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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Deposit amount: $450; total deposits: 60; interest rate: 4.5%, compounded quarterly
For the following exercises, use the information provided to graph the first five terms of the geometric sequence. a1 = 1, r = 1/2
For the following exercises, find the distinct number of arrangements.A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra’s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings
For the following exercises, graph the first five terms of the indicated sequence an = 4+n 2n 3+ n if n is odd if n in even
For the following exercises, write an explicit formula for each arithmetic sequence.a = {−18.1, −16.2, −14.3, ... }
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Deposit amount: $100; total deposits: 120; interest rate: 10%, compounded semi-annually
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.a1 = 3, an = 2an − 1
For the following exercises, find the distinct number of arrangements.A motorcycle shop has 10 choppers, 6 bobbers, and 5 café racers—different types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 café racers for a weekend showcase?
For the following exercises, write an explicit formula for each arithmetic sequence.a = {15.8, 18.5, 21.2, ... }
For the following exercises, graph the first five terms of the indicated sequencea1 = 2, an = (−an − 1 + 1)2
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.The sum of terms 50 − k2 from k = x through 7 is 115. What is x?
For the following exercises, find the distinct number of arrangements.A skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. How many different skateboards can be constructed?
For the following exercises, write an explicit formula for each arithmetic sequence. 4 a= { }, -, -3, ...} -} 3
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.an = 27 ⋅ 0.3n − 1
For the following exercises, graph the first five terms of the indicated sequencean = 1, an = an − 1 + 8
For the following exercises, find the distinct number of arrangements.Just-For-Kicks Sneaker Company offers an online customizing service. How many ways are there to design a custom pair of Just-For-Kicks sneakers if a customer can choose from a basic shoe up to 11 customizable options?
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Use recursive formulas to give two examples of geometric sequences whose 3rd terms are 200.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. Write an explicit formula for ak such that.Assume this is an arithmetic series. 6 Σ k = 0 a, = 189.
For the following exercises, write an explicit formula for each arithmetic sequence. { { } = y Z
For the following exercises, graph the first five terms of the indicated sequence a = n (n + 1)! (n − 1)!
For the following exercises, find the distinct number of arrangements.A car wash offers the following optional services to the basic wash: clear coat wax, triple foam polish, undercarriage wash, rust inhibitor, wheel brightener, air freshener, and interior shampoo. How many washes are possible if
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Use explicit formulas to give two examples of geometric sequences whose 7th terms are 1024.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Find the smallest value of n such that. η Σ k=1 (3k – 5) > 100
For the following exercises, write an explicit formula for each arithmetic sequence. a= -5, 10 3 5 동... 3 ..
For the following exercises, write an explicit formula for the sequence using the first five points shown on the graph. an 15- 13+ 11+ 9+ 7+ 5- 3+ 0 • (2,7) • (1,5) (3,9) • (5, 13) (4, 11) +n 1 2 3 4 5 6 7
For the following exercises, find the distinct number of arrangements.Susan bought 20 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 6 roses, and 8 daisies?
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Find the 5th term of the geometric sequence {b, 4b, 16b, ...}.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.How many terms must be added before the series −1 − 3 − 5 − 7.... has a sum less than −75?
For the following exercises, write an explicit formula for the sequence using the first five points shown on the graph. ап 8 7 6 5 Сл 4 3 2+ 1 (2, 1) • (3, 2) . (1, 0.5) +++ 0 1 2 3 . (5,8) . (4,4) 2 3 4 5 6 7
For the following exercises, find the number of terms in the given finite arithmetic sequence. a = {3, −4, −11, ... , −60}
For the following exercises, find the distinct number of arrangements.How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and 12 gold color bulbs?
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Find the 7th term of the geometric sequence {64a(−b), 32a(−3b), 16a(−9b), ...}.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Write 0.65 as an infinite geometric series using summation notation. Then use the formula for finding the sum of an infinite geometric series to
For the following exercises, write an explicit formula for the sequence using the first five points shown on the graph. 18- 15- 12+ 9+ 6+ 3 0 1 (1, 12) (2,9) 2 لیا (3,6) 3 (4,3) 4 5 (5,0) 6 7 H
For the following exercises, find the number of terms in the given finite arithmetic sequence.a = {1.2, 1.4, 1.6, ... , 3.8}
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.At which term does the sequence {10, 12, 14.4, 17.28, ...} exceed 100?
