Student Solutions Manual For Thomas' Calculus Format: Paperback
14th Edition
ISBN: 9780134439334
Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.^heil, Christopher
Publisher: PEARSON
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Chapter 12.4, Problem 22E
To determine
Prove that
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Can you solve this two numerical method eqn and teach me.
Find the area between the following curves.
x=-4, x=2, y=ex, and y = 3 - ex
Set up the integral (or integrals) needed to compute this area. Use the small
(Type exact answers in terms of e.)
3
In
2
A.
S
√ [3-2e*] dx+
-4
2
S [2ex-3] dx
3
In
2
B.
dx
Find the area between the curves.
Area = (Type an exact answer in terms of e.)
Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval.
f(x)=8-2x²: [0,4]
Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to
○ A.
dx
B.
2
S
8-2x² dx+
4
S
2
8-2x2 dx
C.
dx +
S
dx
For the interval [0,4], the area between the x-axis and f(x) is
(Type an integer or a simplified fraction.)
Chapter 12 Solutions
Student Solutions Manual For Thomas' Calculus Format: Paperback
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - Prob. 12ECh. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - Prob. 16ECh. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - Find the distance from the point (3, −4, 2) to...Ch. 12.1 - Find the distance from the point (−2, 1, 4) to...Ch. 12.1 - Find the distance from the point (4, 3, 0) to...Ch. 12.1 - Find the distance from the
x-axis to the plane z =...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - Prob. 38ECh. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - The set of points in space equidistant from the...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Prob. 64ECh. 12.1 - Find a formula for the distance from the point...Ch. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Find an equation for the set of all points...Ch. 12.1 - Find the point on the sphere x2 + (y − 3)2 + (z +...Ch. 12.1 - Prob. 72ECh. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find all points that simultaneously lie 3 units...Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 6ECh. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 12.2 - The unit vector that makes an angle θ = −3π/4 with...Ch. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - In Exercises 17–22, express each vector in the...Ch. 12.2 - Prob. 22ECh. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - Find the vectors whose lengths and directions are...Ch. 12.2 - Find the vectors whose lengths and directions are...Ch. 12.2 - Find a vector of magnitude 7 in the direction of v...Ch. 12.2 - Prob. 34ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - Prob. 36ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - If = i + 4j − 2k and B is the point (5, 1, 3),...Ch. 12.2 - If = −7i + 3j + 8k and A is the point (−2, −3,...Ch. 12.2 - Linear combination Let u = 2i + j, v = i + j, and...Ch. 12.2 - Prob. 42ECh. 12.2 - Linear combination Let u = ⟨ 1, 2, 1 ⟩, v = ⟨ 1,...Ch. 12.2 - Linear combination Let u = ⟨1, 2, 2 ⟩, v = ⟨ 1,...Ch. 12.2 - Velocity An airplane is flying in the direction...Ch. 12.2 - (Continuation of Example 8.) What speed and...Ch. 12.2 - Prob. 47ECh. 12.2 - Consider a 50-N weight suspended by two wires as...Ch. 12.2 - Consider a w-N weight suspended by two wires as...Ch. 12.2 - Consider a 25-N weight suspended by two wires as...Ch. 12.2 - Location A bird flies from its nest 5 km in the...Ch. 12.2 - Use similar triangles to find the coordinates of...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Let ABCD be a general, not necessarily planar,...Ch. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.3 - Prob. 1ECh. 12.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j
v · u, |v|,...Ch. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - 5. v = 5j – 3k, u = i + j + k
v · u, |v|, |u|
the...Ch. 12.3 - Prob. 6ECh. 12.3 - v = 5i + j,
v · u, | v |, | u |
the cosine of the...Ch. 12.3 -
v · u, | v |, | u |
the cosine of the angle...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Prob. 13ECh. 12.3 - Rectangle Find the measures of the angles between...Ch. 12.3 - Direction angles and direction cosines The...Ch. 12.3 - Water main construction A water main is to be...Ch. 12.3 - For Exercises 17 and 18, find the acute angle...Ch. 12.3 - For Exercises 17 and 18, find the acute angle...Ch. 12.3 - Sums and differences In the accompanying figure,...Ch. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Perpendicular diagonals Show that squares are the...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Cauchy–Schwarz inequality Since u · v = |u| |v|...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Cancelation in dot products In real-number...Ch. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Locomotive The Union Pacific’s Big Boy locomotive...Ch. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 -
