Precalculus
7th Edition
ISBN: 9781305761049
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 9, Problem 36RE
(a)
To determine
The dot product of the
(b)
To determine
Whether the vectors
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Solve this differential equation:
dy
0.05y(900 - y)
dt
y(0) = 2
y(t) =
Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The
graph models the depth of the submarine as a function of time.
What is the domain and range of the function in the graph?
1-
t (time)
1 2
4/5 6 7
8
-2
-3
456700
-4
-5
-6
-7
d (depth)
-8
D: 00 t≤
R:
0
5
-1
2
1
N
= 1 to x = 3
Based on the graph above, estimate to one decimal place the average rate of change from x =
Chapter 9 Solutions
Precalculus
Ch. 9.1 - (a) A vector in the plane is a line segment with...Ch. 9.1 - (a) The length of a vector w = a1, a2 is | w | =...Ch. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 5ECh. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 7ECh. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Velocity A river flows due south at 3 mi/h. A...Ch. 9.1 - Velocity Suppose that in Exercise 55 the current...Ch. 9.1 - Velocity The speed of an airplane is 300 mi/h...Ch. 9.1 - Velocity A migrating salmon heads in the direction...Ch. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - True Velocity of a Jet Find the true speed and...Ch. 9.1 - True Velocity of a Jet In what direction should...Ch. 9.1 - Prob. 63ECh. 9.1 - Velocity of a Boat The boater in Exercise 63 wants...Ch. 9.1 - Prob. 65ECh. 9.1 - Velocity A woman walks due west on the deck of an...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Tensions A 100-lb weight hangs from...Ch. 9.1 - Equilibrium of Tensions The cranes in the figure...Ch. 9.1 - DISCUSS: Vectors That Form a Polygon Suppose that...Ch. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Perpendicular Vectors? Determine whether the given...Ch. 9.2 - Dot Products Find the indicated quantity, assuming...Ch. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Dot Products Find the indicated quantity, assuming...Ch. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Projection Show that projv u and u projv u are...Ch. 9.2 - Projection Evaluate v projv u.Ch. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Work A car drives 500 ft on a road that is...Ch. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.3 - The distance between the point P(x1, y1, z1) and...Ch. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Center and Radius of a Sphere Show that the...Ch. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Trace of a Sphere In these exercises we find the...Ch. 9.3 - Spherical Water Tank A water tank is in the shape...Ch. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.4 - A vector in three dimensions can be written in...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Angle Between Two Vectors Find the angle between u...Ch. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Direction Angles of a Vector Find the direction...Ch. 9.4 - Direction Angles of a Vector Find the direction...Ch. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 45ECh. 9.4 - Prob. 46ECh. 9.4 - Parallel Vectors Two nonzero vectors are parallel...Ch. 9.4 - Prob. 48ECh. 9.4 - Prob. 49ECh. 9.4 - Prob. 50ECh. 9.4 - Prob. 51ECh. 9.5 - The cross product of the vectors u = a1, a2, a3...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Orthogonal Vectors Two vectors u and v are given....Ch. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Area of a Parallelogram Find the area of the...Ch. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Rubiks Tetrahedron Rubiks Cube, a puzzle craze of...Ch. 9.5 - Prob. 37ECh. 9.6 - A line in space is described algebraically by...Ch. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Equations of Lines Find parametric equations for...Ch. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - Prob. 15ECh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Equations of Lines A description of a line is...Ch. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Equations of Planes A description of a plane is...Ch. 9.6 - Prob. 33ECh. 9.6 - Prob. 34ECh. 9.6 - DISCOVER: Intersection of a Line and a Plane A...Ch. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9 - Prob. 1RCCCh. 9 - Prob. 2RCCCh. 9 - Prob. 3RCCCh. 