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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, sketch the curve and include the orientation. x(t) = 2sin t [y(t) = 4cos t
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.√z1
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = e²t |y(t) = e6t
For the following exercises, convert the given Cartesian equation to a polar equation.y = 4
For the following exercises, convert the given Cartesian equation to a polar equation.x2 + y2 = 64
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth.a = 12, c = 17, α = 35°
For the following exercises, convert the complex number from polar to rectangular form.z = 7cis (π/6)
For the following exercises, convert the complex number from polar to rectangular form.z = 2cis (π/3)
For the following exercises, use the given vectors to compute u + v, u − v, and 2u − 3v.u = 〈2, − 3〉 , v = 〈1, 5〉
For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.a = 16, b = 31, c = 20; find angle B.
For the following exercises, graph the polar equation. Identify the name of the shape.r = 2 + 2cos θ
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = t³ t5 |y(t) = ¹0
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.Plot the complex number −5 − i in the complex plane.
For the following exercises, convert the given Cartesian equation to a polar equation.y = 4x2
For the following exercises, convert the given Cartesian equation to a polar equation.x2 + y2 = − 2y
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth.a = 20.5, b = 35.0, β = 25°
For the following exercises, convert the complex number from polar to rectangular form.z = 4cis (7π/6)
For the following exercises, use the given vectors to compute u + v, u − v, and 2u − 3v.u = 〈−3, 4〉 , v = 〈−2, 1〉
For the following exercises, sketch the curve and include the orientation. (x(t) = 3cos² t |y(t) = -3sin² t
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.Eliminate the parameter t to rewrite the following parametric equations as a Cartesian equation: [x(t)=t+1 [y(t) = 2t²
For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.a = 13, b = 22, c = 28; find angle A.
For the following exercises, graph the polar equation. Identify the name of the shape.r = 2 − 2cos θ
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 4 cos t |y(t) = 5 sin t
For the following exercises, convert the given Cartesian equation to a polar equation.y = 2x4
For the following exercises, convert the given polar equation to a Cartesian equation. r = 7cos θ
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.β = 50°, a = 105, b = 45
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .Given initial point P1 = (6, 0) and terminal point P2 = (−1, −3), write the vector v in terms of
For the following exercises, write the complex number in polar form.− 1/2 − 1/2 i
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth. α = 119°, a = 14, b = 26
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Convert (7,−2) to polar coordinates.
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = log (2t) |y(t)=√t-1
For the following exercises, sketch the curve and include the orientation. x(t) = 5 -|t| |y(t) = t +2
For the following exercises, convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ θ <2π. Remember to consider the quadrant in which the given point is located.(−10, −13)
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.z1 z2
For the following exercises, test the equation for symmetry.r = 3√1−cos2 θ
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth. α = 36.6°, a = 186.2, b = 242.2
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .Given initial point P1 = (−3, 1) and terminal point P2 = (5, 2), write the vector v in terms of i
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Convertto rectangular coordinates. -2, Зл 2
For the following exercises, write the complex number in polar form. 8 − 4i
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. [x(t) = 4 log (t) |y(t) = 3 + 2t
For the following exercises, use the Law of Sines to solve for the missing side for each oblique triangle. Round each answer to the nearest hundredth. Assume that angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c.Find side c when B = 37°, C = 21, b = 23.
For the following exercises, sketch the curve and include the orientation. x(t) = -√t ly(t) = t
For the following exercises, convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ θ <2π. Remember to consider the quadrant in which the given point is located.(3, −5)
Convert the complex number from polar to rectangular form: z = 5cis (2π/3).
For the following exercises, test the equation for symmetry.r = 2/θ
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.α = 43.1°, a = 184.2, b = 242.8
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .P1 = (8, 3), P2 = (6, 5), P3 = (11, 8), and P4 = (9, 10)
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. [x(t) = e-2t |y(t) = 2e-t
For the following exercises, write the complex number in polar form. 2 + 2i
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Convertto rectangular coordinates. 6, Зл 4 Д
For the following exercises, use the Law of Sines to solve for the missing side for each oblique triangle. Round each answer to the nearest hundredth. Assume that angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c.Find side a when A = 132°, C = 23°, b = 10.
