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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
Find an equation of the plane.The plane passes through the points (4, 2, 1) and (-3, 5, 7) and is parallel to the z-axis.
Repeat Exercise 51 after increasing prices by 4%. Identify the vector operation used to increase prices by 4%.Data from in Exercise 51The vector u = (3240, 1450, 2235) gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week.
The vector v and its initial point are given. Find the terminal point. v = (3, -5, 6) : Initial point: (0, 6, 2)
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.All traces of a hyperboloid of one sheet are hyperboloids.
Find the distance between the point (3, -2, 4) and the plane 2x - 5y + z = 10.
Prove the property of the cross product.c(u x v) = (cu) × v = u × (cv)
Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ||u|| = 1, 0 = 0° ||v|| = 3, 0, 45° = =
Find an equation in rectangular coordinates for the equation given in spherical coordinates, and sketch its graph.ρ = 4 cos Ø
Find an equation of the plane that contains all the points that are equidistant from the given points.(2, 2, 0), (0, 2, 2)
Determine whether u and v are orthogonal, parallel, or neither. u = j + 6k V v=i - 2j - k
Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u = j v=j+ k
Find the angle θ between the vectors (a) In radians (b) In degrees u = 5[cos(3/4)i v = 2[cos(27/3)i + sin(3/4)j] + sin(27/3)j]
Determine whether u and v are orthogonal, parallel, or neither. u = −2i + 3j - k v = 2i + j - k
Find the angle θ between the vectors (a) In radians (b) In degrees u = 6i + 2j - 3k, v=-i + 5j
Find the coordinates of a point P on the line and a vector v parallel to the line. x = 3-1, y = -1 + 2t, z = -2
Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u=i+j+ k v=j+ k
Classify and sketch the quadric surface. Use a computer algebra system or a graphing utility to confirm your sketch.x² - y² + z = 0
Determine whether u and v are orthogonal, parallel, or neither. u = (2, -3, 1) v = (-1,-1,-1)
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph.r = 3
Classify and sketch the quadric surface. Use a computer algebra system or a graphing utility to confirm your sketch. z2 = x2 + Y 9
Find the coordinates of a point P on the line and a vector v parallel to the line. x = 4t, y = 5-t, z = 4 + 3t
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph. Ө || =
Classify and sketch the quadric surface. Use a computer algebra system or a graphing utility to confirm your sketch.3z = -y² + x²
Find the coordinates of a point P on the line and a vector v parallel to the line. x - 7 4 y +6 2 =2+2
Find the angle θ between the vectors (a) In radians (b) In degrees u = (10, 5, 15), v = (-2, 1, -3)
Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u = (3, 2, -1) v = (1, 2, 3)
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph.z = 2
Determine whether u and v are orthogonal, parallel, or neither. u= (cos 0, sin 0, -1) v = (sin 0, -cos 0, 0)
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph. 1 2
Find the coordinates of a point P on the line and a vector v parallel to the line. x + 3 5 Y_Z-3 6 y 8
Find the angle θ between the vectors (a) In radians (b) In degrees u = (1, 0, -3), v = (2, -2, 1)
Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u = (2, -1,0) v = (-1, 2, 0)
Determine whether and are orthogonal, parallel, or neither. u (7, -2, 3) = v = (-1,4,5)
The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. Explain your reasoning. (1, 2, 0), (0, 0, 0), (-2, 1, 0)
Classify and sketch the quadric surface. Use a computer algebra system or a graphing utility to confirm your sketch.x² = 2y² + 2z²
Verify that the points are the vertices of a parallelogram, and find its area. A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2)
Determine whether and are orthogonal, parallel, or neither. u= (-4, 3, 6) v = (16, 12, 24)
Determine whether any of the lines are parallel or identical. L₁: x = 6 - 3t₂ y = −2+2t, z = 5 + 4t L₂: x= 6t, y = 24t, z = 13- 8t L3: x= 1061, y = 3 + 4t, z = 7 + 8t L4: x = −4+ 6t, y = 3 + 4t, z = 5 - 6t
The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. Explain your reasoning. (-3, 0, 0), (0, 0, 0), (1, 2, 3)
State the definition of a cylinder.
Verify that the points are the vertices of a parallelogram, and find its area. A(2, -3, 1), B(6, 5, -1), C(7, 2, 2), D(3, -6, 4)
Find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph.r² + z² = 5
What is meant by the trace of a surface? How do you find a trace?
Let u = PQ̅ and v = PR̅(a) Write u and v in component form (b) Write u and v as the linear combination of the standard unit vectors i and j(c) Find the magnitudes of u and v(d) Find 2u + v P = (1, 2), Q = (4,1), R = (5, 4)
Let u = PQ̅ and v = PR̅(a) Write u and v in component form (b) Write u and v as the linear combination of the standard unit vectors i and j(c) Find the magnitudes of u and v(d) Find 2u + v P = (-2,-1), Q = (5, -1), R = (2, 4)
Find the component form of given its magnitude and the angle it makes with the positive x-axis. ||v|| = 8,0 = 60°
Using vectors, prove the Law of Sines: If a, b and c are the three sides of the triangle shown in the figure, then sin A ||al| sin B ||b|| sin C ||c|| A B b a C
Find(a) u · v(b) u · u(c) (d) (u · v) v(e) u · (2v) || u ²,
Using vectors, prove that the line segments joining the midpoints of the sides of a parallelogram form a parallelogram (see figure). D
Classify the conics by their eccentricities.
