; “S* ? sino + 91 drdo [ 169 6.0 +90 021 1950 6:0 + 2250)." 0 + 2250 2K olume - ason ft3

Paraboloid 2 = 22 + y2 + 1 Planes no y= 0 2 = 0 x+y = 4 y = 4-4 solid (Modified eah) Volume of V V = SS z da Now, y = 4.1 and it is observed from the given equations of planes that y varies from o to 4-1 and 4 varies from 0 to 4. Volume = s t ( 2 + y²1) dy dx first compute the integral with respect to y v = 2 4 [m² y + y² + y de * J * [uicunang 14:30] du = 5 (11-23 + stex? 48*124* 4x]dx

1 = St une n²+ 64-43 482 + 12 22 +4 -21 du va 90° 4.59* 2. 3. 4.132 4 4 311 . 3 3 v= 512 64 - 64 14 4256 4 16 - 8 Va 5127256208 - 56 V= 768 - 208 - 56 v=760 - 208 - 56 V = 560 56 V 560-168 Tv = 392 or 130 2 or 130.666 3 3 3 3 3