Calculus: Early Transcendentals, Loose-leaf Version, 9th
9th Edition
ISBN: 9780357022290
Author: Stewart
Publisher: Cengage Learning Acquisitions
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Chapter 12, Problem 11CC
To determine
To find: A
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Chapter 12 Solutions
Calculus: Early Transcendentals, Loose-leaf Version, 9th
Ch. 12.1 - Suppose you start at the origin, move along the...Ch. 12.1 - Sketch the points (1, 5, 3), (0, 2, 3), (3, 0, 2),...Ch. 12.1 - Which of the points A(4, 0, 1), B(3, 1, 5), and...Ch. 12.1 - Prob. 4ECh. 12.1 - What does the equation x = 4 represent in 2? What...Ch. 12.1 - What does the equation y = 3 represent in 3? What...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Find the distance between the given points. 9....Ch. 12.1 - Prob. 10E
Ch. 12.1 - Find the lengths of the sides of the triangle PQR....Ch. 12.1 - Find the lengths of the sides of the triangle PQR....Ch. 12.1 - Determine whether the points lie on a straight...Ch. 12.1 - Find the distance from (4, 2, 6) to each of the...Ch. 12.1 - Find an equation of the sphere with center (3, 2,...Ch. 12.1 - Find an equation of the sphere with center (2, 6,...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Midpoint Formula Prove that the midpoint of the...Ch. 12.1 - Prob. 24ECh. 12.1 - Which coordinate plane is closest to the point...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Write inequalities to describe the region. 39. The...Ch. 12.1 - Write inequalities to describe the region. 40. The...Ch. 12.1 - Write inequalities to describe the region. 41. The...Ch. 12.1 - Write inequalities to describe the region. 42. The...Ch. 12.1 - The figure shows a line L1 in space and a second...Ch. 12.1 - Consider the points P such that the distance from...Ch. 12.1 - Find an equation of the set of all points...Ch. 12.1 - Find the volume of the solid that lies inside both...Ch. 12.1 - Find the distance between the spheres x2 + y2 + z2...Ch. 12.1 - Describe and sketch a solid with the following...Ch. 12.2 - What is the relationship between the point (4, 7)...Ch. 12.2 - Name all the equal vectors in the parallelogram...Ch. 12.2 - Using the vectors shown in the figure, write each...Ch. 12.2 - Copy the vectors in the figure and use them to...Ch. 12.2 - In the figure, the tip of c and the tail of d are...Ch. 12.2 - If the vectors in the figure satisfy |u | = | v |...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Prob. 14ECh. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find a + b, 4a + 2b, | a |, and | a b | 19. a =...Ch. 12.2 - Find a + b, 4a + 2b, | a |, and | a b | 20. a =...Ch. 12.2 - Find a + b, 4a + 2b, | a |, and | a b | 21. a =...Ch. 12.2 - Find a + b, 4a + 2b, | a |, and | a b | 22. a =...Ch. 12.2 - Find a unit vector that has the same direction as...Ch. 12.2 - Prob. 24ECh. 12.2 - Find a unit vector that has the same direction as...Ch. 12.2 - Find the vector that has the same direction as 6,...Ch. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - The initial point of a vector v in V2 is the...Ch. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Find the magnitude of the resultant force and the...Ch. 12.2 - Find the magnitude of the resultant force and the...Ch. 12.2 - Prob. 34ECh. 12.2 - A block-and-tackle pulley hoist is suspended in a...Ch. 12.2 - The tension vector at each end of a chain has...Ch. 12.2 - Three forces act on an object. Two of the forces...Ch. 12.2 - Prob. 38ECh. 12.2 - A ship is sailing west at a speed of 32km/h and a...Ch. 12.2 - Find the unit vectors that are parallel to the...Ch. 12.2 - Prob. 42ECh. 12.2 - If A, B, and C are the vertices of a triangle,...Ch. 12.2 - Let C be the point on the line segment AB that is...Ch. 12.2 - (a) Draw the vectors a = 3, 2, b = 2, 1, and c =...Ch. 12.2 - Suppose that a and b are nonzero vectors that are...Ch. 12.2 - If r = x, y, z and r0 = x0, y0, z0, describe the...Ch. 12.2 - If r = x, y, r1 = x1, y1, and r2 = x2, y2,...Ch. 12.2 - Figure 16 gives a geometric demonstration of...Ch. 12.2 - Prove Property 5 of vectors algebraically