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study help
mathematics
precalculus
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions
In Problems 15 – 20, find the distance from P1 to P2.P1 = (−2, 2, 3) and P2 = (4, 0, −3)
In Problems 16–18, write each complex number in rectangular form, and plot each in the complex plane. 2e¹.5x/6
In Problems 15 – 20, find the distance from P1 to P2.P1 = (−1, 2, −3) and P2 = (0, −2, 1)
In Problems 15 – 22 , find(a) v × w,(b) w × v,(c) w × w,(d) v × v. v = 2i - 3j + k w = 3i - 2j - k
In Problems 15 – 20, find the distance from P1 to P2.P1 = (4, −2, −2) and P2 = (3, 2, 1)
In Problems 19–21, find zw and z/w. Write your answers in polar form and in exponential form. 4π Os +isin- 9 57 п w = cos + i sin 18 4π z = cos 5T 18
Find a so that the vectors v = i − aj and w = 2i + 3j are orthogonal.
If z = x + yi is a complex number, then the magnitude of z is: (a) x² + y2 (c) x² + y² (b) |x|+[y] (d) V[x] + 1y[
In Problems 19–22, v1 = 4i + 6j, v2 = −3i − 6j, v3 = −8i + 4j, and v4 = 10i + 15j.Find the vector v1 + 2v2 − v3.
In Problems 10–12, perform the given operation, whereWrite the answer in polar form and in exponential form. = 2(cos. COS 17π 36 z = + i sin 17T 36 and w= = 3( cos 11TT 90 11π + i sin- 90
In Problems 7 – 14, find the value of each determinant. A B 2 1 13 C 4 1
Rose curves are characterized by equations of the form r = a cos(nθ) or r = a sin(nθ), a ≠ 0. If n ≠ 0 is even, the rose has______ petals; if n ≠ ±1 is odd, the rose has______ petals.
In Problems 13 – 20, match each point in polar coordinates with either A, B, C, or D on the graph. -4- B -+----+ C D 1/60 -+-
In Problems 7 – 14, find the value of each determinant. A B C 4 3 02 31
For a positive real number a , which polar equation is a circle with radius a and center (a, 0) in rectangular coordinates? (a) r= 2a sin (c) r = 2a cos (b) r2a sin (d) r = -2a cos 0
In Problems 7 – 14, find the value of each determinant. A -1 C 5 в 3 50-2
In Problems 11–18, use the vectors in the figure at the right to graph each of the following vectors.2w W V ▬▬▬▬
In Problems 14–18,Find the position vector v equal to P1P2. P₁ = (3√2, 7√2) and P₂ = (8√2, 2√2).
If two nonzero vectors v and w are orthogonal, then the angle between them has what measure? (a) ㅠ (b) 2 (c) Зп 2 (d) 2
In Problems 7 – 14, find the value of each determinant. -2 2 5 -3
Find all the complex cube roots of −8 + 8√3i. Then plot them in the complex plane.
In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line θ= π/2. 2 r² cos0 = 5
In Problems 14 and 15, write each complex number in polar form and in exponential form.−1 − i
In Problems 9 – 18,(a) Find the dot product v · w;(b) Find the angle between v and w ;(c) State whether the vectors are parallel, orthogonal, or neither.v = i + 3j, w = i − j
If P is a point with polar coordinates (r,θ), the rectangular coordinates (x, y) of P are given by x = ____and y = ______.
True or False If z = reiθ is a complex number and n is an integer, then zn = rneiθ.
In Problems 7 – 14, describe the set of points (x, y, z) defined by the equation(s).x = 0
In a rectangular coordinate system, where does the point with polar coordinates(a) In quadrant IV(b) On the y-axis(c) In quadrant II(d) On the x-axis (1, FIN 2 lie?
True or False The tests for symmetry in polar coordinates are always conclusive.
If v is a vector with initial point (x1, y1) and terminal point (x2 , y2), then which of the following is the position vector that equals v? (a)(xz - X1, Y2 - Yi〉 (c) 2017.12말) (b) (X1 - X2, Y1 - Y2> (X1 + X2, Y1 + Yz Y2' 2 2 (d)
In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line θ= π/2. r = 5 sin cos²0
Graph the function y = |sin x|.
The pointcan also be represented by which polar coordinates? (5₁ ㅠ 6.
In Problems 7 – 14, find the value of each determinant. 6 -2 5 -1
Find the exact value of sin-¹(-1).
In Problems 7 – 10, the variables r and θ represent polar coordinates.(a) Write each polar equation as an equation in rectangular coordinates (x, y).(b) Identify the equation and graph it. r² + 4r sin0 - 8r cose = 5
In Problems 10–12, perform the given operation, whereWrite the answer in polar form and in exponential form. = 2(cos. COS 17π 36 z = + i sin 17T 36 and w= = 3( cos 11TT 90 11π + i sin- 90
In Problems 7 – 14, find the value of each determinant. -4 0 53
If v is a nonzero vector with direction angle α, 0° ≤ α < 360°, between v and i , then v equals which of the following? (a) |v|| (cosai sinaj) (c) ||v|| (sin ai cosaj) - (b) |v||(cosai + sin aj) (d) |v||(sin ai + cosaj)
Solve the each equation. sin 5 = 5π 4
True or Falsewhere θ is the angle between u and v . ||ux v|| = ||u|| ||v|| cose,
In space, points of the form (x, y, 0) lie in: xy-plane (a) the (c) the yz-plane (b) the xz-plane (d) none of these
The angle θ, 0 ≤ θ ≤ π, between two nonzero vectors u and v can be found using what formula? (a) sin (c) sin = ||u|| ||v|| u. V ||u|| ||v|| (b) cose (d) cose ||u|| ||v|| u. V ||u|| ||v||
If v = 3w, then the two vectors v and w are _______.
