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mathematics
calculus early transcendentals

Questions and Answers of Calculus Early Transcendentals

Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = x2 and y = 0. Sketch a figure of this set of points.
Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0 and x2 + y2 = 1. Sketch a figure of this set of points.
Describe with a sketch the sets of points (x, y, z) satisfying the following equations.y - z = 0
Describe with a sketch the sets of points (x, y, z) satisfying the following equations.x2y2z2 > 0
Describe with a sketch the sets of points (x, y, z) satisfying the following equations.(x + 1)(y - 3) = 0
Determine whether the following statements are true and give an explanation or counterexample. a. Suppose u and v both make a 45° angle with w in R3. Then u + v makes a 45° angle with w.b.
An object is acted upon by the forces F1 = (10, 6, 3) and F2 = (0, 4, 9). Find the force F3 that must act on the object so that the sum of the forces is zero.
A submarine climbs at an angle of 30° above the horizontal with a heading to the northeast. If its speed is 20 knots, find the components of the velocity in the east, north, and vertical directions.
An object at the origin is acted on by the forces F1 = 20i - 10j, F2 = 30j + 10k, and F3 = 40i + 20k. Find the magnitude of the combined force and describe the approximate direction of the force.
A small plane is flying horizontally due east in calm air at 250 mi/hr when it is hit by a horizontal crosswind blowing southwest at 50 mi/hr and a 30-mi/hr updraft. Find the resulting speed of the
A model airplane is flying horizontally due east at 10 mi/hr when it encounters a horizontal crosswind blowing south at 5 mi/hr and an updraft blowing vertically upward at 5 mi/hr.a. Find the
A model airplane is flying horizontally due north at 20 mi/hr when it encounters a horizontal crosswind blowing east at 20 mi/hr and a downdraft blowing vertically downward at 10 mi/hr.a. Find the
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(a, b, c), Q(1, 1, -1) (a, b,
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(0, 0, 2), Q(-2, 4, 0) PO PQ.
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(3, 8, 12), Q(3, 9, 11) PO
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(-3, 1, 0), Q(-3, -4, 1) PO
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(5, 11, 12), Q(1, 14, 13) PO
Consider the following points P and Q.a. Find and state your answer in two forms: (a, b, c) and ai + bj + ck.b. Find the magnitude ofc. Find two unit vectors parallel toP(1, 5, 0), Q(3, 11, 2) PO PQ.
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (-4, -8√3, 2√2), v = (2, 3√3, -√2)
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (-7, 11, 8) v = (3, -5, -1)
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (-5, 0, 2), v = (3, 1, 1)
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (-2, 1, -2), v = (1, 1, 1)
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (-2, -3, 0), v = (1, 2, 1)
For the given vectors u and v, evaluate the following expressions.a. 3u + 2v b. 4u - v c. |u + 3v|u = (4, -3, 0), v = (0, 1, 1)
Give a geometric description of the following sets of points.x2 - 4x + y2 + 6y + z2 + 14 = 0
Give a geometric description of the following sets of points.x2 - 2x + y2 + 6y + z2 + 10 = 0
Give a geometric description of the following sets of points.x2 + y2 + z2 - 8x + 14y - 18z ≥ 65
Give a geometric description of the following sets of points.x2 + y2 + z2 - 8x - 14y - 18z ≤ 79
Give a geometric description of the following sets of points.x2 + y2 - 14y + z2 ≤ -13
Give a geometric description of the following sets of points.x2 + y2 - 14y + z2 ≥ -13
Give a geometric description of the following sets of points.x2 + y2 + z2 - 6x + 6y - 8z - 2 = 0
Give a geometric description of the following sets of points.x2 + y2 + z2 - 2y - 4z - 4 = 0
Give a geometric description of the following sets of points.(x + 1)2 + y2 + z2 - 2y - 24 = 0
Give a geometric description of the following sets of points.(x - 1)2 + y2 + z2 - 9 = 0
Find an equation of the sphere passing through P(-4, 2, 3) and Q(0, 2, 7) with its center at the midpoint of PQ.