Use this fact and the results of Exercise 33 or...Ch. 12.3 -
Use this fact and the results of Exercise 33 or...Ch. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 12.4 - Compute (i × j) × j and i × (j × j). What can you...Ch. 12.4 - Let u, v, and w be vectors. Which of the following...Ch. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Double cancelation If u ≠ 0 and if u × v = u × w...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the volume of a parallelepiped with one of...Ch. 12.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 12.4 - Prob. 50ECh. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Prob. 7ECh. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Prob. 17ECh. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Planes
Find equations for the planes in Exercises...Ch. 12.5 - Planes
Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - In Exercises 29 and 30, find the plane containing...Ch. 12.5 - Prob. 30ECh. 12.5 - Find a plane through P0(2, 1, –1) and...Ch. 12.5 - Find a plane through the points P1(1, 2, 3), P2(3,...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - Find the distance from the plane x + 2y + 6z = 1...Ch. 12.5 - Find the distance from the line x = 2 + t, y = 1 +...Ch. 12.5 - Find the angles between the planes in Exercises 47...Ch. 12.5 - Find the angles between the planes in Exercises 47...Ch. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Use a calculator to find the acute angles between...Ch. 12.5 - Prob. 55ECh. 12.5 - Use a calculator to find the acute angles between...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - Prob. 60ECh. 12.5 - Prob. 61ECh. 12.5 - Find parametrizations for the lines in which the...Ch. 12.5 - Prob. 63ECh. 12.5 - Prob. 64ECh. 12.5 - Given two lines in space, either they are...Ch. 12.5 - Given two lines in space, either they are...Ch. 12.5 - Use Equations (3) to generate a parametrization of...Ch. 12.5 - Prob. 68ECh. 12.5 - Prob. 69ECh. 12.5 - Prob. 70ECh. 12.5 - Is the line x = 1 − 2t, y = 2 + 5t, z = −3t...Ch. 12.5 - Prob. 72ECh. 12.5 - Prob. 73ECh. 12.5 - Prob. 74ECh. 12.5 - Prob. 75ECh. 12.5 - Prob. 76ECh. 12.5 - Prob. 77ECh. 12.5 - Hidden lines in computer graphics Here is another...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13-44.
x2...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Sketch the surfaces in Exercises 13−44.
39. x2 +...Ch. 12.6 - Prob. 40ECh. 12.6 - Sketch the surfaces in Exercises 13−44.
41. z =...Ch. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Express the area A of the cross-section cut from...Ch. 12.6 - The barrel shown here is shaped like an ellipsoid...Ch. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12 - Prob. 1GYRCh. 12 - How are vectors added and subtracted...Ch. 12 - Prob. 3GYRCh. 12 - Prob. 4GYRCh. 12 - Prob. 5GYRCh. 12 - Prob. 6GYRCh. 12 - Prob. 7GYRCh. 12 - Prob. 8GYRCh. 12 - What geometric or physical interpretations do...Ch. 12 - Prob. 10GYRCh. 12 - Prob. 11GYRCh. 12 - Prob. 12GYRCh. 12 - Prob. 13GYRCh. 12 - Prob. 14GYRCh. 12 - Prob. 15GYRCh. 12 - Prob. 16GYRCh. 12 - Prob. 17GYRCh. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Prob. 4PECh. 12 - Prob. 5PECh. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - The vector 5 units long in the direction opposite...Ch. 12 - Express the vectors in Exercises 9–12 in terms of...Ch. 12 - Prob. 10PECh. 12 - Prob. 11PECh. 12 - Prob. 12PECh. 12 - Prob. 13PECh. 12 - Prob. 14PECh. 12 - Prob. 15PECh. 12 - Prob. 16PECh. 12 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 12 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 12 - Prob. 19PECh. 12 - In Exercises 19 and 20, find projv u.
u = i − 2j
v...Ch. 12 - Prob. 21PECh. 12 - Prob. 22PECh. 12 - Prob. 23PECh. 12 - For what value or values of a will the vectors u =...Ch. 12 - In Exercises 25 and 26, find (a) the area of the...Ch. 12 - Prob. 26PECh. 12 - Suppose that n is normal to a plane and that v is...Ch. 12 - Find a vector in the plane parallel to the line ax...Ch. 12 - In Exercises 29 and 30, find the distance from the...Ch. 12 - Prob. 30PECh. 12 - Prob. 31PECh. 12 - Parametrize the line segment joining the points...Ch. 12 - In Exercises 33 and 34, find the distance from the...Ch. 12 - In Exercises 33 and 34, find the distance from the...Ch. 12 - Prob. 35PECh. 12 - Find an equation for the plane that passes through...Ch. 12 - In Exercises 37 and 38, find an equation for the...Ch. 12 - Prob. 38PECh. 12 - Prob. 39PECh. 12 - Prob. 40PECh. 12 - Prob. 41PECh. 12 - Prob. 42PECh. 12 - Prob. 43PECh. 12 - Show that the line in which the planes