Match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 3 6 4 Z 56 У
Using vectors, prove that the diagonals of a rhombus are perpendicular (see figure). + +
Convert the point from cylindrical coordinates to rectangular coordinates.(2, -π, -4)
Find the component form of given its magnitude and the angle it makes with the positive x-axis. ||v|| = 1, 0 = 225°
Convert the point from cylindrical coordinates to rectangular coordinates. 6,
Match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 3 6 4 Z 56 У
Find(a) u · v(b) u · u(c) (d) (u · v) v(e) u · (2v) || u ²,
Match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 3 6 4 Z 56 У
Orthogonal Vectors Let Po be a point in the plane with normal vector n. Describe the set of points P in the plane for which is orthogonal to (n + PP)
Find the cross product of the unit vectors and sketch your result.k × j
Convert the point from cylindrical coordinates to rectangular coordinates. 77 4, 3 6
Find the coordinates of the point located in the xy-plane, four units to the right of the xz-plane, and five units behind the yz-plane.
(a) Find the volume of the solid bounded below by the paraboloid z = x² + y² and above by the plane z = 1.(b) Find the volume of the solid bounded below by theelliptic paraboloidand above by the plane z = k, where k > 0.(c) Show that the volume of the solid in part (b) is equal to one-half the
Find(a) u · v(b) u · u(c) (d) (u · v) v(e) u · (2v) || u ²,
Find(a) u × v(b) v x u (c) v x v u = -2i+ 4j v = 3i+2j + 5k
(a) Find the shortest distance between the point Q(2, 0, 0) and the line determined by the points P₁(0, 0, 1) and P₂(0, 1, 2).(b) Find the shortest distance between the point Q(2, 0, 0) andthe line segment joining the points P₁(0, 0, 1) andP₂(0, 1, 2).
Find the distance between the points. (1, 6, 3), (-2, 3, 5)
Find the cross product of the unit vectors and sketch your result.i × k
Find(a) u · v(b) u · u(c) (d) (u · v) v(e) u · (2v) || u ²,
Find the coordinates of the point located on the y-axis and seven units to the left of the xz-plane.
Describe and sketch the surface.y = 5
Find the distance between the points. (-2, 1, 5), (4,-1,-1)
Convert the point from rectangular coordinates to cylindrical coordinates.(0, 5, 1)
(a) Use the disk method to find the volume of the sphere(b) Find the volume of the ellipsoid 2 x² + y² + z² = p².
Find(a) u × v(b) v x u (c) v x v u = 3i+5k v = 21 +3j - 2k 2i
Find(a) u · v(b) u · u(c) (d) (u · v) v(e) u · (2v) || u ²,
Find the angle θ between the vectors (a) In radians (b) In degrees u = (1, 1), v = (2,-2)
Find(a) u × v(b) v x u (c) v x v u = (7, 3, 2) V v = (1, -1,5)
Describe and sketch the surface.z = 2
Find sets of (a) Parametric equations(b) Symmetric equations of the line through the two points (if possible). (For each line, write the direction numbers as integers.) (0, 4, 3), (1, 2, 5)
Prove the following property of the cross product. (u x v) x (w x z) = (u × v z)w (ux vw)z -
Convert the point from rectangular coordinates to cylindrical coordinates.(2√2, -2√2, 4)
Find (a) u × v(b) v x u (c) v x v u =(3, -2,-2) v = (1, 5, 1)
Find the standard equation of the sphere.Center: (3, -2, 6); Diameter: 15
Find the angle θ between the vectors (a) In radians (b) In degrees u =(3, 1), v = (2, -1)
Find sets of (a) Parametric equations(b) Symmetric equations of the line through the two points (if possible). (For each line, write the direction numbers as integers.) (7, -2, 6), (-3, 0, 6)
Find the angle θ between the vectors (a) In radians (b) In degrees u = 3i + j, v = −2i + 4j
Convert the point from rectangular coordinates to cylindrical coordinates.(2, -2, -4)
Find u × v and show that it is orthogonal to both u and v. u = (12, -3,0) V v = (-2, 5, 0)
Find the standard equation of the sphere.Endpoints of a diameter: (0, 0, 4), (4, 6, 0)
Complete the square to write the equation of the sphere in standard form. Find the center and radius. x² + y² + z²4x6y + 4 = 0 y2
Describe and sketch the surface.y² + z = 6
Find sets of (a) Parametric equations(b) Symmetric equations of the line through the two points (if possible). (For each line, write the direction numbers as integers.) (0, 0, 25), (10, 10, 0)
Convert the point from rectangular coordinates to cylindrical coordinates.(3, -3, 7)
Find u × v and show that it is orthogonal to both u and v. u = (-1, 1, 2) v = (0, 1, 0)
Find the angle θ between the vectors (a) In radians (b) In degrees u Cos TT 6 i + sin 6 j, v = cos 3 TT 4 3 T i + sin j 4
Describe and sketch the surface.4x² + y² = 4
Complete the square to write the equation of the sphere in standard form. Find the center and radius. x² + y² + z² - 10x + 6y - 4z + 34 = 0
Sketch the graph of each equation given in spherical coordinates.(a) p = 2 sin Ø (b) p = 2 cos Ø
Convert the point from rectangular coordinates to cylindrical coordinates.(1,√3, 4)
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