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mathematics
precalculus

Questions and Answers of Precalculus

Plot point given in polar coordinates.(5, 5π/3)
Plot point given in polar coordinates.(6, π/6)
Plot point given in polar coordinates.(-3, π)
Plot point given in polar coordinates.(-2, 0)
Plot point given in polar coordinates.(4, 270°)
Plot point given in polar coordinates.(3, 90°)
Match the point in polar coordinates with either A, B, C, or D on the graph. (2, 11π/6) --. -4--
Match the point in polar coordinates with either A, B, C, or D on the graph. (-2, 7π/6) --. -4--
Match the point in polar coordinates with either A, B, C, or D on the graph. (-2, 5π/6) --. -4--
Match the point in polar coordinates with either A, B, C, or D on the graph. (2, 5π/6) --. -4--
Match the point in polar coordinates with either A, B, C, or D on the graph. (2, -7π/6) --. -4--
Match the point in polar coordinates with either A, B, C, or D on the graph. (-2, π/6) --. -4--
Use the figure at the right. Determine whether the given statement is true or false. H - C = G - F
Use the figure at the right. Determine whether the given statement is true or false. E + D = G + H
Use the figure at the right. Determine whether the given statement is true or false. G + H + E = D
Use the figure at the right. Determine whether the given statement is true or false. C = D - E + F
Use the figure at the right. Determine whether the given statement is true or false. K + G = F
Use the figure at the right. Determine whether the given statement is true or false. A + B = F
Use the vectors in the figure at the right to graph each of the following vectors. 2u - 3v + w W
Use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2w W
Use the vectors in the figure at the right to graph each of the following vectors. u - v W
Use the vectors in the figure at the right to graph each of the following vectors. u - w W
Use the vectors in the figure at the right to graph each of the following vectors. 4w W
Use the vectors in the figure at the right to graph each of the following vectors. 3v W
Use the vectors in the figure at the right to graph each of the following vectors. u + v W
Use the vectors in the figure at the right to graph each of the following vectors. v + w W
True or False. Mass is an example of a vector.
True or False. Force is an example of a vector.
If F1 and F2 are two forces simultaneously acting on an object, the vector sum F1 + F2 is called the ________ force.
If v = ai + bj then a is called the component of v and b is called the component of v.
If is v = an algebraic vector whose initial point is the origin, then v is called a(n) ________ vector.
A vector u for which |u| = 1 is called a(n) _______ vector.
If v is a vector, then v + (-v) = ______ .
A _________ is a quantity that has both magnitude and direction.
(a) Considered the expression an = (an-1)2 +Z , where z is some complex number (called the seed) and a0 = z. Compute a1(=a20 + z), a2(=a21 + z), a3(=a22 + z), a4, a5 and a6 for the following seeds:
Prove equation (6). [cos(01 – 02) + i sin(0, – 02)] Z2 Z1 (6) r2
Refer to Problem 64. Show that the complex nth roots of a nonzero complex number w are equally spaced on the circle.
Use the result of Problem 63 to draw the conclusion that each complex nth root lies on a circle with center at the origin. What is the radius of this circle?
Show that each complex nth root of a nonzero complex number w has the same magnitude.
Find the six complex sixth roots of unity (1) and plot them.
Find the four complex fourth roots of unity (1) and plot them.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fifth roots of -i.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fifth roots of i.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex cube roots of -8.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of -16i.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex cube roots of -8 - 8i
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of 4 - 4√3i.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of √3 - i.
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex cube roots of 1 + i.
Write the expression in the standard form a + bi. (1 - √5i )8
Write the expression in the standard form a + bi. (√2 – i)6
Write the expression in the standard form a + bi. (√3 – i)6
Write the expression in the standard form a + bi. (1 – i)5
Write the expression in the standard form a + bi. 5 /3 cos + i sin 18 [v{(com 18
Write the expression in the standard form a + bi. 14 Зт V5 Зп + i sin Cos 16 16
Write the expression in the standard form a + bi. (cos 72° + i sin 72°) 75
Write the expression in the standard form a + bi. 16 [V3 (cos 10° + i sin 10°) |º
Write the expression in the standard form a + bi. 5п + i sin 16 COS 16
Write the expression in the standard form a + bi. 15 п 21 cos 10 m + i sin 10
Write the expression in the standard form a + bi. [3(cos 80° + i sin 80°)]3
Write the expression in the standard form a + bi. [4(cos 40° + i sin 40°)]3
Find zw and z/w Leave your answers in polar form.z = 1 - i w = 1 - √3i
Find zw and z/w Leave your answers in polar form.z = 2 + 2i w = √3 - i
Find zw and z/w Leave your answers in polar form. Зт Зп + i sin z = 4| coS 9п 92 i sin w = 2| cos + 16 16
Find zw and z/w Leave your answers in polar form. + i sin cos z = 2| cOS т COS 10 т + i sin w = 2 cos cos 10,
Find zw and z/w Leave your answers in polar form.z = 2(cos 80° + i sin 80°) w = 6(cos 200° + i sin 200°)
Graph the system of linear inequalities. | 4х — 5y < 0 |2х — у2 2
Graph the system of linear inequalities. 2х — уS 4 Зх + 2у 2-6 -6
Graph the system of linear inequalities. [3x - y z 6 3.x x + 2y < 2
Graph the system of linear inequalities. Sx + y< 2 | 2x + y z 4
Graph the inequality. xy ≤ 1
Graph the inequality. xy ≥ 4
Graph the inequality. y > x2 + 2
Graph the inequality. y ≤ x2 - 1
Graph the inequality. x2 + y2 ≤ 9
Graph the inequality. x2 + y2 > 1
Graph the inequality. 3x + 2y ≤ 6
Graph the inequality. 2x + y ≥ 6
Graph the inequality. y ≤ 2
Graph the inequality. x ≥ 4
Graph the inequality. y ≥ 0
Graph the inequality. x ≥ 0
If a graph of a system of linear inequalities cannot be contained in any circle, then it is said to be _______.
True or False.The graph of a system of inequalities must have an overlapping region.
The graph of the corresponding equation of a linear inequality is a line that separates the xy-plane into two regions. The two regions are called_______.
When graphing an inequality in two variables, if the inequality is strict use ________; if the inequality is nonstrict use a________mark.
The graph of y = (x - 2)2 may be obtained by shifting the graph of _____ to the (left/right) a distance of _____ units.
True or False. The lines 2x + y = 4 and 4x + 2y = 0 are parallel.
Graph the equation: Y = x2 + 4.
Graph the equation: x2 + y2 = 9.
Graph the equation: 3x - 2y = 6
Solve the inequality: 3x + 4 < 8 - x.
Suppose that you are the manager of a sheet metal shop. A customer asks you to manufacture 10,000 boxes, each box being open on top. The boxes are required to have a square base and a 9-cubic-foot
A circle and a line intersect at most twice. A circle and a parabola intersect at most four times. Deduce that a circle and the graph of a polynomial of degree 3 intersect at most six times. What do
If r1 and r2 are two solutions of a quadratic equation ax2 + bx + c = 0Solve this system of equations for and r1 and r2 ь and riľ2 ri + r2 =
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. 2y2 – x2 = 14; at (2, 3)
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. x2 – y2 = 3; at (2, 1)
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. 3x2 + y2 = 7; at (-1, 2)
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. 2x2 + 3y2 = 14; at (1, 2)
Use Descartes’s method to find the equation of the line tangent to each graph at the given point. x2 + y = 5; at (-2, 1)

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