Thomas' Calculus (14th Edition)
14th Edition
ISBN: 9780134438986
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 16.3, Problem 2E
To determine
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Chapter 16 Solutions
Thomas' Calculus (14th Edition)
Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Match the vector equations in Exercises 1–8 with...Ch. 16.1 - Evaluate ∫C (x + y) ds, where C is the...Ch. 16.1 - Evaluate ∫C (x − y + z − 2) ds, where C is the...
Ch. 16.1 - Evaluate ∫C (xy + y + z) ds along the curve r(t) =...Ch. 16.1 - Evaluate along the curve r(t) = (4 cos t)i + (4...Ch. 16.1 - Prob. 13ECh. 16.1 - Find the line integral of over the curve r(t) =...Ch. 16.1 - Integrate over the path C1 followed by C2 from...Ch. 16.1 - Integrate over the path C1 followed by C2...Ch. 16.1 - Integrate f(x, y, z) = (x + y + z)/(x2 + y2 + z2)...Ch. 16.1 - Integrate over the circle r(t) = (a cos t)j + (a...Ch. 16.1 - Evaluate ∫C x ds, where C is
the straight-line...Ch. 16.1 - Evaluate , where C is
the straight-line segment x...Ch. 16.1 - Find the line integral of along the curve r(t) =...Ch. 16.1 - Find the line integral of f(x, y) = x − y + 3...Ch. 16.1 - Evaluate , where C is the curve x = t2, y = t3,...Ch. 16.1 - Find the line integral of along the curve , 1/2 ≤...Ch. 16.1 - Evaluate ,where C is given in the accompanying...Ch. 16.1 - Evaluate , where C is given in the accompanying...Ch. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - In Exercises 27–30, integrate f over the given...Ch. 16.1 - In Exercises 27–30, integrate f over the given...Ch. 16.1 - Prob. 31ECh. 16.1 - Find the area of one side of the “wall” standing...Ch. 16.1 - Mass of a wire Find the mass of a wire that lies...Ch. 16.1 - Center of mass of a curved wire A wire of density ...Ch. 16.1 - Mass of wire with variable density Find the mass...Ch. 16.1 - Center of mass of wire with variable density Find...Ch. 16.1 - Moment of inertia of wire hoop A circular wire...Ch. 16.1 - Inertia of a slender rod A slender rod of constant...Ch. 16.1 - Two springs of constant density A spring of...Ch. 16.1 - Wire of constant density A wire of constant...Ch. 16.1 - Prob. 41ECh. 16.1 - Center of mass and moments of inertia for wire...Ch. 16.2 - Find the gradient fields of the functions in...Ch. 16.2 - Find the gradient fields of the functions in...Ch. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - Prob. 8ECh. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - In Exercises 7−12, find the line integrals of F...Ch. 16.2 - Prob. 11ECh. 16.2 - Line Integrals of Vector Fields
In Exercises 7−12,...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - In Exercises 13–16, find the line integrals along...Ch. 16.2 - Prob. 17ECh. 16.2 - Along the curve , , evaluate each of the following...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - In Exercises 19–22, find the work done by F over...Ch. 16.2 - Evaluate along the curve from (–1, 1) to (2,...Ch. 16.2 - Prob. 24ECh. 16.2 - Evaluate for the vector field along the curve ...Ch. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Circulation and flux Find the circulation and flux...Ch. 16.2 - Flux across a circle Find the flux of the...Ch. 16.2 - Prob. 31ECh. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - In Exercises 31–34, find the circulation and flux...Ch. 16.2 - Flow integrals Find the flow of the velocity field...Ch. 16.2 - Flux across a triangle Find the flux of the field...Ch. 16.2 - Prob. 37ECh. 16.2 - The flow of a gas with a density of over the...Ch. 16.2 - Find the flow of the velocity field F = y2i + 2xyj...Ch. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.2 - A field of tangent vectors
