Any help w k? COMPOSITION OF FUNCTIONSYou just received a mystery discount coupon for a local department store. When the discount wasrevealed you were in luck, it was a 30% discount on all purchases. (Neglect sales tax in this application).rot madA. If your retail price for all merchandise purchased today is $105. 00 how much money do youneed to give to the cashier? Show your work.105 x.30: 31.50105-31.50 F1350B. Define the discount function, D(x) symbolically that represents the amount spent at the storebased on a retail price of x dollars.D CX = 30TooDU)= •3x/ade on #2) CC. Now let's say you have $20.00 in Krazy Cash for this same store. If you only used this "purchaseperk" how much money would you need to give the cashier?105-2085D. Define the Krazy cash function, K(x) symbolically that represents the amount spent at the storees down bybased on a retail price of x dollars.K(X)X =$105KLI05) :05-20=485=X-20E. Let's now say that the store will allow you to use both the 30%.discount and your $20.00 KrazyCash for your purchase, the $20. Krazy Cash first followed by the 30%. If you bought $105.00dollars today how much money would you give the cashier? Show your work.105-20: 85year.కం: 25585-25 559.5F. Define the composition (D o K)(x) symbolicallyFirst Krazy cash applied & then discounted,that is the first Kcx) functnon applied t after thatPx) firthon applied & KU) comes Inside ofthe funclon Dx) that is DCK(») G. Evaluate(Do K)(105). Does this agree with vour answer to part E? Explain.D (K(105)- Clo5)= 105-20=85 yes it agrees w/ the a boveNow DIKCX)) =D(85)=85-.30:85=59,50Parts Both results in$59,50H. Now let's assume the store will allow you to use the discount first followed by the $20.00 krazycas. ir you bought $105.00 dollars today how much monev would you give the cashier? Showyour work.105 x.30=31.50los -31 5073,5073.50-20 053.50I.Is this the same result as your answer in part E? Explain.nothey are not the Samebe cand the 30%. dedu ch nIS being tacen off Wi differen# Pnces.J.Define this composition as (K D)(x). Form this new composition symbolically.D(2)2.34(KOD)(x) 2 3K-20(K•D) (1O5),s: 3XLO5-20K. Evaluate (K D)(105).L Which is the better deal?

Answered: s: 3x K. Evaluate (K D)(105).

Math

Advanced Math

s: 3x K. Evaluate (K D)(105).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Question

Any help w k?

COMPOSITION OF FUNCTIONS
You just received a mystery discount coupon for a local department store. When the discount was
revealed you were in luck, it was a 30% discount on all purchases. (Neglect sales tax in this application).
rot mad
A. If your retail price for all merchandise purchased today is $105. 00 how much money do you
need to give to the cashier? Show your work.
105 x.30: 31.50
105-31.50 F1350
B. Define the discount function, D(x) symbolically that represents the amount spent at the store
based on a retail price of x dollars.
D CX = 30
Too
DU)= •3x/
ade on #2) C
C. Now let's say you have $20.00 in Krazy Cash for this same store. If you only used this "purchase
perk" how much money would you need to give the cashier?
105-2085
D. Define the Krazy cash function, K(x) symbolically that represents the amount spent at the store
es down by
based on a retail price of x dollars.
K(X)
X =$105
KLI05) :05-20=485
=X-20
E. Let's now say that the store will allow you to use both the 30%.discount and your $20.00 Krazy
Cash for your purchase, the $20. Krazy Cash first followed by the 30%. If you bought $105.00
dollars today how much money would you give the cashier? Show your work.
105-20: 85
year.
కం: 255
85-25 559.5
F. Define the composition (D o K)(x) symbolically
First Krazy cash applied & then discounted,
that is the first Kcx) functnon applied t after that
Px) firthon applied & KU) comes Inside of
the funclon Dx) that is DCK(»)

G. Evaluate(Do K)(105). Does this agree with vour answer to part E? Explain.
D (K(105)
- Clo5)= 105-20=85 yes it agrees w/ the a bove
Now DIKCX)) =D(85)=85-.30:85=59,50
Parts Both results in$59,50
H. Now let's assume the store will allow you to use the discount first followed by the $20.00 krazy
cas. ir you bought $105.00 dollars today how much monev would you give the cashier? Show
your work.
105 x.30=31.50
los -31 5073,50
73.50-20 053.50
I.
Is this the same result as your answer in part E? Explain.
nothey are not the Same
be cand the 30%. dedu ch n
IS being tacen off Wi differen
# Pnces.
J.
Define this composition as (K D)(x). Form this new composition symbolically.
D(2)2.34
(KOD)(x) 2 3K-20
(K•D) (1O5),
s: 3XLO5-20
K. Evaluate (K D)(105).
L Which is the better deal?

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