Write the vector v in terms of i and j whose magnitude and direction angle θ are given.
= 8, θ = 30°
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Select the representation that does not change the location of the given point. (4, 110°)
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Find the quotient of the complex numbers. Leave answer in polar form.
z1 = z2 =
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Find the unit vector that has the same direction as the vector v. v = 3i + j
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Polar coordinates of a point are given. Find the rectangular coordinates of the point.
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Find the work done by a force of 4 pounds acting in the direction of 41° to the horizontal in moving an object 5 feet from (0, 0) to (5, 0).
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Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 11, B = 109°
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Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49
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Find all the complex roots. Write the answer in the indicated form. The complex cube roots of 27(cos 234° + i sin 234°) (polar form)
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Find the specified vector or scalar.
u = -4i + 1j and v = 4i + 1j; Find .
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Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = j, w = 4i
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Write the complex number in polar form. Express the argument in degrees. 4i
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The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot wind that produces maximum sailing speed. This situation is now represented by the polar graph in the figure shown below. Each point (r, θ) on the graph gives the sailing speed, r, in knots, at an angle θ to the 10-knot wind. What is the speed to the nearest knot, of the sailboat sailing at 120° angle to the wind?
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Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 7, b = 7, c = 5
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Plot the complex number. 2 + i
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Find the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i – 3j
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Find the quotient of the complex numbers. Leave answer in polar form.
z1 =
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Graph the polar equation.
r = 2 + 2sin θ
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Polar coordinates of a point are given. Find the rectangular coordinates of the point. (-5, -180°)
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Plot the complex number.
-5– 5i
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