Find a field G = P(x,...Ch. 16.2 - A field of tangent vectors
Find a field G = P(x,...Ch. 16.2 - Unit vectors pointing toward the origin Find a...Ch. 16.2 - Prob. 52ECh. 16.2 - Prob. 53ECh. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - In Exercises 55–58, F is the velocity field of a...Ch. 16.2 - In Exercises 55–58, F is the velocity field of a...Ch. 16.2 - Circulation Find the circulation of F = 2xi + 2zj...Ch. 16.2 - Prob. 60ECh. 16.2 - Flow along a curve The field F = xyi + yj − yzk is...Ch. 16.2 - Flow of a gradient field Find the flow of the...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1–6 are conservative,...Ch. 16.3 - Which fields in Exercises 1−6 are conservative,...Ch. 16.3 - Which fields in Exercises 1−6 are conservative,...Ch. 16.3 - Finding Potential Functions
In Exercises 7–12,...Ch. 16.3 -
In Exercises 7–12, find a potential function f...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - In Exercises 7–12, find a potential function f for...Ch. 16.3 - Prob. 13ECh. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - Prob. 15ECh. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - In Exercises 13–17, show that the differential...Ch. 16.3 - Prob. 18ECh. 16.3 -
Although they are not defined on all of space R3,...Ch. 16.3 - Although they are not defined on all of space R3,...Ch. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Evaluate
along the line segment C joining (0, 0,...Ch. 16.3 - Independence of path Show that the values of the...Ch. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - In Exercises 27 and 28, find a potential function...Ch. 16.3 - Work along different paths Find the work done by F...Ch. 16.3 - Work along different paths Find the work done by F...Ch. 16.3 - Evaluating a work integral two ways Let F =...Ch. 16.3 - Integral along different paths Evaluate the line...Ch. 16.3 - Exact differential form How are the constants a,...Ch. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Gravitational field
Find a potential function for...Ch. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - Prob. 2ECh. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - In Exercises 1–6, find the k-component of curl(F)...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 7–10, verify the conclusion of...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - In Exercises 11–20, use Green’s Theorem to find...Ch. 16.4 - Prob. 20ECh. 16.4 - Find the counterclockwise circulation and outward...Ch. 16.4 - Find the counterclockwise circulation and the...Ch. 16.4 - Prob. 23ECh. 16.4 - Find the counterclockwise circulation of around...Ch. 16.4 - In Exercises 25 and 26, find the work done by F in...Ch. 16.4 - Prob. 26ECh. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Apply Green’s Theorem to evaluate the integrals in...Ch. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Use the Green’s Theorem area formula given above...Ch. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Integral dependent only on area Show that the...Ch. 16.4 - Evaluate the integral
for any closed path C.
Ch. 16.4 - Evaluate the integral
for any closed path C.