Find an equation of the sphere passing through P(1, 0, 5) and Q(2, 3, 9) with its center at the midpoint of PQ.
Find an equation or inequality that describes the following objects.A ball with center (0, -2, 6) with the point (1, 4, 8) on its boundary
Find an equation or inequality that describes the following objects.A ball with center (-2, 0, 4) and radius 1
Find an equation or inequality that describes the following objects.A sphere with center (1, 2, 0) passing through the point (3, 4, 5)
Find an equation or inequality that describes the following objects.A sphere with center (1, 2, 3) and radius 4
Sketch the plane parallel to the yz-plane through (2, 4, 2) and find its equation.
Sketch the plane parallel to the xy-plane through (2, 4, 2) and find its equation.
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].The plane parallel to the xz-plane containing the point (1, 2, 3)
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].The plane that passes through (2, 0, 0), (0, 3, 0), and (0, 0, 4)
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].z = y
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].y = 2
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].z = 3
Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5].x = 2
For each point P(x, y, z) given below, let A(x, y, 0), B(x, 0, z), and C(0, y, z) be points in the xy-, xz-, and yz-planes, respectively. Plot and label the points A, B, C, and P in R3.a. P(-3, 2,
For each point P(x, y, z) given below, let A(x, y, 0), B(x, 0, z), and C(0, y, z) be points in the xy-, xz-, and yz-planes, respectively. Plot and label the points A, B, C, and P in R3.a. P(2, 2,
Find the coordinates of the vertices A, B, and C of the following rectangular boxes.Assume all the edges have the same length. ZA (0, –3, 0) х
Find the coordinates of the vertices A, B, and C of the following rectangular boxes. ZA (0, 0, 5) B y (3, -4, 0) х
Find the coordinates of the vertices A, B, and C of the following rectangular boxes. (0, 0, 10) B (5, 8, 0)
Find the coordinates of the vertices A, B, and C of the following rectangular boxes. (3, 4, 5) х
Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.
Which point is farther from the origin, (3, -1, 2) or (0, 0, -4)?
What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?
Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.
What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?
Describe the plane x = 4.
What is the y-coordinate of all points in the xz-plane?
Explain how to plot the point (3, -2, 1) in R3.
Suppose u and v are vectors in the plane.a. Use the Triangle Rule for adding vectors to explain why |u + v| ≤ |u| + |v|. This result is known as the Triangle Inequality.b. Under what conditions is
Let u = (a, 5) and v = (2, 6).a. Find the value of a such that u is parallel to v.b. Find the value of a such that u is perpendicular to v.
Show that two nonzero vectors u = (u1, u2) and v = (v1, v2) are perpendicular to each other if u1v1 + u2v2 = 0.
A pair of nonzero vectors in the plane is linearly dependent if one vector is a scalar multiple of the other. Otherwise, the pair is linearly independent. a. Which pairs of the following vectors
AssumeequalsDoes it follow thatis equal toExplain your answer. PO RŠ.
Prove that |cv| = |c||v|, where c is a scalar and v is a vector.
