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Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 11.3 - Problem 4
Get Full Access to Calculus: Early Transcendental Functions - 6 Edition - Chapter 11.3 - Problem 4

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# ?In Exercises 1-8, find (a) $$\mathbf{u} \cdot \mathbf{v}$$, (b) $$\mathbf{u} \cdot \mathbf{u}$$, (c) $$\|\mathbf{u}\|^{2} ISBN: 9781285774770 141 ## Solution for problem 4 Chapter 11.3 Calculus: Early Transcendental Functions | 6th Edition • Textbook Solutions • 2901 Step-by-step solutions solved by professors and subject experts • Get 24/7 help from StudySoup virtual teaching assistants Calculus: Early Transcendental Functions | 6th Edition 4 5 1 268 Reviews 30 0 Problem 4 In Exercises 1-8, find (a) \(\mathbf{u} \cdot \mathbf{v}$$,

(b) $$\mathbf{u} \cdot \mathbf{u}$$,

(c) $$\|\mathbf{u}\|^{2}$$,

(d) $$(\mathbf{u} \cdot \mathbf{v}) \mathbf{v}$$, and

(e) $$\mathbf{u} \cdot(\mathbf{2 v})$$.

$$\mathbf{u}=\langle-4,8\rangle, \mathbf{v}=\langle 7,5\rangle$$

Text Transcription:

u dot v

u dot u

||u||^2

(u dot v) v

u dot(2 v)

u=langle-4,8 rangle, v=langle 7,5 rangle

Step-by-Step Solution:

Step 1 of 5) To evaluate the integrals in Equations (5), we picture the plate in the coordinate plane and sketch a strip of mass parallel to one of the coordinate axes. We then express the strip’s mass dm and the coordinates (x , y ) of the strip’s center of mass in terms of x or y. Finally, we integrate y dm, x dm, and dm between limits of integration determined by the plate’s location in the plane.

Step 2 of 2

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?In Exercises 1-8, find (a) $$\mathbf{u} \cdot \mathbf{v}$$, (b) $$\mathbf{u} \cdot \mathbf{u}$$, (c) \(\|\mathbf{u}\|^{2}