EBK THOMAS' CALCULUS
14th Edition
ISBN: 9780134654874
Author: WEIR
Publisher: VST
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Chapter 12, Problem 16GYR
To determine
Define cylinder and give some examples of equations that define the cylinder in Cartesian coordinates.
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Chapter 12 Solutions
EBK THOMAS' CALCULUS
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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- Q2/ verify that grad (hgrad f- f grad h) 1 E = 11 h h₂ where and h are scalar factions.arrow_forward(b) Find the value of each of these sums. Στο 3 • 21 =0 (i) (ii) Σ=1 Σ=023 2arrow_forward(b) For each of the following sets, 6 is an element of that set. (i) {x ER|x is an integer greater than 1} (ii) {x ЄR|x is the cube of an integer} (iii) {6, {6}} (iv) {{6},{6, {6}}} (v) {{{2}}}arrow_forward
- Question 1 Reverse the order of integration to calculate .8 .2 A = = So² Son y1/3 cos² (x²) dx dy. Then the value of sin(A) is -0.952 0.894 0.914 0.811 0.154 -0.134 -0.583 O 0.686 1 ptsarrow_forward3 Calculate the integral approximations T and M6 for 2 x dx. Your answers must be accurate to 8 decimal places. T6= e to search M6- Submit answer Next item Answers Answer # m 0 T F4 F5 The Weather Channel UP DELL F6 F7 % 5 olo in 0 W E R T A S D F G ZX C F8 Score & 7 H FO F10 8 の K B N Marrow_forwardStart with a circle of radius r=9. Form the two shaded regions pictured below. Let f(6) be the area of the shaded region on the left which has an arc and two straight line sides. Let g(6) be the area of the shaded region on the right which is a right triangle. Note that the areas of these two regions will be functions of 6; r=9 is fixed in the problem. 0 f(0) (a) Find a formula for f(6)= | | (b)Find a formula for g(6)= lim ƒ (6) (c) 80 = lim g (0) (d) 80 = lim (e) [f(8)/g(6)]= 0 g(0)arrow_forward
- i need the solution of part d and bonus. THANK YOUarrow_forwardDraw the following solid and explain each step to obtain the final result of the volume (see image):arrow_forwardA cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 20°C and the temperature of the cake when it was taken out of the oven is 160°C (a) Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: dT dt =-K(T-Ta), where K is a constant and Ta is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 20 + 140e Kt, where K is a (c) constant. Given that the cake has cooled to 90°C after 1 hour, determine the constant K. (d) The cook decides that the cake is cool enough to be taken out of the cake pan when its temperature lowers to 40 degrees C. Find when this will happen, both in exact form and as a decimal approximation to at least 2 decimal places, showing all working.arrow_forward
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