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mathematics
precalculus

Questions and Answers of Precalculus

Problems 105 – 11. 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
Problems 105 – 113. 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
Problems 113–122. 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
Problems 113–122. 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
Problems 113–122. 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
Problems 113–122. 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
In Problems 69–82, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
In Problems 49–58, expand each sum. n k=1 (2k + 1)
In Problems 39–56, find each sum. 80 Σ(4n – 9) n=1
Find the coefficient of x4 in - - +. 0₁ (₂x − 1 ) +₁ + z(₂x − 1) + (₂x − 1) = (x)ƒ - OT
In Problems 49–58, expand each sum. k=1 k² 2 2
In Problems 39–56, find each sum. 90 Σ(3 – 2n) n=1
In the expansion offind the coefficient of the term containing a5b4c2. [a + (b + c)²],
In Problems 49–58, expand each sum. n k=1 (k + 1)2
In Problems 39–56, find each sum. 100 1 Σ(6-7η) n=1
Problems 53–62. 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
In Problems 49–58, expand each sum. n k=0 1 3k
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 2+ + ∞010 +=+
In Problems 39–56, find each sum. 80 1 Σ(n + 3)
Problems 53–62. 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.56.
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 2-13/1/201 + 8 1 32 +
Problems 53–62. 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
Problems 53–62. 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
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. ∞0 k=1 5 (1) ²-1
Problems 53–62. 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.
For v = 2i + 3j and w = 3i − 2j:(a) Find the dot product v · w.(b) Find the angle between v and w.(c) Are the vectors parallel, orthogonal, or neither?
In Problems 59–68, express each sum using summation notation. ਭੈ 3 + 13 13+1
In Problems 59–68, express each sum using summation notation. 11 3 3 - 1 + 12/17 - -- + (-¹) ²2 ( ²3 ) " (−1) 3/
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.8 + 4 + 2 + . . .
In Problems 59–68, express each sum using summation notation. 1+ 3 + 5 + 7 + + [2(12) - 1]
Problems 53–62. 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
In Problems 59–68, express each sum using summation notation. (뜬),(-) -... --+-1
Problems 53–62. 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
In Problems 69–80, find the sum of each sequence. 40 Σ5 k=1
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.8 + 12 + 18 + 27 + . . .
In Problems 59–68, express each sum using summation notation. 3+2 + +.
Problems 53–62. 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
In Problems 53–68, determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 은아름 3/ k=1 k-1
In Problems 59–68, express each sum using summation notation.1 + 2 + 3 + . . . + 20
In Problems 59–68, express each sum using summation notation.13 + 23 + 33 + . . . + 83
Old Faithful is a geyser in Yellowstone National Park named for its regular eruption pattern. Past data indicates that the average time between eruptions is 1h 35m.(a) Suppose rangers log the first
For Problems 47 – 52, use a graphing utility to find the sum of each geometric sequence. 15 n=1 n
Find the value of 2 + (5)(-4)³ + ({))*(³) · +(34)*()' + (4G)* + (0) (³3)² 5 5 5
In Problems 49–58, expand each sum. n + 2) k=1
In Problems 39–56, find each sum. 8 +81 +81 +8² + 4 8+8+9+ +50
The entries in the Pascal Triangle can, for n ≥ 2, be used to determine the number of k-sided figures that can be formed using a set of n points on a circle. In general, the first entry in a row
In Problems 41 – 46, find each sum. Η 24.31-1 k=1
Problems 37–45. 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
In Problems 41 – 46, find each sum. n k=1 ald 3/ k
Problems 37–45. 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
In Problems 35–48, a sequence is defined recursively. List the first five terms.a1 = 1; a2 = 2; an = an−1 · an−2
Problems 37–45. 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
Problems 113–122. 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
In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that х у u V 1 2 Z W 3 4
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. x *> 0 0 y > x + y 2 2 2x + 3y ≤ 12 3x + y ≤ 12
In Problems 17–50, find the partial fraction decomposition of each rational expression. 4 2x²5x 3 –
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x- y-z=1 2x+3y + z = 2 3x +
In Problems 25 – 54, solve each system. Use any method you wish. Х x² - 3xy + 2у2 = 0 x2 + xy = 6
In Problems 25 – 54, solve each system. Use any method you wish. x² - xy - 2y² = 0 xy + x + 6 = 0
In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that х у u V 1 2 Z W 3 4
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 2x + y = 0 x + y = 5
In Problems 17–50, find the partial fraction decomposition of each rational expression. 4x 2x² + 3x - 2 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x-3y - z = 0 - -x+2y + 2 =
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x - y = -1 x + 1/2y = 3/2
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. *> 0 yΣ 0 x + y> 1 x + y < 7 2x + y < 10
Maximize z = 10x + 4y subject to the constraints x ≥ 0, y ≥ 0, 4x − y ≥ −9, x − 2y ≥ −25, x + 2y ≥ 31, x + y ≥ 19, 4x + y ≥ 43, 5x − y ≥ 38, x − 2y ≥ 4
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 3x - y = 4 -2x+y= 5
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. х- у- у-2= = 1 -x + 2y - 3z
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x - y = 2x - 3z = 6 16 2y+z= 4
In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that х у u V 1 2 Z W 3 4
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 6x + 5y = 7 2x + 2y = 2
In Problems 25 – 54, solve each system. Use any method you wish. y² + y + x² - x - 2 = 0 x-2 y + 1 + y = 0
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x + y = -2y + 4z = 3x - 2z 2z -4 0 = -11
In Problems 17–50, find the partial fraction decomposition of each rational expression. 2x + 3 x4 - 9x² 2
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. -4x + y = 0 6x-2y = 14
In Problem 51–58, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the
In Problems 17–50, find the partial fraction decomposition of each rational expression. 2 x² +9 x4 - 2x² 8
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x - 3y z = 0 - 3x + 2y + 2z =
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x-2y + 3z = 6 4x-3y + 2z
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 6x + 5y = = 2x + 2y = = 13 5
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x - 4y + 2z =-9 3x + y + 2 = у+ -2x + 3y - 3z = 4 7
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. -4x + y = 5 6x - 2y =-9
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x + y - 3z = 0 -2x+2y +z=-1 -7 3x-4y-3z = 7
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x - 2y 2z = 2 2x + 3y + z = 2 3x + 2y = 0
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x+y - 2= 6 z = -5 3x-2y + x +
In Problem 51–58, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 3x-2y 7x-3y + 2z = -1 2x-3y +
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 2x + y = ax + ay = -3 -a a = 0
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x = y + z = -4 - 2x - 3y + 4z =
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -x + y + z = -1 -x + 2y3z = -4 3x - 2y 7z = 0 -
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + 2y z = -3 2x - 4y + z =
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 0 2x-3y-z = -x+2y + z = 5 3x-4y = 2=1 1 - z
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 7 a ax + ay = 5 2x + y = a=0
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. bx + 3y bx + 2y = 2b + 2 = 2b + 3 b = 0
In Problem 51–58, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x = y + z = -2y + z = 1 -2x - 3y = -4 4
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х Зу 2x-3y - z = 0 3x + 2y + 2z = 2 x +5y +3z = 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + 4y - 3z = -8 3x у + 3z
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x - 2y + 3z = 6 4x - 3y + 2z = 0 -2x + 3y - 7z = 1
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-2y 7x-3y 2x-3y + 2z 6 = + 2z = –1 + 4z = 0 =

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