90'

Mathematics

1 answer:

love history [14]3 years ago

8 0

Step-by-step explanation:

right triangle is A right triangle or right-angled triangle is a triangle in which one angle is a right angle
acute triangle is An acute triangle is a triangle with three acute angles. An obtuse triangle is a triangle with one obtuse angle and two acute angles
obtuse triangle is An obtuse triangle is one that has an angle greater than 90°. Because all the angles in a triangle add up to 180°, the other two angles have to be acute (less than 90°). It's impossible for a triangle to have more than one obtuse angle.

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Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

maksim [4K]

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

$S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)$

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to

$ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv$