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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented.r = 4
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using x(t) = a cos t and y(t) = b sin t. Identify the curve.x2 + y2 = 16
For the following exercises, find the length of side x. Round to the nearest tenth. 123⁰ X 1
For the following exercises, find the quotient z1/z2 in polar form.z1 = 12cis(55°), z2 = 3cis(18°)
For the following exercises, given v, draw v, 3v and 1/2 v.〈−1, 4〉
For the following exercises, find the powers of each complex number in polar form.Find z2 when z = 3cis(120°).
For the following exercises, graph the polar equation. Identify the name of the shape.r = 3cos(2θ)
For the following exercises, use the parametric equations for integers a and b:x(t) = acos((a + b)t) y(t) = acos((a − b)t)Graph on the domain [−π,0], where a = 5 and b = 4,
For the following exercises, find the measurement of angle A. A 2.5 1.5 2.3
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented.r2 = 4
For the following exercises, find the measure of angle x, if possible. Round to the nearest tenth. X 11 37° 8
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using x(t) = a cos t and y(t) = b sin t. Identify the curve.x2 + y2 = 10
For the following exercises, find the quotient z1/z2 in polar form.z1 = 27cis (5π/3), z2 = 9cis (π/3)
For the following exercises, find the powers of each complex number in polar form. Find z4 when z = 2cis(70°)
For the following exercises, given v, draw v, 3v and 1/2 v.〈−3, −2〉
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r= 1 4cos - 3sin 0
For the following exercises, graph the polar equation. Identify the name of the shape.r = 5sin(3θ)
For the following exercises, use the parametric equations for integers a and b:x(t) = acos((a + b)t) y(t) = acos((a − b)t)If a is 1 more than b, describe the effect the values of a and
For the following exercises, find the measure of angle x, if possible. Round to the nearest tenth. 5 X 13 22°
For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u. " 14
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using x(t) = a cos t and y(t) = b sin t. Identify the curve.Parameterize the line from (3, 0) to
For the following exercises, find the powers of each complex number in polar form.Find z2 when z = 5cis (3π/4)
For the following exercises, find the measurement of angle A. 115 125 100
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r = 3 cos - 5sin 0
For the following exercises, find the powers of each complex number in polar form.Find z4 when z = cis (3π/16).
For the following exercises, graph the polar equation. Identify the name of the shape.r = 4sin(4θ)
For the following exercises, use the parametric equations for integers a and b:x(t) = acos((a + b)t) y(t) = acos((a − b)t)Describe the graph if a = 100 and b = 99.
For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u. [ n
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using x(t) = a cos t and y(t) = b sin t. Identify the curve.Parameterize the line from (−1,0)
For the following exercises, find the measurement of angle A. 6.8 4.3 8.2
For the following exercises, find the polar coordinates of the point. TE 2 + Зл 0
For the following exercises, find the powers of each complex number in polar form.Find z3 when z = 3cis (5π/3).
For the following exercises, find the measure of angle x, if possible. Round to the nearest tenth. Notice that x is an obtuse angle. 24 21 x -55°
For the following exercises, use the parametric equations for integers a and b:x(t) = acos((a + b)t) y(t) = acos((a − b)t)What happens if b is 1 more than a? Describe the graph.
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using x(t) = a cos t and y(t) = b sin t. Identify the curve.Parameterize the line from (−1,5)
For the following exercises, evaluate each root.Evaluate the square root of z when z = 25cis (3π/2).
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r= 4 sin +7cos
For the following exercises, find z1/z2 in polar form.z1 = √2 cis(90°); z2 = 2cis(60°)
For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.a = 12.4 ft, b = 13.7 ft, c = 20.2 ft
For the following exercises, graph the polar equation. Identify the name of the shape.r = 2 + 4cos θ
For the following exercises, graph the equation and include the orientation.x = t, y = √25 − t2 , 0 < t ≤ 5
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by setting x(t) = t or by setting y(t) = t. y(x) = 3x2 + 3
Write the complex number in polar form. 5 + 9i
For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.a = 7.2, b = 4.5, γ = 43°
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.〈−4, −6〉
For the following exercises, find z1/z2 in polar form.z1 = 15cis(120°); z2 = 3cis(40°)
For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth. a = 1.6 yd, b = 2.6 yd, c = 4.1 yd
For the following exercises, graph the polar equation. Identify the name of the shape.r = 5 + 6cos θ
For the following exercises, graph the equation and include the orientation.x(t) = −t, y(t) = √t , t ≥ 5
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r= 6 cos 0 + 3sin
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by setting x(t) = t or by setting y(t) = t.y(x) = 2 sin x + 1
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.Given u = 〈−1, 6〉 and v = 〈6, − 1〉, calculate u ⋅ v.