9 - (a) Describe the three-dimensional coordinate...Ch. 9 - Prob. 5RCCCh. 9 - Prob. 6RCCCh. 9 - Prob. 7RCCCh. 9 - Prob. 8RCCCh. 9 - Prob. 9RCCCh. 9 - Prob. 10RCCCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - True Velocity of a Plane An airplane heads N 60 E...Ch. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Finding an Equation of a Sphere Find an equation...Ch. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - A river is flowing due east at 8 mi/h. A man heads...Ch. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Calculate the given quantity if u = i + j 2k v =...Ch. 9 - Find two unit vectors that are perpendicular to...Ch. 9 - (a) Find a vector perpendicular to the plane that...Ch. 9 - Prob. 11TCh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Prob. 9PCh. 9 - Prob. 10PCh. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15PCh. 9 - Prob. 16PCh. 9 - Prob. 17PCh. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Prob. 19P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Complete the description of the piecewise function graphed below. Use interval notation to indicate the intervals. -7 -6 -5 -4 30 6 5 4 3 0 2 1 -1 5 6 + -2 -3 -5 456 -6 - { 1 if x Є f(x) = { 1 if x Є { 3 if x Єarrow_forwardComplete the description of the piecewise function graphed below. 6 5 -7-6-5-4-3-2-1 2 3 5 6 -1 -2 -3 -4 -5 { f(x) = { { -6 if -6x-2 if -2< x <1 if 1 < x <6arrow_forwardLet F = V where (x, y, z) x2 1 + sin² 2 +z2 and let A be the line integral of F along the curve x = tcost, y = t sint, z=t, starting on the plane z = 6.14 and ending on the plane z = 4.30. Then sin(3A) is -0.598 -0.649 0.767 0.278 0.502 0.010 -0.548 0.960arrow_forward
- Let C be the intersection of the cylinder x² + y² = 2.95 with the plane z = 1.13x, with the clockwise orientation, as viewed from above. Then the value of cos (₤23 COS 2 y dx xdy+3 z dzis 3 z dz) is 0.131 -0.108 -0.891 -0.663 -0.428 0.561 -0.332 -0.387arrow_forward2 x² + 47 The partial fraction decomposition of f(x) g(x) can be written in the form of + x3 + 4x2 2 C I where f(x) = g(x) h(x) = h(x) + x +4arrow_forwardThe partial fraction decomposition of f(x) 4x 7 g(x) + where 3x4 f(x) = g(x) = - 52 –10 12x237x+28 can be written in the form ofarrow_forward
- 1. Sketch the following piecewise function on the graph. (5 points) x<-1 3 x² -1≤ x ≤2 f(x) = = 1 ४ | N 2 x ≥ 2 -4- 3 2 -1- -4 -3 -2 -1 0 1 -1- --2- -3- -4- -N 2 3 4arrow_forward2. Let f(x) = 2x² + 6. Find and completely simplify the rate of change on the interval [3,3+h]. (5 points)arrow_forward(x)=2x-x2 2 a=2, b = 1/2, C=0 b) Vertex v F(x)=ax 2 + bx + c x= Za V=2.0L YEF(- =) = 4 b (글) JANUARY 17, 2025 WORKSHEET 1 Solve the following four problems on a separate sheet. Fully justify your answers to MATH 122 ล T earn full credit. 1. Let f(x) = 2x- 1x2 2 (a) Rewrite this quadratic function in standard form: f(x) = ax² + bx + c and indicate the values of the coefficients: a, b and c. (b) Find the vertex V, focus F, focal width, directrix D, and the axis of symmetry for the graph of y = f(x). (c) Plot a graph of y = f(x) and indicate all quantities found in part (b) on your graph. (d) Specify the domain and range of the function f. OUR 2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1 and u is the unit step function: u(x) = { 0 1 if x ≥0 0 if x<0 y = u(x) 0 (a) Write a piecewise formula for the function g. (b) Sketch a graph of y = g(x). (c) Indicate the domain and range of the function g. X фирм where u is the unit step function defined in problem 2. 3. Let…arrow_forward
- Question 1arrow_forward"P3 Question 3: Construct the accessibility matrix Passociated with the following graphs, and compute P2 and identify each at the various two-step paths in the graph Ps P₁ P₂arrow_forwardA cable television company estimates that with x thousand subscribers, its monthly revenue and cost (in thousands of dollars) are given by the following equations. R(x) = 45x - 0.24x2 C(x) = 257 + 13xarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
How to find the magnitude and direction of a given vector; Author: Brian McLogan;https://www.youtube.com/watch?v=4qE-ZrR_NxI;License: Standard YouTube License, CC-BY
Linear Algebra for Computer Scientists. 2. Magnitude of a Vector; Author: Computer Science;https://www.youtube.com/watch?v=ElnuSJyUdR4;License: Standard YouTube License, CC-BY