Solve the each equation. 2m cos 3 نیا
Solve the each equation.Simplify: e2· e5 = ______; (e4)3 =_____ .
True or False Given two nonzero, nonorthogonal vectors v and w, it is always possible to decompose v into two vectors, one parallel to w and the other orthogonal to w .
If P = (x, y) is a point on the terminal side of the angle θ at a distance r from the origin, then tanθ= _____.
Test the equation x2 + y3 = 2x4 for symmetry with respect to the x-axis, the y-axis, and the origin.
Suppose are two complex numbers. Then z1 z2 = ________. Z1 = re¹ and 2₂ = 72018₂
True or False Work is a physical example of a vector.
Solve the each equation.tan−1 (−1) = ______.
In Problems 7 – 14, find the value of each determinant. 3 12
The origin in rectangular coordinates coincides with the______ in polar coordinates; the positive x -axis in rectangular coordinates coincides with the______ _____ in polar coordinates.
In Problems 1–3, plot each point given in polar coordinates. Зп ( 2 ) 4
Find the real solutions, if any, of the equation ex²-9 = 1
In Problems 1–3, plot each point given in polar coordinates. 3, ㅠ 6.
In Problems 5–7, convert the polar equation to a rectangular equation. Graph the equation.r sin2θ+ 8 sinθ= r
Solve the each equcation. sin 2πT 3 ; COS 4π 3
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Write the equation of a circle with radius r = √5 and center (−4, 0) in standard from.
In Problems 1–3, plot each point given in polar coordinates. (-4, ㅠ r 3
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the domain of g (x) = 3|x2 − 1|− 5.
Plot the point whose rectangular coordinates are (3, −1). What quadrant does the point lie in?
The distance d from P1 = (x1, y1 ) to P2 = (x2 , y2) is d = _____.
The conjugate of − 4 − 3i is _______.
Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find an equation of the line perpendicular tothat contains the
Problems 71–80. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the horizontal asymptote of h(x) = -3x² 7x + 1 4 - 9x²
If the rectangular coordinates of a point are (4, −6), the point symmetric to it with respect to the origin is ____.
If v = a1i + b1 j and w = a2i + b2 j are two vectors, then the_____ _______ is defined as v · w = a1a2 + b1b2.
The distance between two points P1 = (x1, y1) and P2= ( x2 , y2 ) is d (P1, P2) = _______.
The Sum Formulas for the sine and cosine functions are:(a) sin(A + B) = ______.(b) cos(A + B) = _______.
True or False F or any vector v, v × v = 0.
If v · w = 0, then the two vectors v and w are ______.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.IfRound results to three decimal places. f(x) = f(4) x - 4 f(x)=√√x, find. for x = 5, 4.5, and
To complete the square of x2 + 6x, add ______.
The squares of the direction cosines of a vector in space add up to _________.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If the two triangles shown are similar, find x. 14 X 8 3
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve: |4x − 3| ≥ x + 1
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If h(x) is a function with range [−5, 8 ], what is the range of h(2x + 3)?
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Convert 96° to radians.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. ,(e²x - 1)² + (2e* )² 2 (e²x + 1)² Simplify
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve: x2 (5x − 3)( x + 2) ≤ 0
Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Determine whether h(x) = 5x3 − 4x + 1 is even, odd, or
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If f (x) = ax2 − 2x + 5 and a < 0, in which quadrant is the vertex located? How many x -intercepts
Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve: 1/3(x − 6) + 4x > 0
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Iffind the exact value of each of the four remaining trigonometric functions. tan 2√6 5 and cos 5 ן
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Determine whether x − 3 is a factor of x4 + 2x3 − 21x2 + 19x − 3.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the exact value of sin π/12.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve 2 sin2 θ − sinθ + 5 = 6 for 0 ≤θ < 2π.
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If a 4th degree polynomial function with real coefficients has zeros of 2 , 7, and 3 − √5, what
Problems 86 – 95. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.What is the remainder when P (x) = 2x4 − 3x3 − x + 7 is divided by x + 2?
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. If cos a (a) cos 2 3,0 < a < , find the exact value of: a 2 (b) sin- 8|2 (c) tan-
Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the exact value of 7 ₁ [cos-¹ (-3) ]- COS-1 8. tan
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find an equation for the graph. VA 3 A TT -3 TT 15/00 TIT 4 3п п 8 2 577 8 X
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. 2 √3-5x and g(x) = x² + 7, find g(f(x)) and If f(x)= its domain.
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. 1 - Inx. 2x x².1 x2 Solve:- 2 (x²)² 2 = 0
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. 4 3* In 3 x1/2 - 4.3x (√x)² Simplify:- 1 2 x-1/2
Problems 70–79. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Find f-1(x) if f(x) A 5x+2 A = 0.
Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. If cos 0 = 5 7 and tan < 0, what is the value of csc ?? and
Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.GraphShow at least two periods. y = 4 sin (1x).
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