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mathematics
precalculus

Questions and Answers of Precalculus

Graph the system of linear inequalities. x - 4y < 4 x – 4y 2 0
Graph the system of linear inequalities. | 2х (2х + у + y 2 -2 2
Graph the system of linear inequalities. x + 4y < 8 x + 4y 2 4
Graph the system of linear inequalities. – 2y < 6 х — 2у |2х — 4у 2 0 2.x
Graph the system of linear inequalities. 4x - y> 2 x + 2y 2 2
Graph the system of linear inequalities. | 2.х — Зу 0 Зу
An m by n rectangular array of numbers is called a(n)________.
A parabolic reflector (paraboloid of revolution) is used by TV crews at football games to pick up the referee’s announcements, quarterback signals, and so on. A microphone is placed at the focus of
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation for the curve. x = 3t – 2, y = - √t, 0 ≤ t ≤ 9
Identify the conic represented by the polar equation Find the rectangular equation. 1 - 2 cos 0
Given the equation 41x2 – 24xy + 34y2 – 25 = 0, rotate the axes so that there is no xy-term. Analyze and graph the new equation.
Identify each conic without completing the square or rotating axes. x2 – 6xy + 9y2 + 2x – 3y – 2 = 0
Identify each conic without completing the square or rotating axes. 3x2 – xy + 2y2 + 3y + 1 =
Projectile Motion Drew Brees throws a football with an initial speed of 80 feet per second at an angle of 35° to the horizontal.The ball leaves Brees’s hand at a height of 6 feet. (a) Find
Find zw and z/w Leave your answers in polar form.z = 3(cos 130° + i sin 130°) w = 4(cos 270° + i sin 270°)
Find zw and z/w Leave your answers in polar form.z = cos 120° + i sin 120°w = cos 100° + i sin 100°
Find zw and z/w Leave your answers in polar form.z = 2(cos 40° + i sin 40°)w = 4(cos 20° + i sin 20°)
Write a complex number in rectangular form. + i sin т 31 cos 10 т 10
Write a complex number in rectangular form. TT 2 cos cos + i sin 18 18
Write a complex number in rectangular form.0.4(cos 200° + i sin 200°)
Write a complex number in rectangular form.0.2(cos 100° + i sin 100°)
Write a complex number in rectangular form. IT + i sin 2. 4 cos cos 2
Write a complex number in rectangular form. Зт Зт + i sin 2 3 cos cos
Write a complex number in rectangular form. 5т 5п 2 cos + i sin 6.
Write a complex number in rectangular form. 4 cos + i sin 4
Write a complex number in rectangular form.3(cos 210° + i sin 210°)
Write a complex number in rectangular form.2(cos 120° + i sin 120°)
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. √5 - i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. -2 + 3i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 2 + √3i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 3 - 4i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 9√3 + 9i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 4 - 4i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. -2
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. - 3i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 1 - √3i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. √3 - i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. -1 + i
Plot complex number in the complex plane and write it in polar form. Express the argument in degrees. 1 + i
True or False. The polar form of a nonzero complex number is unique.
Every nonzero complex number will have exactly______distinct cube roots.
If z = r(cosθ + isinθ) is a complex number, then zn = ____ [cos(____) + isin(____)].
Let z1 = r1(cosθ1 + isinθ1) and z2 = r2(cosθ2 +isinθ2) be two complex. Then z1z2 = _____ [cos(____) + isin (____)].
When a complex number z is written in the polar form z = r(cosθ + isinθ), the nonegative number r is the _____ or _____ of z, and the angle θ, 0 ≤ θ < 2π is the _______ of
In the complex plane, the x-axis is referred to as the______ axis and the y-axis is called_______the axis.
sin 120° = ________; cos 240° = ______.
The sum formula for the cosine function is cos(A+B) = _______.
The sum formula for the sine function is sin(A+B) = _______.