for the...Ch. 12.2 - Use vectors to prove that the line joining the...Ch. 12.3 - Which of the following expressions are meaningful?...Ch. 12.3 - Find a b. 2. a = 5, 2, b = 3, 4Ch. 12.3 - Find a b. 3. a = 1.5, 0.4, b = 4, 6Ch. 12.3 - Find a b. 4. a = 6, 2, 3, b = 2, 5, 1Ch. 12.3 - Find a b. 5. a = 4, 1, 14, b = 6, 3, 8Ch. 12.3 - Find a b. 6. a. = p, p, 2p, b = 2q, q, qCh. 12.3 - Find a b. 7. a = 2i + j, b = i j + kCh. 12.3 - Find a b. 8. a = 3i + 2j k, b = 4i + 5kCh. 12.3 - Find a b. 9. | a | = 7, | b | = 4, the angle...Ch. 12.3 - Find a b. 10. | a | = 80, | b | = 50, the angle...Ch. 12.3 - If u is a unit vector, find u v and u w.Ch. 12.3 - If u is a unit vector, find u v and u w.Ch. 12.3 - (a) Show that i j = j k = k i = 0. (b) Show...Ch. 12.3 - A street vendor sells a hamburgers, b hot dogs,...Ch. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Find the angle between the vectors. (First find an...Ch. 12.3 - Find the angle between the vectors. (First find an...Ch. 12.3 - Find, correct to the nearest degree, the three...Ch. 12.3 - Find, correct to the nearest degree, the three...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Use vectors to decide whether the triangle with...Ch. 12.3 - Find the values of x such that the angle between...Ch. 12.3 - Find a unit vector that is orthogonal to both i +...Ch. 12.3 - Find two unit vectors that make an angle of 60...Ch. 12.3 - Find the acute angle between the lines. Use...Ch. 12.3 - Find the acute angles between the curves at their...Ch. 12.3 - Find the acute angles between the curves at their...Ch. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Find the direction cosines and direction angles of...Ch. 12.3 - Prob. 38ECh. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Suppose that a and b are nonzero vectors. (a)...Ch. 12.3 - Prob. 49ECh. 12.3 - A tow truck drags a stalled car along a road. The...Ch. 12.3 - Prob. 51ECh. 12.3 - A boat sails south with the help of a wind blowing...Ch. 12.3 - Distance from a Point to a Line Use a scalar...Ch. 12.3 - If r = x, y, z a = a1, a2, a3, and b = b1, b2, b3,...Ch. 12.3 - Prob. 55ECh. 12.3 - Prob. 56ECh. 12.3 - Prob. 57ECh. 12.3 - If c = | a | b + | b | a, where a, b, and c are...Ch. 12.3 - Prove Properties 2.4, and 5 of the dot product...Ch. 12.3 - Suppose that all sides of a quadrilateral are...Ch. 12.3 - Cauchy-Schwartz Inequality Use Theorem 3 to prove...Ch. 12.3 - Triangle Inequality The Triangle Inequality for...Ch. 12.3 - Parallelogram Identity The Parallelogram Identity...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.4 - Find the cross product a b and verify that it is...Ch. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Find the cross product a b and verify that it is...Ch. 12.4 - Prob. 7ECh. 12.4 - If a = i 2k and b = j + k, find a b. Sketch a,...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - Find the vector, not with determinants, but by...Ch. 12.4 - State whether each expression is meaningful. If...Ch. 12.4 - Find uv and determine whether uv is directed into...Ch. 12.4 - Find uv and determine whether uv is directed into...Ch. 12.4 - Prob. 16ECh. 12.4 - If a = 2, 1, 3 and b = 4, 2, 1, find a b and b ...Ch. 12.4 - Prob. 18ECh. 12.4 - Find two unit vectors orthogonal to both 3, 2, 1...Ch. 12.4 - Find two unit vectors orthogonal to both j k and...Ch. 12.4 - Show that 0 a = 0 = a 0 for any vector a in V3.Ch. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - (a) Find a nonzero vector orthogonal to the plane...Ch. 12.4 - Find the volume of the parallelepiped determined...Ch. 12.4 - Find the volume of the parallelepiped determined...Ch. 12.4 - Find the volume of the parallelepiped with...Ch. 12.4 - Find the volume of the parallelepiped with...Ch. 12.4 - Use the scalar triple product to verify that the...Ch. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Let v = 5j and let u be a vector with length 3...Ch. 12.4 - If a b = 3 and a b = 1, 2, 2, find the angle...Ch. 12.4 - (a) Find all vectors v such that 1, 2, 1 x v = 3,...Ch. 12.4 - Show that | a b |2 = | a |2| b |2 (a b)2Ch. 12.4 - Prob. 48ECh. 12.4 - Prove that (a b) (a + b) = 2(a b).Ch. 12.4 - Prove Properly 6 of cross products, that is, a (b...Ch. 12.4 - Use Exercise 50 to prove that a (b c) + b (c ...Ch. 12.4 - Prove that (ab)(cd)=|acbcadbd|Ch. 12.4 - Suppose that a 0. (a) If a b = a c, does it...Ch. 12.4 - If v1, v2, and v3 are noncoplanar vectors, let...Ch. 12.4 - Prob. 1DPCh. 12.4 - Prob. 2DPCh. 12.4 - Prob. 3DPCh. 12.5 - Determine whether each statement is true or false...Ch. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Find a vector equation and parametric equations...Ch. 12.5 - Prob. 6ECh. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Prob. 9ECh. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Find parametric equations and symmetric equations...Ch. 12.5 - Is the line through (4, 6, 1) and (2, 0, 3)...Ch. 12.5 - Is the line through (2, 4, 0) and (1, 1, 1)...Ch. 12.5 - (a) Find symmetric equations for the line that...Ch. 12.5 - (a) Find parametric equations for the line through...Ch. 12.5 - Find a vector equation for the line segment from...Ch. 12.5 - Find parametric equations for the line segment...Ch. 12.5 - Determine whether the lines L1 and L2 are...Ch. 12.5 - Determine whether the lines L1 and L2 are...Ch. 12.5 - Determine whether the lines L1 and L2 are...Ch. 12.5 - Determine whether the lines L1 and L2 are...Ch. 12.5 - Find an equation of the plane. 23. The plane...Ch. 12.5 - Find an equation of the plane. 24. The plane...Ch. 12.5 - Prob. 25ECh. 12.5 - Find an equation of the plane. 26. The plane...Ch. 12.5 - Find an equation of the plane. 27. The plane...Ch. 12.5 - Find an equation of the plane. 28. The plane...Ch. 12.5 - Find an equation of the plane. 29. The plane...Ch. 12.5 - Find an equation of the plane. 30. The plane that...Ch. 12.5 - Find an equation of the plane. 31. The plane...Ch. 12.5 - Find an equation of the plane. 32. The plane...Ch. 12.5 - Find an equation of the plane. 33. The plane...Ch. 12.5 - Find an equation of the plane. 34. The plane...Ch. 12.5 - Find an equation of the plane. 35. The plane that...Ch. 12.5 - Find an equation of the plane. 36. The plane that...Ch. 12.5 - Find an equation of the plane. 37. The plane that...Ch. 12.5 - Find an equation of the plane. 38. The plane that...Ch. 12.5 - Find an equation of the plane. 39. The plane that...Ch. 12.5 - Find an equation of the plane. 40. The plane that...Ch. 12.5 - Use intercepts to help sketch the plane. 41. 2x +...Ch. 12.5 - Use intercepts to help sketch the plane. 42. 3x +...Ch. 12.5 - Use intercepts to help sketch the plane. 43. 6x ...Ch. 12.5 - Use intercepts to help sketch the plane. 44. 6x +...Ch. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Find the point at which the line intersects the...Ch. 12.5 - Where does the line through (3, 1, 0) and (1, 5,...Ch. 12.5 - Find direction numbers for the line of...Ch. 12.5 - Find the cosine of the angle between the planes x...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Determine whether the planes are parallel,...Ch. 12.5 - Find symmetric equations for the line of...Ch. 12.5 - Find symmetric equations for the line of...Ch. 12.5 - Find an equation for the plane consisting of all...Ch. 12.5 - Find an equation for the plane consisting of all...Ch. 12.5 - Find an equation of the plane with x-intercept a,...Ch. 12.5 - (a) Find the point at which the given lines...Ch. 12.5 - Find parametric equations for the line through the...Ch. 12.5 - Find parametric equations for the line through the...Ch. 12.5 - Which of the following four planes are parallel?...Ch. 12.5 - Which of the following four lines are parallel?...Ch. 12.5 - Use the formula in Exercise 12.4.45 to find the...Ch. 12.5 - Use the formula in Exercise 12.4.45 to find the...Ch. 12.5 - Find the distance from the point to the given...Ch. 12.5 - Find the distance from the point to the given...Ch. 12.5 - Find the distance between the given parallel...Ch. 12.5 - Find the distance between the given parallel...Ch. 12.5 - Prob. 75ECh. 12.5 - Find equations of the planes that are parallel to...Ch. 12.5 - Show that the lines with symmetric equations x = y...Ch. 12.5 - Find the distance between the skew lines with...Ch. 12.5 - Let L1 be the line through the origin and the...Ch. 12.5 - Let L1 be the line through the points (1, 2, 6)...Ch. 12.5 - Prob. 81ECh. 12.5 - Prob. 82ECh. 12.5 - If a, b, and c are not all 0, show that the...Ch. 12.6 - (a) What does the equation y = x2 represent as a...Ch. 12.6 - (a)Sketch the graph of y = ex as a curve in 2. (b)...Ch. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Describe and sketch the surface. xy = 1Ch. 12.6 - Describe and sketch the surface. z = sin yCh. 12.6 - Write an equation whose graph could be the surface...Ch. 12.6 - Write an equation whose graph could be the surface...Ch. 12.6 - (a) Find and identify the traces of the quadric...Ch. 12.6 - (a) Find and identify the traces of the quadric...Ch. 12.6 - Use traces to sketch and identify the surface. x =...Ch. 12.6 - Use traces to sketch and identify the surface. 4x2...Ch. 12.6 - Use traces to sketch and identify the surface. x2...Ch. 12.6 - Use traces to sketch and identify the surface. z2 ...Ch. 12.6 - Use traces to sketch and identify the surface. 9y2...Ch. 12.6 - Use traces to sketch and identify the surface. 3x2...Ch. 12.6 - Use traces to sketch and identify the surface....Ch. 12.6 - Use traces to sketch and identify the surface. 3x2...Ch. 12.6 - Use traces to sketch and identify the surface. y =...Ch. 12.6 - Use traces to sketch and identify the surface. x =...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Match the equation with its graph (labeled...Ch. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Reduce the equation to one of the standard forms,...Ch. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Sketch the region bounded by the surfaces z=x2+y2...Ch. 12.6 - Sketch the region bounded by the paraboloids z =...Ch. 12.6 - Find an equation for the surface obtained by...Ch. 12.6 - Find an equation for the surface obtained by...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Traditionally, the earths surface has been modeled...Ch. 12.6 - A cooling tower for a nuclear reactor is to be...Ch. 12.6 - Show that if the point (a, b, c) lies on the...Ch. 12.6 - Show that the curve of intersection of the...Ch. 12 - What is the difference between a vector and a...Ch. 12 - Prob. 2CCCh. 12 - Prob. 3CCCh. 12 - How do you find the vector from one point to...Ch. 12 - Prob. 5CCCh. 12 - Prob. 6CCCh. 12 - Prob. 7CCCh. 12 - Prob. 8CCCh. 12 - Prob. 9CCCh. 12 - (a) How do you find the area of the parallelogram...Ch. 12 - Prob. 11CCCh. 12 - Prob. 12CCCh. 12 - Prob. 13CCCh. 12 - Write a vector equation and a scalar equation for...Ch. 12 - Prob. 15CCCh. 12 - Prob. 16CCCh. 12 - Prob. 17CCCh. 12 - Prob. 18CCCh. 12 - Prob. 19CCCh. 12 - Determine whether the statement is true or false....Ch. 12 - Prob. 2TFQCh. 12 - Prob. 3TFQCh. 12 - Prob. 4TFQCh. 12 - Prob. 5TFQCh. 12 - Prob. 6TFQCh. 12 - Prob. 7TFQCh. 12 - Prob. 8TFQCh. 12 - Determine whether the statement is true or false....Ch. 12 - Prob. 10TFQCh. 12 - Prob. 11TFQCh. 12 - Prob. 12TFQCh. 12 - Prob. 13TFQCh. 12 - Prob. 14TFQCh. 12 - Prob. 15TFQCh. 12 - Prob. 16TFQCh. 12 - Prob. 17TFQCh. 12 - Prob. 18TFQCh. 12 - Prob. 19TFQCh. 12 - Prob. 20TFQCh. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - (a) Find an equation of the sphere that passes...Ch. 12 - Copy the vectors in the figure and use them to...Ch. 12 - Prob. 3ECh. 12 - Calculate the given quantity if a = i + j 2k b =...Ch. 12 - Prob. 5ECh. 12 - Find two unit vectors that are orthogonal to both...Ch. 12 - Suppose that u (v w) = 2. Find (a) (u v) w (b)...Ch. 12 - Prob. 8ECh. 12 - Find the acute angle between two diagonals of a...Ch. 12 - Given the points A( 1, 0, 1), B(2, 3, 0), C(l,...Ch. 12 - (a) Find a vector perpendicular to the plane...Ch. 12 - Prob. 12ECh. 12 - Prob. 13ECh. 12 - Prob. 14ECh. 12 - Find parametric equations for the line. 15. The...Ch. 12 - Find parametric equations for the line. 16. The...Ch. 12 - Find parametric equations for the line. 17. The...Ch. 12 - Find an equation of the plane. 18. The plane...Ch. 12 - Find an equation of the plane. 