Ch. 16.4 - Prob. 39ECh. 16.4 - Definite integral as a line integral Suppose that...Ch. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Green’s Theorem and Laplace’s equation Assuming...Ch. 16.4 - Maximizing work Among all smooth, simple closed...Ch. 16.4 - Regions with many holes Green’s Theorem holds for...Ch. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - In Exercises 1–16, find a parametrization of the...Ch. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - Prob. 19ECh. 16.5 - Prob. 20ECh. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - Prob. 23ECh. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - In Exercises 17–26, use a parametrization to...Ch. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Prob. 29ECh. 16.5 - Prob. 30ECh. 16.5 - A torus of revolution (doughnut) is obtained by...Ch. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.5 - Prob. 35ECh. 16.5 - Prob. 36ECh. 16.5 - Find the area of the surface cut from the...Ch. 16.5 - Find the area of the band cut from the paraboloid...Ch. 16.5 - Find the area of the region cut from the plane x +...Ch. 16.5 - Find the area of the portion of the surface x2 –...Ch. 16.5 - Prob. 41ECh. 16.5 - Prob. 42ECh. 16.5 - Find the area of the ellipse cut from the plane z...Ch. 16.5 - Find the area of the upper portion of the cylinder...Ch. 16.5 - Prob. 45ECh. 16.5 - Prob. 46ECh. 16.5 - Prob. 47ECh. 16.5 - Find the area of the surface 2x3/2 + 2y3/2 – 3z =...Ch. 16.5 - Prob. 49ECh. 16.5 - Prob. 50ECh. 16.5 - Prob. 51ECh. 16.5 - Prob. 52ECh. 16.5 - Prob. 53ECh. 16.5 - Find the area of the surfaces in Exercises...Ch. 16.5 - Use the parametrization
and Equation (5) to...Ch. 16.5 - Prob. 56ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Prob. 5ECh. 16.6 - Prob. 6ECh. 16.6 - Prob. 7ECh. 16.6 - In Exercises 1–8, integrate the given function...Ch. 16.6 - Integrate G(x, y, z) = x + y + z over the surface...Ch. 16.6 - Integrate G(x, y, z) = y + z over the surface of...Ch. 16.6 - Prob. 11ECh. 16.6 - Prob. 12ECh. 16.6 - Integrate G(x, y, z) = x + y + z over the portion...Ch. 16.6 - Prob. 14ECh. 16.6 - Prob. 15ECh. 16.6 - Prob. 16ECh. 16.6 - Prob. 17ECh. 16.6 - Prob. 18ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 21ECh. 16.6 - Prob. 22ECh. 16.6 - Prob. 23ECh. 16.6 - Prob. 24ECh. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - In Exercises 19–28, use a parametrization to find...Ch. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Prob. 30ECh. 16.6 - In Exercises 31–36, use Equation (7) to find the...Ch. 16.6 - Prob. 32ECh. 16.6 - Prob. 33ECh. 16.6 - Prob. 34ECh. 16.6 - Prob. 35ECh. 16.6 - In Exercises 31–36, use Equation (7) to find the...Ch. 16.6 - Find the flux of the field through the surface...Ch. 16.6 - Find the flux of the field F(x, y, z) = 4xi + 4yj...Ch. 16.6 - Let S be the portion of the cylinder y = ex in the...Ch. 16.6 - Let S be the portion of the cylinder y = ln x in...Ch. 16.6 - Find the outward flux of the field F = 2xyi+ 2yzj...Ch. 16.6 - Find the outward flux of the field F = xzi + yzj +...Ch. 16.6 - Prob. 43ECh. 16.6 - Prob. 44ECh. 16.6 - Prob. 45ECh. 16.6 - Conical surface of constant density Find the...Ch. 16.6 - Prob. 47ECh. 16.6 - Prob. 48ECh. 16.6 - Prob. 49ECh. 16.6 - A surface S lies on the paraboloid directly above...Ch. 16.7 - In Exercises 1–6, find the curl of each vector...Ch. 16.7 - Prob. 2ECh. 16.7 - In Exercises 1–6, find the curl of each vector...Ch. 16.7 - Prob. 4ECh. 16.7 - Prob. 5ECh. 16.7 - Prob. 6ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Prob. 8ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Prob. 10ECh. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - In Exercises 7–12, use the surface integral in...Ch. 16.7 - Let n be the unit normal in the direction away...Ch. 16.7 - Prob. 14ECh. 16.7 - Prob. 15ECh. 16.7 - Prob. 16ECh. 16.7 - Prob. 17ECh. 16.7 - Prob. 18ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 22ECh. 16.7 - Prob. 23ECh. 16.7 - In Exercises 19–24, use the surface integral in...Ch. 16.7 - Prob. 25ECh. 16.7 - Verify Stokes’ Theorem for the vector field F =...Ch. 16.7 - Prob. 27ECh. 16.7 - Prob. 28ECh. 16.7 - Prob. 29ECh. 16.7 - Prob. 30ECh. 16.7 - Prob. 31ECh. 16.7 - Prob. 32ECh. 16.7 - Prob. 33ECh. 16.7 - Prob. 34ECh. 16.8 - In Exercises 1–8, find the divergence of the...Ch. 16.8 - Prob. 2ECh. 16.8 - Prob. 3ECh. 16.8 - Prob. 4ECh. 16.8 - Prob. 5ECh. 16.8 - Prob. 6ECh. 16.8 - Prob. 7ECh. 16.8 - Prob. 8ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 13ECh. 16.8 - Prob. 14ECh. 16.8 - Prob. 15ECh. 16.8 - Prob. 16ECh. 16.8 - Prob. 17ECh. 16.8 - Prob. 18ECh. 16.8 - Prob. 19ECh. 16.8 - In Exercises 9–20, use the Divergence Theorem to...Ch. 16.8 - Prob. 21ECh. 16.8 - Prob. 22ECh. 16.8 - Prob. 23ECh. 16.8 - Prob. 24ECh. 16.8 - Prob. 25ECh. 16.8 - Prob. 26ECh. 16.8 - Prob. 27ECh. 16.8 - Prob. 28ECh. 16.8 - Prob. 29ECh. 16.8 - Prob. 30ECh. 16.8 - Prob. 31ECh. 16.8 - Prob. 32ECh. 16.8 - Prob. 33ECh. 16.8 - Prob. 34ECh. 16.8 - Prob. 35ECh. 16.8 - Prob. 36ECh. 16 - Prob. 1GYRCh. 16 - How can you use line integrals to find the centers...Ch. 16 - Prob. 3GYRCh. 16 - Prob. 4GYRCh. 16 - Prob. 5GYRCh. 16 - Prob. 6GYRCh. 16 - Prob. 7GYRCh. 16 - Prob. 8GYRCh. 16 - Prob. 9GYRCh. 16 - Prob. 10GYRCh. 16 - How do you calculate the area of a parametrized...Ch. 16 - Prob. 12GYRCh. 16 - What is an oriented surface? What is the surface...Ch. 16 - Prob. 14GYRCh. 16 - Prob. 15GYRCh. 16 - Prob. 16GYRCh. 16 - Prob. 17GYRCh. 16 - Prob. 18GYRCh. 16 - The accompanying figure shows two polygonal paths...Ch. 16 - The accompanying figure shows three polygonal...Ch. 16 - Integrate over the circle r(t) = (a cos t)j + (a...Ch. 16 - Prob. 4PECh. 16 - Evaluate the integrals in Exercises 5 and 6.
5.
Ch. 16 - Prob. 6PECh. 16 - Prob. 7PECh. 16 - Integrate F = 3x2yi + (x3 + l)j + 9z2k around the...Ch. 16 - Prob. 9PECh. 16 - Evaluate the integrals in Exercises 9 and...Ch. 16 - Prob. 11PECh. 16 - Prob. 12PECh. 16 - Prob. 13PECh. 16 - Hemisphere cut by cylinder Find the area of the...Ch. 16 - Prob. 15PECh. 16 - Prob. 16PECh. 16 - Circular cylinder cut by planes Integrate g(x, y,...Ch. 16 - Prob. 18PECh. 16 - Prob. 19PECh. 16 - Prob. 20PECh. 16 - Prob. 21PECh. 16 - Prob. 22PECh. 16 - Prob. 23PECh. 16 - Prob. 24PECh. 16 - Prob. 25PECh. 16 - Prob. 26PECh. 16 - Prob. 27PECh. 16 - Prob. 28PECh. 16 - Which of the fields in Exercises 29–32 are...Ch. 16 - Prob. 30PECh. 16 - Which of the fields in Exercises 29–32 are...Ch. 16 - Prob. 32PECh. 16 - Prob. 33PECh. 16 - Prob. 34PECh. 16 - In Exercises 35 and 36, find the work done by each...Ch. 16 - In Exercises 35 and 36, find the work done by each...Ch. 16 - Finding work in two ways Find the work done...Ch. 16 - Flow along different paths Find the flow of the...Ch. 16 - Prob. 39PECh. 16 - Prob. 40PECh. 16 - Prob. 41PECh. 16 - Prob. 42PECh. 16 - Prob. 43PECh. 16 - Prob. 44PECh. 16 - Prob. 45PECh. 16 - Prob. 46PECh. 16 - Prob. 47PECh. 16 - Moment of inertia of a cube Find the moment of...Ch. 16 - Use Green’s Theorem to find the counterclockwise...Ch. 16 - Prob. 50PECh. 16 - Prob. 51PECh. 16 - Prob. 52PECh. 16 - In Exercises 53–56, find the outward flux of F...Ch. 16 - In Exercises 53–56, find the outward flux of F...Ch. 16 - Prob. 55PECh. 16 - Prob. 56PECh. 16 - Prob. 57PECh. 16 - Prob. 58PECh. 16 - Prob. 59PECh. 16 - Prob. 60PECh. 16 - Prob. 1AAECh. 16 - Use the Green’s Theorem area formula in Exercises...Ch. 16 - Prob. 3AAECh. 16 - Use the Green's Theorem area formula in Exercises...Ch. 16 - Prob. 5AAECh. 16 - Prob. 6AAECh. 16 - Prob. 7AAECh. 16 - Prob. 8AAECh. 16 - Prob. 9AAECh. 16 - Prob. 10AAECh. 16 - Prob. 11AAECh. 16 - Prob. 12AAECh. 16 - Archimedes’ principle If an object such as a ball...Ch. 16 - Prob. 14AAECh. 16 - Faraday’s law If E(t, x, y, z) and B(t, x, y, z)...Ch. 16 - Prob. 16AAECh. 16 - Prob. 17AAECh. 16 - Prob. 18AAECh. 16 - Prob. 19AAECh. 16 - Prob. 20AAECh. 16 - Prob. 21AAE