The conjugate of -4 -3i is_______.
The tests for symmetry given are sufficient, but not necessary. Explain what this means.
Explain why the following test for symmetry is valid: Replace r by -r and θ by -θ in a polar equation. If an equivalent equation results, the graph is symmetric with respect to the line θ =
Show that the graph of the equation r = -2acosθ, a > 0 is a circle of radius a with center(-a,0) at in rectangular coordinates.
Show that the graph of the equation r = 2acosθ, a > 0 is a circle of radius a with center(a,0) at in rectangular coordinates.
Show that the graph of the equation r = -2asinθ, a > 0, is a circle of radius a with center at (0,-a) in rectangular coordinates.
Show that the graph of the equation r = 2asinθ, a > 0, is a circle of radius a with center at (0,a) in rectangular coordinates.
Show that the graph of the equation rcosθ = a is a vertical line a units to the right of the pole if a ≥ 0 and |a| units to left of the pole if a < 0.
Show that the graph of the equation r sinθ = a is a horizontal line a units above the pole a ≥ 0 if and units below the pole if a < 0.
Graph polar equation. r = cosθ/2
Graph polar equation. r = tanθ, -π/2 < θ < π/2 (kappa curve)
Graph polar equation. r = sinθ tanθ (cissoid)
Graph polar equation. r = cscθ - 2, 0 < θ < π (conchoid)
Graph polar equation. r = 3/θ, (reciprocal spiral)
Graph polar equation. r = θ, θ ≥ 0( spiral Archimedes)
Graph polar equation. (parabola) 1- cos e
Graph polar equation. (ellipse) 3 - 2 cos e
Graph polar equation. (hyperbola) 1- 2 cos e
Graph polar equation. (parabola) 1- cos 0
The polar equation for each graph is either r = a + bcosθ or r = a + bsinθ, a > 0 .Select the correct equation and find the values of a and b. (5. F)_= 7 (1,0) 2345 х e = 0 `'0 = 0 = 2
The polar equation for each graph is either r = a + bcosθ or r = a + bsinθ, a > 0 .Select the correct equation and find the values of a and b. (5. ) - ,0 = 7 8 = (4,0) х 123 A5 0 = 0 0 =
The polar equation for each graph is either r = a + bcosθ or r = a + bsinθ, a > 0 .Select the correct equation and find the values of a and b. в -7 в - в- т Зп х (6. 0- п e = 0
The polar equation for each graph is either r = a + bcosθ or r = a + bsinθ, a > 0 .Select the correct equation and find the values of a and b. Зп в - 3. 0 = (6, 0) х 0- т 02 458 100 = 0 в
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 1 + cosθ; r = 3cosθ
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 1+ sinθ; r = 1 + cosθ
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 3; r = 2 + 2cosθ
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = sinθ; r = 1 + cosθ
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 8sinθ; r = 4cscθ
Graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 8cosθ; r = 2secθ
Identify and graph the polar equation. r = 4cos(3θ)
Identify and graph the polar equation. r = 1- 3cosθ
Identify and graph the polar equation. r = 3 + cosθ
Identify and graph the polar equation. r = 1 - cosθ
Identify and graph the polar equation. r = 3θ
Identify and graph the polar equation. r = 2θ
Identify and graph the polar equation. r2 = cos(2θ)
Identify and graph the polar equation. r2 = 9cos(2θ)
Identify and graph the polar equation. r = 3cos(4θ)
Identify and graph the polar equation. r = 4sin(5θ)
Identify and graph the polar equation. r = 2sin(3θ)
Identify and graph the polar equation. r = 3cos(2θ)
Identify and graph the polar equation. r = 2 + 4cosθ
Identify and graph the polar equation. r = 2 - 3cosθ
Identify and graph the polar equation. r = 1 - 2sinθ
Identify and graph the polar equation. r = 1 + 2sinθ
Identify and graph the polar equation. r = 4 + 2sinθ
Identify and graph the polar equation. r = 4 - 2cosθ
Identify and graph the polar equation. r = 2 - cosθ
Identify and graph the polar equation. r = 2 + sinθ
Identify and graph the polar equation. r = 2 - 2cosθ
Identify and graph the polar equation. r = 3 - 3sinθ
Identify and graph the polar equation. r = 1+ sinθ

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