For the following exercises, sketch the curve and include the orientation. x(t) = t [y(t) = Vt
For the following exercises, convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ θ <2π. Remember to consider the quadrant in which the given point is located.(−4, 6)
For the following exercises, test the equation for symmetry.r = 4cos θ/2
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.β = 67°, a = 49, b = 38
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 2et |y(t) = 1 - 5t
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Plot the point with polar coordinates 5, 2п 3
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .P1 = (3, 7), P2 = (2, 1), P3 = (1, 2), and P4 = (−1, −4)
For the following exercises, find the absolute value of the given complex number.2.2 − 3.1i
For the following exercises, use the Law of Sines to solve for the missing side for each oblique triangle. Round each answer to the nearest hundredth. Assume that angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c. Find side b when A = 37°, B = 49°, c = 5.
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. x(t) = 1² |y(t)=1+3
For the following exercises, convert the given Cartesian coordinates to polar coordinates with r > 0, 0 ≤ θ <2π. Remember to consider the quadrant in which the given point is located.(4, 2)
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.γ = 113°, b = 10, c = 32
For the following exercises, find the absolute value of the given complex number.2i
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .P1 = (−1, −1), P2 = (−4, 5), P3 = (−10, 6), and P4 = (−13,12)
For the following exercises, test the equation for symmetry.r = 2θ
Find the absolute value of the complex number 5 − 9i.
Write the complex number in polar form: 4 + i.
Test the equation for symmetry: r = − 4sin (2θ).
For the following exercises, test the equation for symmetry.r = 3 + 2sin θ
Compare right triangles and oblique triangles.
What does the absolute value of a complex number represent?
Given a vector with initial point (5, 2) and terminal point (−1,−3), find an equivalent vector whose initial point is (0, 0). Write the vector in component form 〈a, b〉.
Convert the polar equation to a Cartesian equation: x2 + y2 = 5y.
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. [x(t) = t (y(t) = t²-1
For the following exercises, convert the given polar coordinates to Cartesian coordinates with r > 0 and 0 ≤ θ ≤2π. Remember to consider the quadrant in which the given point is located when determining θ for the point. (7, 7π/6)
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Solve the triangle, rounding to the nearest tenth, assuming α is opposite side a, β is opposite side b, and γ is
For the following exercises, find the absolute value of the given complex number. 5 + 3i
Given a vector with initial point (−4, 2) and terminal point (3,− 3), find an equivalent vector whose initial point is (0, 0). Write the vector in component form 〈a, b〉.
For the following exercises, test the equation for symmetry.r = 3 − 3cos θ
Convert to rectangular form and graph: r = − 3csc θ.
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Solve the triangle in Figure 2, rounding to the nearest tenth. 13 B 54° a Figure 2 15 C
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.α = 35°, γ = 73°, c = 20
For the following exercises, find the absolute value of the given complex number.−7 + i
Given a vector with initial point (7,−1) and terminal point (−1,−7), find an equivalent vector whose initial point is (0, 0). Write the vector in component form 〈a, b〉.
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. x(t)=2+t [y(t) = 3-2t
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.β = 58.7°, a = 10.6, c = 15.7
For the following exercises, convert the given polar coordinates to Cartesian coordinates with r > 0 and 0 ≤ θ ≤2π. Remember to consider the quadrant in which the given point is located when determining θ for the point.(6, −π/4)
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 6 - 3t |y(t) = 10-t
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.Find the area of a triangle with sides of length 8.3, 6.6, and 9.1.
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.α = 60°, β = 60°, γ = 60°
For the following exercises, find the absolute value of the given complex number.−3 − 3i
For the following exercises, determine whether the two vectors u and v are equal, where u has an initial point P1 and a terminal point P2 and v has an initial point P3 and a terminal point P4 .P1 = (5, 1), P2 = (3, −2), P3 = (−1, 3), and P4 = (9, −4)
For the following exercises, graph each set of parametric equations by making a table of values. Include the orientation on the graph. x(t)=-2-2t y(t) = 3+ t
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. If possible, solve each triangle for the unknown side. Round to the nearest tenth.γ = 115°, a = 18, b = 23
For the following exercises, test the equation for symmetry.r = 3sin 2θ
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 2t + 1 |y(t) = 3√t
For the following exercises, convert the given polar coordinates to Cartesian coordinates with r > 0 and 0 ≤ θ ≤2π. Remember to consider the quadrant in which the given point is located when determining θ for the point.(−3, π/6)
For the following exercises, assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve each triangle, if possible. Round each answer to the nearest tenth.To find the distance between two cities, a satellite calculates the distances and angle shown in Figure 3 (not to
For the following exercises, find the absolute value of the given complex number. √2 – бі
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