
University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)
3rd Edition
ISBN: 9780321999573
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 11.2, Problem 17E
To determine
Express the given
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A building that is 205 feet tall casts a shadow of various lengths æ as the day goes by. An angle of
elevation is formed by lines from the top and bottom of the building to the tip of the shadow, as
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seen in the following figure. Find the rate of change of the angle of elevation when x 278 feet.
dx
Round to 3 decimal places.
Γ
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radians per foot
Use the information in the following table to find h' (a) at the given value for a.
x|f(x) g(x) f'(x) g(x)
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7
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3
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9
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h(x) = f(g(x)); a = 0
h' (0) =
Use the information in the following table to find h' (a) at the given value for a.
x f(x) g(x) f'(x) g'(x)
0
0
3
2
1
1
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0
2
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43
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h(x) = (1/(2) ²;
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h' (3)=
=
; a=3
Chapter 11 Solutions
University Calculus: Early Transcendentals Plus MyLab Math -- Access Card Package (3rd Edition) (Integrated Review Courses in MyMathLab and MyStatLab)
Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...
Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - Prob. 16ECh. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - The set of points in space equidistant from the...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - Prob. 34ECh. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find the perimeter of the triangle with vertices...Ch. 11.1 - Show that the point P(3, 1, 2) is equidistant from...Ch. 11.1 - Find an equation for the set of all points...Ch. 11.1 - Prob. 64ECh. 11.1 - Find the point on the sphere x2 + (y − 3)2 + (z +...Ch. 11.1 - Find the point equidistant from the points (0, 0,...Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 4ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 6ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 11.2 - The unit vector that makes an angle θ = −3π/4 with...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 18ECh. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - In Exercises 25–30, express each vector as a...Ch. 11.2 - Prob. 30ECh. 11.2 - Find the vectors whose lengths and directions are...Ch. 11.2 - Prob. 32ECh. 11.2 - Find a vector of magnitude 7 in the direction of v...Ch. 11.2 - Prob. 34ECh. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - Prob. 38ECh. 11.2 - If = i + 4j − 2k and B is the point (5, 1, 3),...Ch. 11.2 - Prob. 40ECh. 11.2 - Linear combination Let u = 2i + j, v = i + j, and...Ch. 11.2 - Linear combination Let u = i − 2j, v = 2i + 3j,...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Consider a 100-N weight suspended by two wires as...Ch. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Location A bird flies from its nest 5 km in the...Ch. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Vectors are drawn from the center of a regular...Ch. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.3 - Prob. 1ECh. 11.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j
v · u, |v|,...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - 5. v = 5j – 3k, u = i + j + k
v · u, |v|, |u|
the...Ch. 11.3 - Prob. 6ECh. 11.3 - v = 5i + j,
v · u, | v |, | u |
the cosine of the...Ch. 11.3 -
v · u, | v |, | u |
the cosine of the angle...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Prob. 13ECh. 11.3 - Rectangle Find the measures of the angles between...Ch. 11.3 - Direction angles and direction cosines The...Ch. 11.3 - Water main construction A water main is to be...Ch. 11.3 - Sums and differences In the accompanying figure,...Ch. 11.3 - Prob. 18ECh. 11.3 - Diagonals of a rhombus Show that the diagonals of...Ch. 11.3 - Perpendicular diagonals Show that squares are the...Ch. 11.3 - When parallelograms are rectangles Prove that a...Ch. 11.3 - Diagonal of parallelogram Show that the indicated...Ch. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Cauchy–Schwarz inequality Since u · v = |u| |v|...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Cancelation in dot products In real-number...Ch. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Sailboat The wind passing over a boat’s sail...Ch. 11.3 -
Use this fact and the results of Exercise 33 or...Ch. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 4ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 7ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 11.4 - Compute (i × j) × j and i × (j × j). What can you...Ch. 11.4 - Let u, v, and w be vectors. Which of the following...Ch. 11.4 - Prob. 32ECh. 11.4 - Cancelation in cross products If u × v = u × w and...Ch. 11.4 - Double cancelation If u ≠ 0 and if u × v = u × w...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 46ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Find the volume of a parallelepiped with one of...Ch. 11.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 11.4 - Triangle area Find a concise 3 × 3 determinant...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 7ECh. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 14ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 16ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 20ECh. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Planes