x + 2y −...Ch. 12 - The planes 3x + 6z = 1 and 2x + 2y − z = 3...Ch. 12 - Find an equation for the plane that passes through...Ch. 12 - Prob. 47PECh. 12 - Prob. 48PECh. 12 - Find the distance from the point P(1, 4, 0) to the...Ch. 12 - Find the distance from the point (2, 2, 3) to the...Ch. 12 - Find a vector parallel to the plane 2x − y − z = 4...Ch. 12 - Prob. 52PECh. 12 - Prob. 53PECh. 12 - Prob. 54PECh. 12 - Prob. 55PECh. 12 - Prob. 56PECh. 12 - The line
intersects the plane x + 3y − z = −4...Ch. 12 - Show that for every real number k, the...Ch. 12 - Prob. 59PECh. 12 - Is the line related in any way to the plane ?...Ch. 12 - Prob. 61PECh. 12 - The parallelogram shown here has vertices at A(2,...Ch. 12 - Prob. 63PECh. 12 - Prob. 64PECh. 12 - Prob. 65PECh. 12 - Prob. 66PECh. 12 - Prob. 67PECh. 12 - Prob. 68PECh. 12 - Prob. 69PECh. 12 - Prob. 70PECh. 12 - Prob. 71PECh. 12 - Prob. 72PECh. 12 - Prob. 73PECh. 12 - Prob. 74PECh. 12 - Prob. 75PECh. 12 - Prob. 76PECh. 12 - Prob. 1AAECh. 12 - Prob. 2AAECh. 12 - Prob. 3AAECh. 12 - Prob. 4AAECh. 12 - Prob. 5AAECh. 12 - Prob. 6AAECh. 12 - Prob. 7AAECh. 12 - Prob. 8AAECh. 12 - Consider a regular tetrahedron of side length...Ch. 12 - Prob. 10AAECh. 12 - Prob. 11AAECh. 12 - Use vectors to show that the distance from to the...Ch. 12 - Prob. 13AAECh. 12 - Prob. 14AAECh. 12 - The projection of a vector on a plane Let P be a...Ch. 12 - The accompanying figure shows nonzero vectors v,...Ch. 12 - Prob. 17AAECh. 12 - Prob. 18AAECh. 12 - Prob. 19AAECh. 12 - Prob. 20AAECh. 12 - Prob. 21AAECh. 12 - Prob. 22AAECh. 12 - Prob. 23AAECh. 12 - Prob. 24AAECh. 12 - Prob. 25AAE
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- Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time t is 5 given by P'(t) = 126t², where t is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a total level of pollution of 600 units before all the fish life in the lake ends. Can the factory operate for 2 years without killing all the fish in the lake? Set up the integral that would determine the pollution level after 2 years. 2 5 126t 2 dt Can the factory operate for 2 years without killing all the fish in the lake? Thee factory can operate for 2 years without killing all the fish in the lake because the value of the integral is , which is less than 600. (Round to the nearest integer as needed.)arrow_forwardUse the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x)=4x-12; [2,6] The area between the x-axis and f(x) is (Type an integer or a simplified fraction.)arrow_forwardEvaluate the definite integral. 70 √5√2-6 3 dz 70 S 5√2-6 dz= 7 江 (Type an integer or decimal rounded to two decimal places as needed.)arrow_forward
- Find the area between the following curves. 2 y=x³-x²+x+4; y=5x² -7x+4 The area between the curves is (Simplify your answer.) ...arrow_forwardFind the area of the shaded region. 3- -1 -3- Q The total area of the shaded regions is (Simplify your answer.) y=9-x² Q 1 3 5 Xarrow_forwardFind the area of the region bounded by the graphs of the given equations. y=17x, y=x² ... The area is (Type an integer or a simplified fraction.)arrow_forward
- Find the area between the curves. y=x-26, y=9-2x ... The area between the curves is (Type an integer or decimal rounded to the nearest tenth as needed.)arrow_forwardYou are constructing a box out of cardboard with the dimensions 5 m by 6 m. You then cut equal-size squares from each corner so you may fold the edges. Let x be the side length of each square. Find that maximizes the volume of the box. Answer exactly. 8 x x H x ४ x ४ ४ marrow_forward× Question 2 ▾ Score on last try: 0 of 1 pts. See Details for more. > Next question You can retry this question below Find two positive numbers x and y such that x + y = 14 and they minimize x² + y². x = Уarrow_forward
- Sup the is a -12 -10 -8 -6 -4 -2 16 Af(x) 8 -8- -16arrow_forwardThe function f is given by f(x) = cos(x + 1). The solutions to which 6 of the following equations on the interval 0≤ x ≤ 2 are the solutions to f(x) = 1½ on the interval 0 < x < 2π? 2 A √√3 cos x - sin x = 1 B √√3 cos x + sin x = 1 C √3 sin x COS x = 1 D √√3 sin x + cos x = 1arrow_forwardSuppose that the graph below is the graph of f'(x), the derivative of f(x). Find the locations of all relative extrema, and tell whether each extremum is a relative maximum or minimum. Af'(x) Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Use a comma to separate answers as needed.) -10 86-4-2 -9- B 10 X G A. The function f(x) has a relative maximum at x= relative minimum at x = and a B. The function f(x) has a relative maximum at x= no relative minimum. and has C. There is not enough information given. D. The function f(x) has a relative minimum at x= no relative maximum. and has E. The function f(x) has no relative extrema.arrow_forward
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