EBK CALCULUS
10th Edition
ISBN: 9780100453777
Author: Larson
Publisher: YUZU
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Question
Chapter 12.1, Problem 87E
To determine
If the particles collides with each other or not if particle travel along r ( t ) = t 2 i + ( 9 t − 20 ) j + t 2 k and u ( t ) = ( 3 t + 4 ) i + t 2 j + ( 5 t − 4 ) k .
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Students have asked these similar questions
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
The correct answer is C,i know that we need to use stokes theorem and parametrize the equations then write the equation F with respect to the curve but i cant seem to find a way to do it, the integral should be from 0 to 2pi but i might be wrongcould you show me the steps to get to 18pi
Chapter 12 Solutions
EBK CALCULUS
Ch. 12.1 - Finding the Domain In exercises 310 find the...Ch. 12.1 - Finding the domain In exercises 310 find the...Ch. 12.1 - Prob. 3ECh. 12.1 - Finding the domain In exercises 3-10 find the...Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Finding the domain In exercises 310 find the...Ch. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Evaluating a function In Exercises 11 and 12...
Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Writing a Vector-Valued FunctionIn Exercises 1316,...Ch. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 43ECh. 12.1 - Transformations of Vector-Valued Functions In...Ch. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Representing a Graph by a Vector-Valued Function...Ch. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Representing a Graph by Vector-Valued Function In...Ch. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Prob. 71ECh. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.1 - Prob. 75ECh. 12.1 - Prob. 76ECh. 12.1 - Prob. 77ECh. 12.1 - Prob. 78ECh. 12.1 - Prob. 79ECh. 12.1 - Prob. 80ECh. 12.1 - Prob. 81ECh. 12.1 - HOW DO YOU SEE IT? The four figures below are...Ch. 12.1 - Prob. 83ECh. 12.1 - Prob. 84ECh. 12.1 - Prob. 85ECh. 12.1 - Prob. 86ECh. 12.1 - Prob. 87ECh. 12.1 - Prob. 88ECh. 12.1 - Prob. 89ECh. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Prob. 93ECh. 12.1 - Prob. 94ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Finding a Derivative In Exercises 9–20, find...Ch. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Finding a Derivative In Exercises 11-18, find...Ch. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Higher-Order DifferentiationIn Exercises 1922,...Ch. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Finding Intervals on Which a Curve Is Smooth In...Ch. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Using Properties of the Derivative In Exercises 35...Ch. 12.2 - Using Properties of the DerivativeIn Exercises 35...Ch. 12.2 - Using Two MethodsIn Exercises 37 and 38, find (a)...Ch. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 48ECh. 12.2 - Finding an Indefinite Integral In Exercises 39-46,...Ch. 12.2 - Prob. 51ECh. 12.2 - Evaluating a Definite Integral In Exercises 47-52,...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Evaluating a Definite Integral In Exercises 47-52,...Ch. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Prob. 61ECh. 12.2 - Finding an Antiderivative In Exercises 53-58, find...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 64ECh. 12.2 - 63. Differentiation State the definition of the...Ch. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Prob. 69ECh. 12.2 - Prob. 70ECh. 12.2 - Prob. 71ECh. 12.2 - Prob. 72ECh. 12.2 - Prob. 73ECh. 12.2 - Prob. 74ECh. 12.2 - Particle MotionA particle moves in the xy-plane...Ch. 12.2 - Particle MotionA particle moves in the yz-plane...Ch. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Prob. 79ECh. 12.2 - True or False? In Exercises 73-76, determine...Ch. 12.2 - Prob. 81ECh. 12.2 - Prob. 82ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Finding Velocity and Acceleration Vectors in Space...Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - A baseball player at second base throws a ball 90...Ch. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - A bomber is flying horizontally at an altitude of...Ch. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Projectile Motion In Exercises 41 and 42, use the...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - 57095-12.3-49E-Question-Digital.docx Circular...Ch. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.3 - Prob. 53ECh. 12.3 - Prob. 54ECh. 12.3 - Particle Motion Consider a particle moving on an...Ch. 12.3 - Prob. 57ECh. 12.3 - Prob. 55ECh. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - Prob. 61ECh. 12.3 - Prob. 62ECh. 12.4 - Prob. 44ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Finding the Unit Tangent Vector In Exercises 3-8,...Ch. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Finding Vectors In Exercises 37–42, find T(t),...Ch. 12.4 - Prob. 43ECh. 12.4 - Prob. 45ECh. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - Cycloidal Motion The figure shows the path of a...Ch. 12.4 - Motion Along an Involute of a Circle The figure...Ch. 12.4 - Prob. 51ECh. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.4 - Prob. 58ECh. 12.4 - Prob. 59ECh. 12.4 - Prob. 60ECh. 12.4 - Projectile Motion Find the tangential and normal...Ch. 12.4 - Prob. 62ECh. 12.4 - Prob. 63ECh. 12.4 - Prob. 64ECh. 12.4 - Air Traffic ControlBecause of a storm, ground...Ch. 12.4 - Projectile Motion A plane flying at an altitude of...Ch. 12.4 - Prob. 67ECh. 12.4 - Prob. 68ECh. 12.4 - Prob. 69ECh. 12.4 - Prob. 70ECh. 12.4 - Prob. 71ECh. 12.4 - Prob. 72ECh. 12.4 - Prob. 73ECh. 12.4 - Prob. 74ECh. 12.4 - Prob. 75ECh. 12.4 - Proof Prove that the principal unit normal vector...Ch. 12.4 - Prob. 77ECh. 12.4 - Prob. 78ECh. 12.4 - Prob. 79ECh. 12.4 - Prob. 80ECh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - 57095-12.5-7E-Question-Digital.docx Projectile...Ch. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Investigation Consider the helix represented by...Ch. 12.5 - Prob. 16ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Finding Curvature In Exercises 19–22, find the...Ch. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Finding CurvatureIn Exercises 2936, find the...Ch. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Finding Curvature in Rectangular Coordinates In...Ch. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Prob. 48ECh. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - Prob. 59ECh. 12.5 - Prob. 60ECh. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - Motion of a Particle A particle moves along the...Ch. 12.5 - Prob. 65ECh. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12.5 - Speed The smaller the curvature of a bend in a...Ch. 12.5 - Prob. 69ECh. 12.5 - Prob. 70ECh. 12.5 - Prob. 71ECh. 12.5 - Prob. 72ECh. 12.5 - Curvature Given the polar curve r=ea,a0, use the...Ch. 12.5 - Prob. 74ECh. 12.5 - Prob. 75ECh. 12.5 - Prob. 76ECh. 12.5 - Prob. 77ECh. 12.5 - Prob. 78ECh. 12.5 - Prob. 79ECh. 12.5 - Prob. 80ECh. 12.5 - Prob. 81ECh. 12.5 - Prob. 82ECh. 12.5 - Prob. 83ECh. 12.5 - Prob. 84ECh. 12.5 - True or False? In Exercises 83-86, determine...Ch. 12.5 - Prob. 86ECh. 12.5 - Prob. 87ECh. 12.5 - Prob. 88ECh. 12.5 - Prob. 89ECh. 12.5 - Prob. 90ECh. 12.5 - Prob. 91ECh. 12.5 - Prob. 92ECh. 12.5 - Kepler's Laws In Exercises 87-94, you are asked to...Ch. 12.5 - Prob. 94ECh. 12.5 - Prob. 95ECh. 12.5 - Prove Keplers Third Law: The square of the period...Ch. 12 - Domain and Continuity In Exercises 1-4, (a) find...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Writing a Vector-Valued Function In Exercises 7...Ch. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Evaluating a Definite Integral In Exercises 31-34,...Ch. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - 57095-12-40RE-Question-Digital.docx Projectile...Ch. 12 - Prob. 41RECh. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 1PSCh. 12 - Prob. 2PSCh. 12 - Prob. 3PSCh. 12 - Prob. 4PSCh. 12 - Cycloid Consider one arch of the cycloid...Ch. 12 - Prob. 6PSCh. 12 - Prob. 7PSCh. 12 - Prob. 8PSCh. 12 - Prob. 9PSCh. 12 - Prob. 10PSCh. 12 - Prob. 11PSCh. 12 - Prob. 12PSCh. 12 - Prob. 13PSCh. 12 - Ferris Wheel You want to toss an object to a...
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