Use vectors to show that the midpoint of the line segment joining P(x1, y1) and Q(x2, y2) is the point Let O be the origin and let M be the midpoint of PQ. Draw a picture and show that Х1 + X2 У1
Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose u, v, and w are vectors in the xy-plane and a and c are scalars.(a + c)v =
Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose u, v, and w are vectors in the xy-plane and a and c are scalars.a(u + v) =
Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose u, v, and w are vectors in the xy-plane and a and c are scalars.a(cv) =
Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose u, v, and w are vectors in the xy-plane and a and c are scalars.(u + v) +
Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose u, v, and w are vectors in the xy-plane and a and c are scalars.u + v = v
A 100-kg object rests on an inclined plane at an angle of 30° to the floor. Find the components of the force perpendicular to and parallel to the plane. (The vertical component of the force exerted
Jack pulls east on a rope attached to a camel with a force of 40 lb. Jill pulls north on a rope attached to the same camel with a force of 30 lb. What is the magnitude and direction of the force on
Three people located at A, B, and C pull on ropes tied to a ring. Find the magnitude and direction of the force with which the person at C must pull so that no one moves (the system is in
Consider the 12 vectors that have their tails at the center of a (circular) clock and their heads at the numbers on the edge of the clock.a. What is the sum of these 12 vectors?b. If the 12:00 vector
An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly, the sheet of paper starts moving southeast at √2 mi/hr. Describe the motion of the ant
Find the following vectors.The position vector for your final location if you start at the origin and walk along (4, -6) followed by (5, 9)
Find the following vectors.The vector in the direction opposite that of (6, -8) with length 10
Find the following vectors.The vector in the direction of (5, -12) with length 3
Find the following vectors.The vector that is 3 times (3, -5) plus -9 times (6, 0)
Solve the following pairs of equations for the vectors u and v. Assume i = (1, 0) and j = (0, 1).2u + 3v = i, u - v = j
Solve the following pairs of equations for the vectors u and v. Assume i = (1, 0) and j = (0, 1).2u = i, u - 4v = j
A sum of scalar multiples of two or more vectors (such as c1u + c2v + c3w, where ci are scalars) is called a linear combination of the vectors. Let i = (1, 0), j = (0, 1), u = (1, 1), and v = (-1,
A sum of scalar multiples of two or more vectors (such as c1u + c2v + c3w, where ci are scalars) is called a linear combination of the vectors. Let i = (1, 0), j = (0, 1), u = (1, 1), and v = (-1,
A sum of scalar multiples of two or more vectors (such as c1u + c2v + c3w, where ci are scalars) is called a linear combination of the vectors. Let i = (1, 0), j = (0, 1), u = (1, 1), and v = (-1,
Use the properties of vectors to solve the following equations for the unknown vector x = (a, b). Let u = (2, -3) and v = (-4, 1).-4x = u - 8v
Use the properties of vectors to solve the following equations for the unknown vector x = (a, b). Let u = (2, -3) and v = (-4, 1).3x - 4u = v
Use the properties of vectors to solve the following equations for the unknown vector x = (a, b). Let u = (2, -3) and v = (-4, 1).2x + u = v
Use the properties of vectors to solve the following equations for the unknown vector x = (a, b). Let u = (2, -3) and v = (-4, 1).10x = u
For the points A(3, 4), B(6, 10), C(a + 2, b + 5), and D(b + 4, a - 2), find the values of a and b such that AB = CD.
a. Find two unit vectors parallel to v = 6i - 8j.b. Find b if v = (1/3, b) is a unit vector. c. Find all values of a such that w = ai - a/3j is a unit vector.
Given the points A(-2, 0), B(6, 16), C(1, 4), D(5, 4), E(√2, √2), and F (3√2, -4√2), find the position vector equal to the following vectors.a.b.c.d. AB AC
Determine whether the following statements are true and give an explanation or counterexample. a. José travels from point A to point B in the plane by following vector u, then vector v, and
Three forces are applied to an object, as shown in the figure. Find the magnitude and direction of the sum of the forces. |F,| = 100 lb F = 60 lb 45° 30° 60° F = 150 lb
If a 500-lb load is suspended by two chains (see figure), what is the magnitude of the force each chain must be able to support? 45° 45° 500 lb
Which has a greater horizontal component, a 100-N force directed at an angle of 60° above the horizontal or a 60-N force directed at an angle of 30° above the horizontal?
Suppose you pull a suitcase with a strap that makes a 60° angle with the horizontal. The magnitude of the force you exert on the suitcase is 40 lb. a. Find the horizontal and vertical

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