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mathematics
precalculus
Calculus Early Transcendentals 8th edition James Stewart - Solutions
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 3i + 4j, w = -6i - 8j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i + √3j, w = i - j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = √3i - j, w = i + j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 2i + 2j, w = i + 2j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 2i + j, w = i - 2j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i + j, w = -i + j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i - j, w = i + j
True or False. Work is a physical example of a vector.
True or False.Given two nonzero vectors v and w, it is always possible to decompose v into two vectors, one parallel to w and the other perpendicular to w.
If v = 3w, then the two vectors v and w are ________.
If v.w = 0 then the two vectors v and w are ________.
If v = a1i + b1j and w = a2i + b2j are two vectors, the _____ is defined as v.w = a1a2 + b1b2.
In a triangle with sides a, b, c and angles A,B,C the Law of Cosines states that _______.
Show on the following graph the force needed for the object at P to be in static equilibrium. (a) Draw v and then use the red vector to show 3v.(b) Use the red vector to show -v.(c) Draw v and w. Then use the red vector to show v + w(d) Use the red vector to show v - w(e) Use the red
A farmer wishes to remove a stump from a field by pulling it out with his tractor. Having removed many stumps before, he estimates that he will need 6 tons (12,000 pounds) of force to remove the stump. However, his tractor is only capable of pulling with a force of 7000 pounds, so he asks his
At a county fair truck pull, two pickup trucks are attached to the back end of a monster truck as illustrated in the figure. One of the pickups pulls with a force of 2000 pounds and the other pulls with a force of 3000 pounds with an angle of between them. With how much force must the monster truck
Repeat Problem 87 if the angle on the left is 3.8° the angle on the right is 2.6°and the weight of the tightrope walker is 135 pounds.
A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 150 pounds, how much tension is in each part of the rope? 4.2° 3.7° 150 pounds
A weight of 800 pounds is suspended from two cables, as shown in the figure. What are the tensions in the two cables? 50° 35° 800 pounds
A weight of 1000 pounds is suspended from two cables as shown in the figure. What are the tensions in the two cables? 25° 40° 1000 pounds
The pilot of an aircraft wishes to head directly east, but is faced with a wind speed of 40 mi/hr from the northwest. If the pilot maintains an airspeed of 250 mi/hr, what compass heading should be maintained to head directly east? What is the actual speed of the aircraft?
A river has a constant current of 3 km/hr. At what angle to a boat dock should a motorboat capable of maintaining a constant speed of 20 km/hr be headed in order to reach a point directly opposite the dock? If the river is 1/2kilometer wide, how long will it take to cross? Current - Boat
A magnitude of 1200 pounds of force is required to prevent a car from rolling down a hill whose incline is 15° to the horizontal.What is the weight of the car?
A magnitude of 700 pounds of force is required to hold a boat and its trailer in place on a ramp whose incline is 10° to the horizontal. What is the combined weight of the boat and its trailer?
An airplane has an airspeed of 600 km/hr bearing S30°E. The wind velocity is 40 km/hr in the direction S45°E. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?
An airplane has an airspeed of 500 kilometers per hour (km/hr) bearing N45°E. The wind velocity is 60 km/hr in the direction N30°W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?
Airbus A320 jet maintains a constant airspeed of 500 mi/hr headed due west. The jet stream is 100 mi/hr in the southeasterly direction. (a) Express the velocity va of the A320 relative to the air and the velocity vw of the jet stream in terms of i and j.(b) Find the velocity of the A320
A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north.The jet stream is 100 mi/hr in the northeasterly direction. (a) Express the velocity va of the 747 relative to the air and the velocity vw of the jet stream in terms of i and j. (b) Find
Two forces of magnitude 30 newtons (N) and 70 N act on an object at angles of 45° and 120° with the positive x-axis, as shown in the figure. Find the direction and magnitude of the resultant force; that is, find F1 + F2. F,| = 70 N УА %3D |F,|| = 30 N 120° 45° х
Two forces of magnitude 40 newtons (N) and 60 N act on an object at angles of 30° and -45° with the positive x-axis, as shown in the figure. Find the direction and magnitude of the resultant force; that is, find F1 + F2. У ||F,|| = 40 N 30° -45° ||F| = 60 N
A man pushes a wheelbarrow up an incline of 20° with a force of 100 pounds. Express the force vector F in terms of i and j.
A child pulls a wagon with a force of 40 pounds. The handle of the wagon makes an angle of 30° with the ground. Express the force vector F in terms of i and j.