19. The plane...Ch. 12 - Find an equation of the plane. 20. The plane...Ch. 12 - Find the point in which the line with parametric...Ch. 12 - Find the distance from the origin to the line x =...Ch. 12 - Determine whether the lines given by the symmetric...Ch. 12 - (a) Show that the planes x + y z = 1 and 2x 3y +...Ch. 12 - Find an equation of the plane through the line of...Ch. 12 - (a) Find an equation of the plane that passes...Ch. 12 - Find the distance between the planes 3x + y 4z =...Ch. 12 - Identify and sketch the graph of each surface. 28....Ch. 12 - Identify and sketch the graph of each surface. 29....Ch. 12 - Identify and sketch the graph of each surface. 30....Ch. 12 - Identify and sketch the graph of each surface. 31....Ch. 12 - Identify and sketch the graph of each surface. 32....Ch. 12 - Identify and sketch the graph of each surface. 33....Ch. 12 - Identify and sketch the graph of each surface. 34....Ch. 12 - Identify and sketch the graph of each surface. 35....Ch. 12 - Prob. 36ECh. 12 - An ellipsoid is created by rotating the ellipse...Ch. 12 - Prob. 38ECh. 12 - Prob. 1PPCh. 12 - Let B be a solid box with length L. width W, and...Ch. 12 - Prob. 3PPCh. 12 - Suppose v1 and v2 are vectors with |v1| = 2, |v2 |...Ch. 12 - Prob. 6PP
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- Determine Whether series converge or diverge if it converge what is the limit. $\{ \frac {(-1)^{n-2}n^{2}}{4+n^{3}}\} _{n=0}^{\infty }$arrow_forwardLet y(t) represent your retirement account balance, in dollars, after t years. Each year the account earns 7% interest, and you deposit 8% of your annual income. Your current annual income is $34000, but it is growing at a continuous rate of 2% per year. Write the differential equation modeling this situation. dy dtarrow_forward8:37 ▬▬▬▬▬▬▬▬▬ Ο Graph of f The figure shows the graph of a periodic function f in the xy-plane. What is the frequency of f? 0.5 B 2 C 3 D 8 3 of 6 ^ Oli Back Next apclassroom.collegeboard.orgarrow_forward
- 2. The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given by f(t)=5000.1 Under certain storage conditions, where t is time in days after packing of the product and the value of f(t) is in millions. The solution to word problems should always be given in a complete sentence, with appropriate units, in the context of the problem. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take? (b) If t=0 corresponds to January 1, what date should be placed on the product?arrow_forward2.6 Applications: Growth and Decay; Mathematics of Finances 1. A couple wants to have $50,000 in 5 years for a down payment on a new house. (a) How much should they deposit today, at 6.2% compounded quarterly, to have the required amount in 5 years? (b) How much interest will be earned? (c) If they can deposit only $30,000 now, how much more will they need to complete the $50,000 after 5 years? Note, this is not 50,000-P3.arrow_forwardThe graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1. Select all that apply: ☐ f(x) is not continuous at x = 1 because it is not defined at x = 1. ☐ f(x) is not continuous at x = 1 because lim f(x) does not exist. x+1 ☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1). x+→1 ☐ f(x) is continuous at x = 1.arrow_forward
- a is done please show barrow_forwardA homeware company has been approached to manufacture a cake tin in the shape of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the games launch. The base of the cake tin has a characteristic dimension / and is illustrated in Figure 1 below, you should assume the top and bottom of the shape can be represented by semi-circles. The vertical sides of the cake tin have a height of h. As the company's resident mathematician, you need to find the values of r and h that minimise the internal surface area of the cake tin given that the volume of the tin is Vfixed- 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and his 2(+1)²h V = 2arrow_forward15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.arrow_forward
- Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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