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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, look at the graphs of each of the four parametric equations. Although they look unusual and beautiful, they are so common that they have names, as indicated in each
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Two search teams spot a stranded climber on a mountain. The first search team is 0.5 miles from the
For the following exercises, find all answers rounded to the nearest hundredth.Use the rectangular to polar feature on the graphing calculator to change 3 − 2i to polar form.
For the following exercises, suppose that x2 = 25 + 36 − 60 cos(52) represents the relationship of three sides of a triangle and the cosine of an angle.Draw the triangle.
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.r = 2sin (θ/2), r = θsin (θ/2)
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis.x2 +(y − 1)2 = 1
For the following exercises, find the magnitude and direction of the vector. 〈6, −2〉
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.Find the magnitude of the horizontal and vertical components of the vector
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.In Figure 26, ABCD is not a parallelogram. ∠m is obtuse. Solve both triangles. Round each answer
For the following exercises, find all answers rounded to the nearest hundredth.Use the rectangular to polar feature on the graphing calculator to change −3 − 8i to polar form.
For the following exercises, suppose that x2 = 25 + 36 − 60 cos(52) represents the relationship of three sides of a triangle and the cosine of an angle.Find the length of the third side.
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis.(x + 2)2 +(y + 3)2 = 13
For the following exercises, find the magnitude and direction of the vector.〈−3, −3〉
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.Find the magnitude of the horizontal and vertical components of a vector
For the following exercises, find all answers rounded to the nearest hundredth.Use the polar to rectangular feature on the graphing calculator to change 4cis(120°) to rectangular form.
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.A pole leans away from the sun at an angle of 7° to the vertical, as shown in Figure 27. When the
For the following exercises, find the area of the triangle. 5.3 22° 3.4
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.On a graphing utility, graph r =
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis.x = 2
For the following exercises, calculate u ⋅ v. u = −2i + j and v = 3i + 7j
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.Find the magnitude of the horizontal and vertical components of the vector
For the following exercises, find all answers rounded to the nearest hundredth.Use the polar to rectangular feature on the graphing calculator to change 2cis(45°) to rectangular form.
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.To determine how far a boat is from shore, two radar stations 500 feet apart find the angles out to
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.On a graphing utility, graph and
For the following exercises, find the area of the triangle. 80° 6 8
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis.x2 + y2 = 5y
For the following exercises, calculate u ⋅ v.u = i + 4j and v = 4i + 3j
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.A woman leaves home and walks 3 miles west, then 2 miles southwest. How far
For the following exercises, find all answers rounded to the nearest hundredth.Use the polar to rectangular feature on the graphing calculator to change 5cis(210°) to rectangular form.
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Figure 29 shows a satellite orbiting Earth. The satellite passes directly over two tracking
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.On a graphing utility, graph each
For the following exercises, find the area of the triangle. 12.8 18⁰ 18.8
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis.x2 + y2 = 3x
For the following exercises, calculate u ⋅ v.Given v = 〈−3, 4〉 draw v, 2v, and 1/2 v.
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.A boat leaves the marina and sails 6 miles north, then 2 miles northeast.
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.A communications tower is located at the top of a steep hill, as shown in Figure 30. The angle of
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.On a graphing utility, graph each
For the following exercises, find the area of the triangle.A surveyor has taken the measurements shown in Figure 14. Find the distance across the lake. Round answers to the nearest tenth. 800
For the following exercises, calculate u ⋅ v.Given the vectors shown in Figure 4, sketch u + v, u − v and 3v. U # V H Figure 4
For the following exercises, convert the equation from polar to rectangular form and graph on the rectangular plane. r = 6
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.The roof of a house is at a 20° angle. An 8-foot solar panel is to be mounted on the roof and
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.A man starts walking from home and walks 4 miles east, 2 miles southeast, 5
For the following exercises, use a graphing utility to graph the given parametric equations.a.b.c.An object is thrown in the air with vertical velocity of 20 ft/s and horizontal velocity of 15 ft/s.
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.On a graphing utility, graph each
For the following exercises, plot the complex number in the complex plane. 2 + 4i
For the following exercises, find the area of the triangle. Round to the nearest hundredth. ن
For the following exercises, plot the complex number in the complex plane.5 − 4i
For the following exercises, use a graphing utility to graph on the window [−3,3] by [−3,3] on the domain [0,2π) for the following values of a and b , and include the orientation.a = 2,
For the following exercises, use a graphing calculator to sketch the graph of the polar equation.r = θ + 1
For the following exercises, plot the points.(3, 5π/6)
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Find m ∠ADC in Figure 20. Round to the nearest tenth. B 8 60° 9 Figure 20 10 C D
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
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.|v| = 8, θ = 220°
For the following exercises, plot the complex number in the complex plane.−4
For the following exercises, find the area of the triangle. Round to the nearest hundredth.A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 12 units. Find the
For the following exercises, use a graphing utility to graph on the window [−3,3] by [−3,3] on the domain [0,2π) for the following values of a and b , and include the orientation.a = 5,
For the following exercises, use a graphing calculator to sketch the graph of the polar equation.r = θsin θ
For the following exercises, plot the points.(−1.5, 7π/6)
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Find AD in Figure 21. Round to the nearest tenth. B 12, 53 A 13 Figure 21 C 44 D
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
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.|v| = 2, θ = 300°
For the following exercises, plot the complex number in the complex plane.6 − 2i
For the following exercises, find the area of the triangle. Round to the nearest hundredth.The sides of a parallelogram are 11 feet and 17 feet. The longer diagonal is 22 feet. Find the length of the
For the following exercises, look at the graphs that were created by parametric equations of the form Use the parametric mode on the graphing calculator to find the values of a, b, c, and d to
For the following exercises, use a graphing calculator to sketch the graph of the polar equation.r = θcos θ
For the following exercises, plot the points.(−2, π/4)
For the following exercises, use the vectors u = 2i − j, v = 4i − 3j, and w = −2i + 5j to evaluate the expression. u − v
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Solve both triangles in Figure 22. Round each answer to the nearest tenth.
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.|v| = 5, θ = 135°
For the following exercises, plot the complex number in the complex plane.−2 + i
For the following exercises, look at the graphs that were created by parametric equations of the form Use the parametric mode on the graphing calculator to find the values of a, b, c, and d to
For the following exercises, find the area of the triangle. Round to the nearest hundredth.The sides of a parallelogram are 28 centimeters and 40 centimeters. The measure of the larger angle is
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.r = θ, r = −θ
For the following exercises, plot the points.(1, 3π/2)
For the following exercises, use the vectors u = 2i − j, v = 4i − 3j, and w = −2i + 5j to evaluate the expression.2v − u + w
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Find AB in the parallelogram shown in Figure 23. C 12 130° D A 130° 10 Figure 23 B
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.A 60-pound box is resting on a ramp that is inclined 12°. Rounding to the
For the following exercises, plot the complex number in the complex plane.1 − 4i
For the following exercises, look at the graphs that were created by parametric equations of the form Use the parametric mode on the graphing calculator to find the values of a, b, c, and d to
For the following exercises, find the area of the triangle. Round to the nearest hundredth.A regular octagon is inscribed in a circle with a radius of 8 inches. (See Figure 12.) Find the perimeter of
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.r = θ, r = θ + sin θ
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis. 5x − y = 6
For the following exercises, find a unit vector in the same direction as the given vector.a = 8i − 6j
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.A 25-pound box is resting on a ramp that is inclined 8°. Rounding to the
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Solve the triangle in Figure 24. Round each answer to the nearest tenth. 20º 10 Figure 24 H K
For the following exercises, find all answers rounded to the nearest hundredth. Use the rectangular to polar feature on the graphing calculator to change 5 + 5i to polar form.
For the following exercises, look at the graphs that were created by parametric equations of the form Use the parametric mode on the graphing calculator to find the values of a, b, c, and d to
For the following exercises, find the area of the triangle. Round to the nearest hundredth.A regular pentagon is inscribed in a circle of radius 12 cm. (See Figure 13.) Find the perimeter of the
For the following exercises, use a graphing utility to graph each pair of polar equations on a domain of [0,4π] and then explain the differences shown in the graphs.r = sin θ + θ, r = sin θ − θ
For the following exercises, convert the equation from rectangular to polar form and graph on the polar axis. 2x + 7y = −3
For the following exercises, find a unit vector in the same direction as the given vector.b = −3i − j
For the following exercises, use the given magnitude and direction in standard position, write the vector in component form.Find the magnitude of the horizontal and vertical components of a vector
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.Solve the triangle in Figure 25. Round each answer to the nearest tenth.
For the following exercises, plot the complex number in the complex plane.2i
For the following exercises, describe the graph of the set of parametric equations.Write the parametric equations of a circle with center (0,0), radius 5, and a counterclockwise orientation.
For the following exercises, use a graphing calculator to complete the table of values for each set of parametric equations. [x₂(t) = t² - 4 y₁ (t)=2t²-1
For the following exercises, plot the points. (−2, π/3)
For the following exercises, find the area of each triangle. Round each answer to the nearest tenth. 4.5 3.5 51° 29
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation.Parameterize (write a parametric equation for) each Cartesian equation by using x(t)
For the following exercises, write the vector shown in component form. commina

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