For the following exercises, find the length of side x. Round to the nearest tenth. x 30 65° 23
For the following exercises, find the powers of each complex number in polar form.Find z3 when z = 5cis(45°).
For the following exercises, graph the polar equation. Identify the name of the shape.r2 = 10sin(2θ)
For the following exercises, use the parametric equations for integers a and b:x(t) = acos((a + b)t) y(t) = acos((a − b)t)Graph on the domain [−π,0], where a = 3 and b = 2,
For the following exercises, sketch the curve and include the orientation. x(t) = 3cos² t y(t) = -3sin² t
For the following exercises, solve the triangle. Round to the nearest tenth.a = 3.1, b = 3.5, c = 5
For the following exercises, graph the polar equation. Identify the name of the shape.r = 5 + 4cos θ
For the following exercises, graph the equation and include the orientation. Then, write the Cartesian equation. x(t) = 2cos t y(t) = sin t
For the following exercises, convert the given Cartesian equation to a polar equation.x2 = 9y
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 2t - 1 |y(t) = t³ - 2
For the following exercises, use the vectors u = i −3j and v = 2i + 3j. Find a unit vector in the same direction as v.
For the following exercises, test each equation for symmetry.Sketch a graph of the polar equation r = 1 − 5sin θ. Label the axis intercepts.
For the following exercises, use the Law of Sines to solve, if possible, the missing side or angle for each triangle or triangles in the ambiguous case. Round each answer to the nearest tenth.Find
For the following exercises, find a unit vector in the same direction as the given vector.u = 100i + 200j
For the following exercises, find z1 z2 in polar form. Z₁ ₁ = 3cis ( 4 ); ²₂ = 5cis (7)
For the following exercises, graph the equation and include the orientation. Then, write the Cartesian equation. x(t) = 7cos t y(t) = 7sin t
For the following exercises, solve the triangle. Round to the nearest tenth.a = 51, b = 25, c = 29
For the following exercises, graph the polar equation. Identify the name of the shape.r = 10 + 9cos θ
For the following exercises, convert the given Cartesian equation to a polar equation.y2 = 9x
For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table. [x(t) = 2t - 1 y(t)=t+4
For the following exercises, use the vectors u = i −3j and v = 2i + 3j.Given vector v has an initial point P1 = (2, 2) and terminal point P2 = (−1, 0), write the vector v in terms of i and j. On
For the following exercises, find z1 z2 in polar form. 5π 2, = √5cis (5): 2, = V15 cis (2) ); 8 12
For the following exercises, test each equation for symmetry.Sketch a graph of the polar equation r = 5sin(7θ).
For the following exercises, use the Law of Sines to solve, if possible, the missing side or angle for each triangle or triangles in the ambiguous case. Round each answer to the nearest tenth.Find
For the following exercises, find a unit vector in the same direction as the given vector.u = −14i + 2j
For the following exercises, graph the equation and include the orientation. Then, write the Cartesian equation. x(t) = e²t y(t) = -e¹
For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.Find the area of a triangle with sides of length 18 in, 21 in, and 32 in. Round to
For the following exercises, graph the polar equation. Identify the name of the shape.r = 1 + 3sin θ
For the following exercises, convert the given Cartesian equation to a polar equation.9xy = 1
For the following exercises, find z1 z2 in polar form. 2,-4cis (2): ², 2cis (1) ; = 4
For the following exercises, test each equation for symmetry.Sketch a graph of the polar equation r = 3 − 3cos θ
For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.a = 5, c = 6, β = 35°
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π. 〈0, 4〉
For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.Find the area of a triangle with sides of length 20 cm, 26 cm, and 37 cm. Round to
For the following exercises, graph the polar equation. Identify the name of the shape.r = 2 + 5sin θ
For the following exercises, graph the equation and include the orientation.x = t2, y = 3t, 0 ≤ t ≤ 5
For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table. x(t) = 2t - 1 y(t) = 5t
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r = 3sin θ
For the following exercises, find the absolute value of each complex number. −2 + 6i
For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.b = 11, c = 8, α = 28°
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.〈6, 5〉
For the following exercises, find z1/z2 in polar form.z1 = 21cis(135°); z2 = 3cis(65°)
For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.a = 1/2 m, b = 1/3 m, c = 1/4 m
For the following exercises, rewrite the parametric equation as a Cartesian equation by building an x-y table. [x(t) = 4t - 1 y(t) = 4t+2
For the following exercises, graph the equation and include the orientation.x = 2t, y = t2 , −5 ≤ t ≤ 5
For the following exercises, convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if possible, and identify the conic section represented. r = 4cos θ
For the following exercises, find the absolute value of each complex number.4 − 3i
For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.a = 32, b = 24, γ = 75°

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