Concept explainers
LINKING
concepts...
For Individual or Group Explorations
Average Cost Per Drink
To save the environment, the Lion's Den Cafeteria sells an empty reusable 24–ounce plastic mug to students for $2.99. Using the mug. a student can get a 24–ounce soft drink for a reduced price of 69 cents.
a) If a student buys the mug and uses it only once, then what is the cost for that one drink?
b) If a student buys the mug and uses it twice, then what is the average cost per drink?
c) Does the average cost per drink increase or decrease as the mug is used more and more?
d) If the regular price of a 24–ounce soft drink is 89 cents, then when does the student start saving money?
e) Write a rational expression for which the value of the expression is the average cost per drink and n is the number of times the mug is used.
f) If a student buys the mug and uses it every day for a semester, then what is the approximate average cost per drink?
g) If a professional student buys the mug and uses it every day for many years, then what value is the average cost per drink approaching?
h) Use a computer to create a graph showing the number of drinks purchased and the average cost per drink. Make sure that the graph illustrates your answer to part (g).
Want to see the full answer?
Check out a sample textbook solutionChapter P Solutions
EBK COLLEGE ALGEBRA
- Question 5. Let A, B, C ben x n-matrices, S is nonsigular. If A = S-1 BS, show that det (A) = det (B) Question 6. For what values of k is the matrix A = (2- k -1 -1 2) singular? karrow_forward1 4 5 Question 3. Find A-1 (if exists), where A = -3 -1 -2 2 3 4 Question 4. State 4 equivalent conditions for a matrix A to be nonsingulararrow_forwardHow long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)arrow_forward
- Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forwardConsider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forward
- Question 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forwardAssume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forward
- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill