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algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

Find standard notation, a + bi. 2 cos TT 2 + i sin E|N
A ranger in fire tower A spots a fire at a direction of 295°. A ranger in fire tower B, located 45 mi at a direction of 45° from tower A, spots the same fire at a direction of 255°. How far from
The vectors u, v, and w are drawn below. Copy them on a sheet of paper. Then sketch each of the vectors in Exercises.u - 2v V W u
The vectors u, v, and w are drawn below. Copy them on a sheet of paper. Then sketch each of the vectors in Exercises.u + v + w V W u
An airplane flies 32° for 210 km, and then 280° for 170 km. How far is the airplane, then, from the starting point and in what direction?
Find (1 - i)7 and write trigonometric notation for the answer.
A boat leaves lighthouse A and sails 5.1 km. At this time it is sighted from lighthouse B, 7.2 km west of A. The bearing of the boat from B is N65°10E. How far is the boat from B? A
An airplane has an airspeed of 150 km/h. It is to make a flight in a direction of 70° while there is a 25-km/h wind from 340°. What will the airplane’s actual heading be?
The vectors u, v, and w are drawn below. Copy them on a sheet of paper. Then sketch each of the vectors in Exercises.1/2 u - w V W u
Miami, Florida, is located 178 mi N73°10W of Nassau. Because of an approaching hurricane, a cruise ship sailing in the region needs to know how far it is from Nassau. The ship’s position is
Find [2(cos 15° + i sin 15°)4] and write standard notation for the answer.
A wind has an easterly component ( from the east) of 10 km/h and a southerly component ( from the south) of 16 km/h. Find the magnitude and the direction of the wind.
Vectors u, v, and w are determined by the sides of ΔABC below.a) Find an expression for w in terms of u and v.b) Find an expression for v in terms of u and w. A u W B C
Multiply or divide and leave the answer in trigonometric notation. 12 (cos 48° + i sin 48°) 3 (cos 6°+ i sin 6°)
Find the square roots of -2 - 2√3i.
Find standard notation, a + bi.√2[cos ( -60°) + i sin ( -60°)]
In ΔABC, vectors u and w are determined by the sides shown, where P is the midpoint of side BC. Find an expression for v in terms of u and w. A B V W P C
A vector w has magnitude 100 and points southeast. Resolve the vector into an easterly component and a southerly component.
A wheelbarrow is pushed by applying a 97-lb force F that makes a 38° angle with the horizontal. Resolve F into its horizontal component and its vertical component. (The horizontal component is the
Find the cube roots of -1.
A vector u with a magnitude of 150 lb is inclined to the right and upward 52° from the horizontal. Resolve the vector into components.
A luggage wagon is being pulled with vector force V, which has a magnitude of 780 lb at an angle of elevation of 60°. Resolve the vector V into components. |VI = 780 60°
Try to solve this triangle using the law of cosines. Then explain why it is easier to solve it using the law of sines.
A hot-air balloon exerts a 1200-lb pull on a tether line at a 45° angle with the horizontal. Resolve the vector B into components. 45° |B| = 1200 W
An airplane takes off at a speed S of 225 mph at an angle of 17° with the horizontal. Resolve the vector S into components.
Find the acute angle A, in both radians and degrees, for the given function value.cos A = 0.2213
Explain why the following statements are not contradictory.The number 1 has one real cube root.The number 1 has three complex cube roots.
Find the acute angle A, in both radians and degrees, for the given function value.cos A = 1.5612
Explain why we cannot solve a triangle given SAS with the law of sines.
Multiply or divide and leave the answer in trigonometric notation.2.5(cos 35° + i sin 35°) · 4.5(cos 21° + i sin 21°)
Explain why the law of sines cannot be used to find the first angle when solving a triangle given three sides.
Convert to trigonometric notation and then multiply or divide. 1-i 1 + i
Explain why trigonometric notation for a complex number is not unique, but rectangular, or standard, notation is unique.
Convert to trigonometric notation and then multiply or divide.(1 - i)(2 + 2i)
An airplane is flying at 200 km/h in a direction of 305°. Find the westerly component and the northerly component of its velocity.
Explain why x6 - 2x3 + 1 = 0 has three distinct solutions, x6 - 2x3 = 0 has four distinct solutions, and x6 - 2x = 0 has six distinct solutions.
A baseball player throws a baseball with a speed S of 72 mph at an angle of 45° with the horizontal. Resolve the vector S into components.
Convert to trigonometric notation and then multiply or divide. 21 2V3-2i 1 + V3i
Express the vector as a linear combination of the unit vectors i and j.w = ( -4, 6)
A shipping crate that weighs 450 kg is placed on a loading ramp that makes an angle of 30° with the horizontal. Find the magnitude of the components of the crate’s weight perpendicular to and
Express the vector as a linear combination of the unit vectors i and j.r = ( -15, 9)
Convert to trigonometric notation and then multiply or divide.(3√3 - 3i)(2i)
An 80-lb block of ice rests on a 37° incline. What force parallel to the incline is necessary in order to keep the ice from sliding down?
Prove the following area formulas for a general triangle ABC with area represented by K. K K a² sin B sin C 2 sin A b² sin C sin A 2 sin B K c² sin A sin B 2 sin C
Express the vector as a linear combination of i and j. PII Y^ Q(-3,3) 4 2. 1-4-2 24 2 IT 4 P(4, -2) ITD X
Express the vector as a linear combination of the unit vectors i and j.s = (2, 5)
What force is necessary to pull a 3500-lb truck up a 9° incline?
Prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle. S $2
Multiply: (1 - i)(1 + i).
Express the vector as a linear combination of i and j. -21 A Q(1, 4) . . X
Find d. 11 in. 150° 12 in. 15 in.
Express the vector as a linear combination of the unit vectors i and j.u = (2, -1)
Raise the number to the given power and write trigonometric notation for the answer. [2(cos TT 3 13 F)] + i sin - 3
Prove that the area of a quadrilateral ABCD is one-half of the product of the lengths of its diagonals and the sine of the angle θ between the diagonals. b Pi D
Sketch (include the unit circle) and calculate the unit vector u = (cos u)i + (sin u)j for the given direction angle. Ө TT 2
Sketch (include the unit circle) and calculate the unit vector u = (cos u)i + (sin u)j for the given direction angle. ㅠ e 3
For Exercises, use the vectors u = 2i + j, v = -3i - 10j, and w = i - 5j.Perform the indicated vector operations and state the answer in two forms: (a) As a linear combination of i and j
Sketch (include the unit circle) and calculate the unit vector u = (cos u)i + (sin u)j for the given direction angle. Ө Зп 2
For Exercises, use the vectors u = 2i + j, v = -3i - 10j, and w = i - 5j.Perform the indicated vector operations and state the answer in two forms: (a) As a linear combination of i and j
Raise the number to the given power and write trigonometric notation for the answer.(1 + i)6
An eagle flies from its nest 7 mi in the direction northeast, where it stops to rest on a cliff. It then flies 8 mi in the direction S30°W to land on top of a tree. Place an xy-coordinate
For Exercises, use the vectors u = 2i + j, v = -3i - 10j, and w = i - 5j.Perform the indicated vector operations and state the answer in two forms: (a) As a linear combination of i and j
For Exercises, use the vectors u = 2i + j, v = -3i - 10j, and w = i - 5j.Perform the indicated vector operations and state the answer in two forms: (a) As a linear combination of i and j
Raise the number to the given power and write standard notation for the answer. 1 /2 1 1 √₂₁) V /2 12
Raise the number to the given power and write standard notation for the answer.[3(cos 20° + i sin 20°)]3
Convert to a rectangular equation. Ө - Зп 4
Raise the number to the given power and write standard notation for the answer.(1 - i)5
Find the square roots of the number.-i
Find the square roots of the number.2√2 - 2√2i
Convert to a rectangular equation.r = 5
Find the cube roots of the number.i
Convert to a rectangular equation. 2 1 sin 0
Convert to a rectangular equation.r sin θ = 2
Find the cube roots of the number.2√3 - 2i
Convert to a rectangular equation.r = -3 sin θ
Convert to a rectangular equation.r + r cos θ = 3
Find and graph the fourth roots of 16.
Convert to a rectangular equation.r - 9 cos θ = 7 sin θ
Find and graph the fifth roots of -1.
Convert to a rectangular equation. 0 = = 5 п 3
Convert to a rectangular equation.r + 5 sin θ = 7 cos θ
Convert to a rectangular equation.r = 5 sec θ
Find the tenth roots of 8.
Convert to a rectangular equation.r = 3 cos θ
Find the sixth roots of -1.
Convert to a rectangular equation.r = cos θ - sin θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = sin θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = 1 - cos θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = 4 cos 2θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = 1 - 2 sin θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = cos θ
Graph the equation by plotting points. Then check your work using a graphing calculator. 1 1 + cos 0
Graph the equation by plotting points. Then check your work using a graphing calculator.r = 2 sec θ
Graph the equation by plotting points. Then check your work using a graphing calculator.r = 2 - cos 3θ
Convert to degree measure.π/12
Convert to degree measure.3π
Where we used the law of cosines and the law of sines to solve the applied problems. For this exercise set, solve the problem using the vector form v =|v |3(cos θ)i + 1sin θ)j].A ship first sails
Convert to radian measure.330°
Find the function value using coordinates of points on the unit circle. sin 2π 3
A boat heads 35°, propelled by a force of 750 lb. A wind from 320° exerts a force of 150 lb on the boat. How large is the resultant force, and in what direction is the boat moving?

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