For the following exercises, find the number of terms in the given finite arithmetic sequence. a 7 = { 1, ², 3 , - , 8} 2, ..., 2 2
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?
For the following exercises, write a recursive formula for the sequence using the first five points shown on the graph. an 22 I 20+ 16+ 12- 8- 0 (1,6) • (3,9) (2,7) + 1 2 3 . (5,21) . (4, 13) 4 5 11
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.At which term does the sequence begin to have integer values? 1 1 1 1 1 2187 729' 243' 81
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.To get the best loan rates available, the Riches want to save enough money to place 20% down on a $160,000 home. They plan to make monthly deposits
For the following exercises, determine whether the graph shown represents an arithmetic sequence. an 5.5 ایا 4.5+ 4+ 3.5+ 3+ 2.5+ 2+ 1.5+ 14 0.5+ -0.50 -0.5+ -1+ -1.5+ -2+ -2.5+ -3+ -3.5- -4+ -4.5+ -5+ -5.5 (1,-4) (4,2) (3,0) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 (2,-2) (5,4)
For the following exercises, write a recursive formula for the sequence using the first five points shown on the graph. 16 12 + 8 4 0 1 (1,16) • (2,8) EN 2 - (3, 4) (4,2). +3 4 (5, 1) +n 5
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.For which term does the geometric sequence first have a non-integer value? a
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Karl has two years to save $10,000 to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he
For the following exercises, determine whether the graph shown represents an arithmetic sequence. 8.55 8+ 7.5+ 7+ 6.5+ 6+ 5.5+ 5+ 4.5+ 4+ 3.5+ 3+ 2.5+ 2+ 1.5+ 1+ 0.5+ برا • (2, 2.25) . (1, 1.5) . (3, 3.375) . (5, 7.5938) . (4, 5.0625) + + +n -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 -0.5t
For the following exercises, use the steps above to find the indicated term or terms for the sequence. Find the first five terms of the sequence a 4 12 37 a 3 n-1 fractional results. 87 111' Use the >Frac feature to give 11
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Use the recursive formula to write a geometric sequence whose common ratio is an integer. Show the first four terms, and then find the 10th term.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Keisha devised a week-long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and each successive day she will
For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence. a1 = 0, d = 4
For the following exercises, use the steps above to find the indicated term or terms for the sequence.Find the 15th term of the sequence a1 = 625, an = 0.8an − 1 + 18.
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Use the explicit formula to write a geometric sequence whose common ratio is a decimal number between 0 and 1. Show the first 4 terms, and then find the 8th term.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.A boulder rolled down a mountain, traveling 6 feet in the first second. Each successive second, its distance increased by 8 feet. How far did the
For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence. a1 = 9; an = an − 1 − 10
For the following exercises, use the steps above to find the indicated term or terms for the sequence.Find the first five terms of the sequence a1 = 2, an = 2[(an − 1) − 1] + 1.
For the following exercises, use the information provided to graph the first five terms of the geometric sequence.Is it possible for a sequence to be both arithmetic and geometric? If so, give an example.
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.A scientist places 50 cells in a petri dish. Every hour, the population increases by 1.5%. What will the cell count be after 1 day?
For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence.an = −12 + 5n
For the following exercises, use the steps above to find the indicated term or terms for the sequence.Find the first ten terms of the sequence a₁ = 8, a 71 (a₁ + 1)! n- a n-1
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels 3/4 the distance of the previous swing. What is
For the following exercises, follow the steps to work with the arithmetic sequence an = 3n − 2 using a graphing calculator:• Press [MODE]› Select [SEQ] in the fourth line› Select [DOT] in the fifth line› Press [ENTER]• Press [Y=]› nMin is the first counting number for the sequence.
For the following exercises, use the steps above to find the indicated term or terms for the sequence.Find the tenth term of the sequence a1 = 2, an = nan − 1
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. List the first five terms of the sequence. a 11 680 -n + 5/3
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Rachael deposits $1,500 into a retirement fund each year. The fund earns 8.2% annual interest, compounded monthly. If she opened her account when
For the following exercises, follow the steps to work with the arithmetic sequence an = 3n − 2 using a graphing calculator:• Press [MODE]› Select [SEQ] in the fourth line› Select [DOT] in the fifth line› Press [ENTER]• Press [Y=]› nMin is the first counting number for the sequence.
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.List the first six terms of the sequence. a = 72 n³ 3.5n² + 4.1n - 1.5 2.4n
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.List the first five terms of the sequence. a = 11 15n-(-2)"-¹ 47
For the following exercises, follow the steps to work with the arithmetic sequence an = 3n − 2 using a graphing calculator:• Press [MODE]› Select [SEQ] in the fourth line› Select [DOT] in the fifth line› Press [ENTER]• Press [Y=]› nMin is the first counting number for the sequence.
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.What are the first seven terms shown in the column with the heading u(n) in the [TABLE] feature?
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.List the first four terms of the sequence. a = 5.7" +0.275(n − 1)! 71
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Graph the sequence as it appears on the graphing calculator. Be sure to adjust the [WINDOW] settings as needed.
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.List the first six terms of the sequence an = n!/n .
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Give two examples of arithmetic sequences whose 4th terms are 9.
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.Consider the sequence defined by an = −6 − 8n. Is an = −421 a term in the sequence? Verify the result.
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Give two examples of arithmetic sequences whose 10th terms are 206.
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.What term in the sequence an = n2 + 4n + 4/2(n + 2) has the value 41? Verify the result.
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Find the 5th term of the arithmetic sequence {9b, 5b, b, … }.
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.Find a recursive formula for the sequence 1, 0, −1, −1, 0, 1, 1, 0, −1, −1, 0, 1, 1, ...
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Find the 11th term of the arithmetic sequence {3a − 2b, a + 2b, −a + 6b, … }.
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.At which term does the sequence begin to have negative values? 17 31 14 36' 3"]
For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary.Calculate the first eight terms of the sequences an = (n + 2)!/(n − 1)! and bn = n3 + 3n2 + 2n, and then make a conjecture about the relationship between
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.For which terms does the finite arithmetic sequencehave integer values? 5 19 9 2 8 4 1 8
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.At which term does the sequence {5.4, 14.5, 23.6, ...} exceed 151?
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Write an arithmetic sequence using a recursive formula. Show the first 4 terms, and then find the 31st term.
For the following exercises, follow the steps given above to work with the arithmetic sequence an = 1/2 n+5 using a graphing calculator.Write an arithmetic sequence using an explicit formula. Show the first 4 terms, and then find the 28th term.
For the following exercises, determine the equation for the parabola from its graph. Vertex (0, 0) Axis of symmetry Focus (0, 1) X
For the following exercises, determine the value of k based on the given equation.Given 6x2 + 12xy + ky2 + 16x + 10y + 4 = 0,find k for the graph to be an ellipse.
For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area = a ⋅ b ⋅ π.An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse, and use that
For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area = a ⋅ b ⋅ π.An arch has the shape of a semi-ellipse. The arch has a height of 12 feet and a span of 40 feet. Find an equation for the ellipse, and use that to find the distance from
For the following exercises, assume an object enters our solar system and we want to graph its path on a coordinate system with the sun at the origin and the x-axis as the axis of symmetry for the object's path. Give the equation of the flight path of each object using the given
For the following exercises, graph the given ellipses, noting center, vertices, and foci.x2 + 8x + 4y2 − 40y + 112 = 0
For the following exercises, graph the given ellipses, noting center, vertices, and foci.16x2 + 64x + 4y2 − 8y + 4 = 0
For the following exercises, use the given information about the graph of each ellipse to determine its equation.Center (4,2); vertex (9,2); one focus: (4 + 2 √6, 2).
For the following exercises, find the equation of the parabola given information about its graph. Vertex is (0,0); directrix is y = 4, focus is (0,−4).
For the following exercises, given information about the graph of a conic with focus at the origin, find the equation in polar form. Directrix is x = 3 and eccentricity e = 1
For the following exercises, determine the angle of rotation in order to eliminate the xy term. Then graph the new set of axes. 6x2 − 5√3 xy + y2 + 10x − 12y = 0
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.Directrix: y = 2/5 ; e = 7/2
For the following exercises, given information about the graph of the hyperbola, find its equation.Center: (3,5); vertex: (3,11); one focus: (3,5+2√10).
For the following exercises, find the equation of the parabola given information about its graph.Vertex is (1,2); directrix is y = 11/3, focus is (1,1/3).
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.Directrix: y = 4; e = 3/2
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