Question

Problem #1: Find the volume of the solid bounded by the graphs of $x^2 + y^2 = 16$, $z = 7x + 8y$, and the coordinate planes, in the first octant.

Name: Problem #1: Find the volume of the solid bounded by the graphs of x^2 + y^2 = 16, z = 7x + 8y, and the coordinate planes, in the first octant.
Uploaded: 2023-06-09T04:26:27-08:00
Duration: 1 min 9 s
Channel: Madhur L
Description: Problem #1: Find the volume of the solid bounded by the graphs of x^2 + y^2 = 16, z = 7x + 8y, and the coordinate planes, in the first octant.

          Problem #1: Find the volume of the solid bounded by the graphs of $x^2 + y^2 = 16$, $z = 7x + 8y$, and the coordinate planes, in the first octant.

Added by Peter F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/09/2023

Step 1

To find the intersection points, we need to solve the equations 2 + y^2 = 16 and z = 7x + 8y simultaneously. From the equation 2 + y^2 = 16, we can solve for y: y^2 = 16 - 2 y^2 = 14 y = ±√14 Substituting y = √14 into the equation z = 7x + 8y, we can solve for Show more…

Show all steps

Thanks for your feedback!

Problem #1: Find the volume of the solid bounded by the graphs of 2 + y2 = 16, z = 7x + 8y, and the coordinate planes, in the first octant. 192 Problem #1: 192 Enter your answer symbolically, as in these examples Just Save Submit Problem #1 for Grading Problem #1 Attempt #1 Your Answer: 128 3 Your Mark: 0/2x Attempt #2 Attempt #3 192 0/2X