Find equations for the planes in Exercises...Ch. 11.5 - Planes
Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39−44, find the distance from the...Ch. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11.5 - Find the distance from the plane x + 2y + 6z = 1...Ch. 11.5 - Find the distance from the line x = 2 + t, y = 1 +...Ch. 11.5 - Find the angles between the planes in Exercises 47...Ch. 11.5 - Prob. 48ECh. 11.5 - Prob. 49ECh. 11.5 - Prob. 50ECh. 11.5 - Prob. 51ECh. 11.5 - Prob. 52ECh. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - Prob. 56ECh. 11.5 - Find parametrizations for the lines in which the...Ch. 11.5 - Prob. 58ECh. 11.5 - Prob. 59ECh. 11.5 - Prob. 60ECh. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Use Equations (3) to generate a parametrization of...Ch. 11.5 - Use the component form to generate an equation for...Ch. 11.5 - Find the points in which the line x = 1 + 2t, y =...Ch. 11.5 - Find equations for the line in the plane z = 3...Ch. 11.5 - Prob. 67ECh. 11.5 - How can you tell when two planes A1x + B1y + C1z =...Ch. 11.5 - Find two different planes whose intersection is...Ch. 11.5 - Find a plane through the origin that is...Ch. 11.5 - The graph of is a plane for any nonzero numbers...Ch. 11.5 - Prob. 72ECh. 11.5 - Prob. 73ECh. 11.5 - Prob. 74ECh. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Drawing
Sketch the surfaces in Exercises...Ch. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Prob. 44ECh. 11.6 - Express the area A of the cross-section cut from...Ch. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11.6 - Prob. 48ECh. 11.6 - Prob. 49ECh. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11 - Prob. 1GYRCh. 11 - How are vectors added and subtracted...Ch. 11 - Prob. 3GYRCh. 11 - Prob. 4GYRCh. 11 - Define the dot product (scalar product) of two...Ch. 11 - Prob. 6GYRCh. 11 - Prob. 7GYRCh. 11 - Prob. 8GYRCh. 11 - Prob. 9GYRCh. 11 - Prob. 10GYRCh. 11 - Prob. 11GYRCh. 11 - Prob. 12GYRCh. 11 - What are box products? What significance do they...Ch. 11 - Prob. 14GYRCh. 11 - Prob. 15GYRCh. 11 - Prob. 16GYRCh. 11 - Prob. 17GYRCh. 11 - In Exercises 1–4, let u = ⟨−3, 4⟩ and v = ⟨2, −5⟩....Ch. 11 - Prob. 2PECh. 11 - Prob. 3PECh. 11 - Prob. 4PECh. 11 - Prob. 5PECh. 11 - In Exercises 5-8, find the component form of the...Ch. 11 - The vector 2 units long in the direction 4i − j
Ch. 11 - The vector 5 units long in the direction opposite...Ch. 11 - Express the vectors in Exercises 9–12 in terms of...Ch. 11 - Prob. 10PECh. 11 - Prob. 11PECh. 11 - Prob. 12PECh. 11 - Prob. 13PECh. 11 - Prob. 14PECh. 11 - Prob. 15PECh. 11 - Prob. 16PECh. 11 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 11 - Prob. 18PECh. 11 - In Exercises 19 and 20, find projv u.
v = 2i + j −...Ch. 11 - Prob. 20PECh. 11 - In Exercises 21 and 22, draw coordinate axes and...Ch. 11 - Prob. 22PECh. 11 - Prob. 23PECh. 11 - Prob. 24PECh. 11 - In Exercises 25 and 26, find (a) the area of the...Ch. 11 - Prob. 26PECh. 11 - Suppose that n is normal to a plane and that v is...Ch. 11 - Find a vector in the plane parallel to the line ax...Ch. 11 - In Exercises 29 and 30, find the distance from the...Ch. 11 - Prob. 30PECh. 11 - Prob. 31PECh. 11 - Parametrize the line segment joining the points...Ch. 11 - In Exercises 33 and 34, find the distance from the...Ch. 11 - Prob. 34PECh. 11 - Prob. 35PECh. 11 - Prob. 36PECh. 11 - In Exercises 37 and 38, find an equation for the...Ch. 11 - Prob. 38PECh. 11 - Prob. 39PECh. 11 - Prob. 40PECh. 11 - Find the acute angle between the planes x = 7 and...Ch. 11 - Prob. 42PECh. 11 - Find parametric equations for the line in which...Ch. 11 - Prob. 44PECh. 11 - Prob. 45PECh. 11 - Prob. 46PECh. 11 - Prob. 47PECh. 11 - Prob. 48PECh. 11 - Prob. 49PECh. 11 - Prob. 50PECh. 11 - Prob. 51PECh. 11 - Prob. 52PECh. 11 - Prob. 53PECh. 11 - Prob. 54PECh. 11 - Find the point in which the line through P(3, 2,...Ch. 11 - Prob. 56PECh. 11 - Prob. 57PECh. 11 - Prob. 58PECh. 11 - Prob. 59PECh. 11 - Is the line related in any way to the plane ?...Ch. 11 - Which of the following are equations for the plane...Ch. 11 - The parallelogram shown here has vertices at A(2,...Ch. 11 - Prob. 63PECh. 11 - Prob. 64PECh. 11 - Prob. 65PECh. 11 - Prob. 66PECh. 11 - Prob. 67PECh. 11 - Prob. 68PECh. 11 - Prob. 69PECh. 11 - Prob. 70PECh. 11 - Prob. 71PECh. 11 - Prob. 72PECh. 11 - Prob. 73PECh. 11 - Prob. 74PECh. 11 - Prob. 75PECh. 11 - Prob. 76PECh. 11 - Prob. 1AAECh. 11 - Prob. 2AAECh. 11 - Prob. 3AAECh. 11 - Prob. 4AAECh. 11 - Prob. 5AAECh. 11 - Prob. 6AAECh. 11 - Prob. 7AAECh. 11 - Prob. 8AAECh. 11 - Prob. 9AAECh. 11 - Prob. 10AAECh. 11 - Prob. 11AAECh. 11 - Prob. 12AAECh. 11 - Prob. 13AAECh. 11 - Prob. 14AAECh. 11 - Prob. 15AAECh. 11 - By forming the cross product of two appropriate...Ch. 11 - Prob. 17AAECh. 11 - Prob. 18AAE
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- do question 2arrow_forwardA chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?arrow_forwardConsider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.arrow_forwardAssuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fParrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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