A tennis club offers two payment options. Members can pay a monthly fee of $30 plus $5 per hour for court rental time. The second option has no monthly fee, but court lime costs $7.50 per hour. a. Write a mathematical model representing total monthly costs for each option for x hours of court rental lime. b. Use a graphing utility to graph the two models in a [0, 15, 11] by [0, 120, 20] viewing rectangle. c. Use your utility's trace or intersection feature to determine where the two graphs intersect Describe what the coordinates of this intersection point represent in practical terms. d. Verify part (c) using an algebraic approach by selling the two models equal to one another and determining how man) hours one has to rent the court so that the two plans result in identical monthly costs.
A tennis club offers two payment options. Members can pay a monthly fee of $30 plus $5 per hour for court rental time. The second option has no monthly fee, but court lime costs $7.50 per hour. a. Write a mathematical model representing total monthly costs for each option for x hours of court rental lime. b. Use a graphing utility to graph the two models in a [0, 15, 11] by [0, 120, 20] viewing rectangle. c. Use your utility's trace or intersection feature to determine where the two graphs intersect Describe what the coordinates of this intersection point represent in practical terms. d. Verify part (c) using an algebraic approach by selling the two models equal to one another and determining how man) hours one has to rent the court so that the two plans result in identical monthly costs.
Solution Summary: The author calculates the model's equation for payment options by tennis club for the members.
A tennis club offers two payment options. Members can pay a monthly fee of $30 plus $5 per hour for court rental time. The second option has no monthly fee, but court lime costs $7.50 per hour.
a. Write a mathematical model representing total monthly costs for each option for x hours of court rental lime.
b. Use a graphing utility to graph the two models in a [0, 15, 11] by [0, 120, 20] viewing rectangle.
c. Use your utility's trace or intersection feature to determine where the two graphs intersect Describe what the coordinates of this intersection point represent in practical terms.
d. Verify part (c) using an algebraic approach by selling the two models equal to one another and determining how man) hours one has to rent the court so that the two plans result in identical monthly costs.
(1) Let M and N be non-empty subsets of a linear space X, show that whether
= U or not, and show that there whether exsits a liear function
from P₂(x) into R' which onto but not one-to-one or not.
ام
(2) Let R be a field of real numbers and P,(x)=(a+bx+cx? / a,b,ce R} be a vector space
over R, show that whether there exsit two hyperspaces A and B such that AUB is a
hyperspace or not.
(3) Let A be an affine set in a linear space X over afield F and tEA, show that A-t is a
subspace of Xand show that if M and N are balanced sets then M+N is balanced set.
(4) Write the definition of bounded set in a normed space, and write with prove
an equivalent statement to definition.
(5) Let d be a metric on a linear space X over a field F, write conditions on d in order to
get that there is a norm on X induced dy d and prove that.
(6) Let M be a non-empty subset of a normed space X, show that xEcl(M) iff for any r>o
there exsits yEM such that llx-yll
Find all solutions to the following equation. Do you get any extraneous solutions? Explain why or why
not.
2
2
+
x+1x-1
x21
Show all steps in your process. Be sure to state your claim, provide your evidence, and provide your
reasoning before submitting.
Directions: For problems 1 through 3, read each question carefully and be sure to show all work.
1. What is the phase shift for y = 2sin(2x-)?
2. What is the amplitude of y = 7cos(2x+л)?
3. What is the period of y = sin(3x-π)?
Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to
include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift
between the two graphs. Write in complete sentences.
4. y 3sin(2x) and y = 3cos(2x)
5. y 4sin(2x) and y = cos(3x- -플)
Chapter 1 Solutions
Algebra And Trigonometry 6th. Edition Annotated Instructor's Copy Blitzer
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.