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- Draw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy. L1 (a) The line L₁ is tangent to the unit circle at the point 0.992 (b) The tangent line 4₁ has equation: y= 0.126 x +0.992 (c) The line L₂ is tangent to the unit circle at the point ( (d) The tangent line L₂ has equation: y= 0.380 x + x × x)arrow_forwardThe cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 40 feet in radius. Your ball is located as in the picture below. The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels 8 ft/sec. Introduce coordinates so that the cup is the origin of an xy-coordinate system and start by writing down the equations of the circle and the linear path of the ball. Provide numerical answers below with two decimal places of accuracy. 50 feet green ball 40 feet 9 cup ball path rough (a) The x-coordinate of the position where the ball enters the green will be (b) The ball will exit the green exactly seconds after it is hit. (c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q: smallest x-coordinate =…arrow_forwardDraw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy. P L1 L (a) The line L₁ is tangent to the unit circle at the point (b) The tangent line L₁ has equation: X + (c) The line L₂ is tangent to the unit circle at the point ( (d) The tangent line 42 has equation: y= x + ).arrow_forward
- What is a solution to a differential equation? We said that a differential equation is an equation that describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential equation, we mean simply a function that satisfies this description. 2. Here is a differential equation which describes an unknown position function s(t): ds dt 318 4t+1, ds (a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate you really do get 4t +1. and check that dt' (b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation? (c) Is s(t)=2t2 + 3t also a solution to this differential equation? ds 1 dt (d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the right side of the equation by multiplying, and then integrate both sides. What do you get? (e) Does this differential equation have a unique solution, or an infinite family of solutions?arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Automobile Department Subject :Engineering Analysis Time: 2 hour Date:27-11-2022 کورس اول تحليلات تعمیر ) 1st month exam / 1st semester (2022-2023)/11/27 Note: Answer all questions,all questions have same degree. Q1/: Find the following for three only. 1- 4s C-1 (+2-3)2 (219) 3.0 (6+1)) (+3+5) (82+28-3),2- ,3- 2-1 4- Q2/:Determine the Laplace transform of the function t sint. Q3/: Find the Laplace transform of 1, 0≤t<2, -2t+1, 2≤t<3, f(t) = 3t, t-1, 3≤t 5, t≥ 5 Q4: Find the Fourier series corresponding to the function 0 -5arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardWhich degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?arrow_forward1/ Solve the following: 1 x + X + cos(3X) -75 -1 2 2 (5+1) e 5² + 5 + 1 3 L -1 1 5² (5²+1) 1 5(5-5)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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