Refer to problem 71. The points (-3,0, (-1,-2), (3,1) and (1,3) are the vertices of a parallelogram ABCD.(a) Find the new vertices of a parallelogram A'B'C'D' if it is translated by v = (3, -2).(b) Find the new vertices of a parallelogram A'B'C'D' if it is translated by -1/2v.Refer to problem 71The
The field of computer graphics utilizes vectors to compute translations of points. For example, if the point (-3,2) is to be translated by v = (5,2), then the new location will be u' = u + v = (-3,2) + (5,2) = (2,4) As illustrated in the figure, the point (-3,2) is translated to (2,4) by v.(a)
Find the direction angle of v for a given vector.v = -i + 3j
Find the direction angle of v for a given vector.v = -i - 5j
Find the direction angle of v for a given vector.v = 6i - 4j
Find the direction angle of v for a given vector.v = 4i - 2j
Find the direction angle of v for a given vector.v = -5i - 5j
Find the direction angle of v for a given vector.v = -3√3i + 3j
Find the direction angle of v for a given vector.v = i + √3j
Find the direction angle of v for a given vector.v = 3i + 3j
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 15, α = 315°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 25, α = 330°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 3, α = 240°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 14, α = 120°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 8, α = 45°
Write the vector v in the form ai + bj given its magnitude |v| and the angle it makes with the positive x-axis. |v| = 5, α = 60°
If P = (-3, 1) and Q = (x,4), find all numbers x such that the vector represented by PQ(vector) has length 5.
If v = 2i - j and w = xi + 3j find all numbers x for which |v + w| = 5.
Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction
Find a vector v whose magnitude is 4 and whose component in the i direction is twice the component in the j direction.
Find the unit vector in the same direction as v. v = 2i - j
Find the unit vector in the same direction as v. v = i - j
Find the unit vector in the same direction as v. v = -5i + 12j
Find the unit vector in the same direction as v.v = 3i - 4j
Find the unit vector in the same direction as v. v = -3j
Find the unit vector in the same direction as v. v = 5i
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v | + |w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v | - |w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v + w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.|v - w|
Find the quantity if v = 3i - 5j and w = -2i + 3j.3v - 2w
Find the quantity if v = 3i - 5j and w = -2i + 3j.2v + 3w
Find |v|. v = 6i + 2j
Find |v|. v = -2i + 3j
Find |v|. v = -i - j
Find |v|. v = i - j
Find |v|. v = -5i + 12j
Find |v|. v = 3i - 4j
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (1, 1); Q = (2, 2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (1, 0); Q = (0, 1)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-1, 4); Q = (6, 2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-2, -1); Q = (6, -2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (-3, 2); Q = (6, 5)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (3, 2); Q = (5, 6)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (0, 0); Q = (-3, -5)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj that is, find its position vector. P = (0, 0); Q = (3, 4)
Use the figure below. Determine whether the given statement is true or false. If |v| = 2, what is |-4v|? B C A K G H D
Use the figure below. Determine whether the given statement is true or false. If |v| = 4, what is |3v|? A ш
Use the figure at the right. Determine whether the given statement is true or false. A + B + C + H + G = 0
Use the figure at the right. Determine whether the given statement is true or false. A + B + K + G = 0
Evaluate the integral. (In x)²dx
Evaluate the integral. х сosh ax dx
Evaluate the integral. |t csc? t dt
Evaluate the integral. tan 2y dy -1
Evaluate the integral. tª In t dt
Evaluate the integral. S In Vr. (x dx
Evaluate the integral. cos x dx
Evaluate the integral. t2 sin ßt dt
Evaluate the integral. | (x2 + 2x) cos x dx
Evaluate the integral. | (х — 1) sin mxх dx
Evaluate the integral. -3t te dt
Evaluate the integral. Гуечз dy ,0.2y
Evaluate the integral. x cos 5x dx
Evaluate the integral using integration by parts with the indicated choices of u and dv. Vx dx || Vx In x dx; u = In x, dv
Evaluate the integral using integration by parts with the indicated choices of u and dv. хе * dx; и %3 х, dv — e2* dx
(a) Find the average value of the function f (x) = 1/√x on the interval [1, 4].(b) Find the value c guaranteed by the Mean Value Theorem for Integrals such that fave = f (c).(c) Sketch the graph of f on [1, 4] and a rectangle whose area is the same as the area under the graph of f.
A steel tank has the shape of a circular cylinder oriented vertically with diameter 4 m and height 5 m. The tank is currently filled to a level of 3 m with cooking oil that has a density of 920 kg/m3. Compute the work required to pump the oil out through a 1-m spout at the top of the tank.
Each integral represents the volume of a solid.Describe the solid. 2т (6 — у)(4у - у?) dy
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