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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.〈2, −5〉
Write the complex number in polar form. 1 2 3 2 i
For the following exercises, find the length of side x. Round to the nearest tenth. 10 70° x 50°
For the following exercises, find z1/z2 in polar form.z1 = 6cis (π/3) ; z2 = 2cis (π/4)
For the following exercises, find the length of side x. Round to the nearest tenth. 6.5 x 72° 5
For the following exercises, graph the polar equation. Identify the name of the shape.r2 = 36cos(2θ)
For the following exercises, graph the equation and include the orientation.x(t) = −2cos t, y = 6sin t 0 ≤ t ≤ π
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 = 2sec θ
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by setting x(t) = t or by setting y(t) = t.x(y) = 3 log (y) + y
For the following exercises, find the length of side x. Round to the nearest tenth. 25° 6 120° X
For the following exercises, convert the complex number from polar to rectangular form. z = 5cis (5π/6)
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.Given u = −i − j and v = i + 5j, calculate u ⋅ v.
For the following exercises, find z1/z2 in polar form.z1 = 5√2 cis(π); z2 = √2 cis (2π/3)
For the following exercises, find the length of side x. Round to the nearest tenth. 42⁰ 3.4 4.5 x
For the following exercises, graph the polar equation. Identify the name of the shape.r2 = 10cos(2θ)
For the following exercises, graph the equation and include the orientation.x(t) = −sec t, y = tan t, −π/2 < t < π/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 = 3csc θ
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by setting x(t) = t or by setting y(t) = t.x(y) = √ y + 2y
For the following exercises, convert the complex number from polar to rectangular form.z = 3cis(40°)
For the following exercises, find the length of side x. Round to the nearest tenth. X 75° 45° 15
For the following exercises, find the magnitude and direction of the vector, 0 ≤ θ < 2π.Given u = 〈−2, 4〉 and v = 〈−3, 1〉, calculate u ⋅ v.
For the following exercises, find z1/z2 in polar form.z1 = 2cis (3π/5); z2 = 3cis (π/4)
For the following exercises, find the length of side x. Round to the nearest tenth. 40° 12 X A 15 B
For the following exercises, graph the polar equation. Identify the name of the shape.r2 = 4sin(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 = 2 and b = 1,
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 = √rcos 0 + 2
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.x2/4 + y2/9 = 1
For the following exercises, find the product z1 z2 in polar form.z1 = 2cis(89°), z2 = 5cis(23°)
For the following exercises, find the length of side x. Round to the nearest tenth. 40° 18 110° X
For the following exercises, find the length of side x. Round to the nearest tenth. 14 50° 42°
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
For the following exercises, convert the complex number from polar to rectangular form.z = 7cis(25°)
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 = 108, b = 132, c = 160; find angle C.
For the following exercises, sketch the curve and include the orientation. x(t) = sec t y(t) = tan t
For the following exercises, graph the polar equation. Identify the name of the shape.r = 5 − 5sin θ
For the following exercises, convert the given Cartesian equation to a polar equation.x2 + y2 = 4y
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 3 sin t y(t) = 6 cos t
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.Parameterize (write a parametric equation for) the following Cartesian equation by using x(t) = acos t and y(t) = bsin t: x2 / 36 +
For the following exercises, convert the given polar equation to a Cartesian equation.r = −2/4cos θ + sin
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
For the following exercises, convert the complex number from polar to rectangular form.z = 3cis(240°)
For the following exercises, sketch the curve and include the orientation. x(t) = sec t |y(t) = tan² t
For the following exercises, solve the triangle. Round to the nearest tenth. A = 35°, b = 8, c = 11
For the following exercises, graph the polar equation. Identify the name of the shape.r = 3 + 3sin θ
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.Graph the set of parametric equations and find the Cartesian equation: x(t) = -2sin t ly(t) = 5cos t
For the following exercises, convert the given Cartesian equation to a polar equation.x2 + y2 = 3x
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = 2 cos² t y(t) = -sin t
For the following exercises, convert to rectangular form and graph. θ = 3π/4
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
For the following exercises, convert the complex number from polar to rectangular form.z = √2 cis(100°)
For the following exercises, solve the triangle. Round to the nearest tenth. B = 88°, a = 4.4, c = 5.2
For the following exercises, graph the polar equation. Identify the name of the shape.r = 3 + 2sin θ
For the following exercises, sketch the curve and include the orientation. [x(1) = y(t) = e-+ elt 2t
For the following exercises, convert the given Cartesian equation to a polar equation.x2 − y2 = x
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = cost +4 y(t) = 2 sin² t
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.A ball is launched with an initial velocity of 95 feet per second at an angle of 52° to the horizontal. The ball is released at a
For the following exercises, convert to rectangular form and graph.r = 5sec θ
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
For the following exercises, find z1 z2 in polar form. z₁ = 2√3cis(116°); z₂ = 2cis(82°)
For the following exercises, find a unit vector in the same direction as the given vector.b = −2i + 5j
For the following exercises, solve the triangle. Round to the nearest tenth.C = 121°, a = 21, b = 37
For the following exercises, graph the equation and include the orientation. Then, write the Cartesian equation. x(t) = t - 1 |y(t) = -f²
For the following exercises, graph the polar equation. Identify the name of the shape.r = 7 + 4sin θ
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = t - 1 |y(t) = 1²
For the following exercises, convert the given Cartesian equation to a polar equation.x2 − y2 = 3y
For the following exercises, use the vectors u = i −3j and v = 2i + 3j. Find 2u − 3v.
For the following exercises, find z1 z2 in polar form. z₁ = √2cis(205°); z₂ = 2√2cis(1189)
For the following exercises, test each equation for symmetry.r = 4 + 4sin θ
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
For the following exercises, find a unit vector in the same direction as the given vector.c = 10i − j
For the following exercises, graph the equation and include the orientation. Then, write the Cartesian equation. x(t) = 1³ y(t) = t + 3
For the following exercises, solve the triangle. Round to the nearest tenth.a = 13, b = 11, c = 15
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = -t |y(t) = t³ + 1
For the following exercises, graph the polar equation. Identify the name of the shape.r = 4 + 3cos θ
For the following exercises, convert the given Cartesian equation to a polar equation.x2 + y2 = 9
For the following exercises, use the vectors u = i −3j and v = 2i + 3j. Calculate u ∙ v.
For the following exercises, find z1 z2 in polar form. z₁ = 3cis(120°); Z₂ -cis(60°) 4
For the following exercises, test each equation for symmetry.r = 7
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
For the following exercises, find a unit vector in the same direction as the given vector.d = − 1/3 i + 5/2 j
For the following exercises, test the equation for symmetry.r = √5sin 2θ
For the following exercises, sketch the curve and include the orientation. x(t) = -t+2 y(t) = 5 -|t|
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.z1/z2
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = t³ - t |y(t) = 2t
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.(8, 8)
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
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
For the following exercises, write the complex number in polar form.√3 + i
For the following exercises, sketch the curve and include the orientation. x(t) = 4sin t y(t) = 2cos t
For the following exercises, use the vectors u = i + 5j, v = −2i − 3j, and w = 4i − j. Find u + (v − w)
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 = 42, b = 19, c = 30; find angle A.
For the following exercises, graph the polar equation. Identify the name of the shape. r = 3cos θ
Given z1 = 8cis(36°) and z2 = 2cis(15°), evaluate each expression.(z2)3
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = t-t4 |y(t)=t+2
For the following exercises, convert the given Cartesian equation to a polar equation. x = 3
For the following exercises, convert the given Cartesian equation to a polar equation. x = −2
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
For the following exercises, write the complex number in polar form.3i
For the following exercises, use the vectors u = i + 5j, v = −2i − 3j, and w = 4i − j. Find 4v + 2u
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 = 14, b = 13, c = 20; find angle C.

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