In matrix C , a coffee shop records the cost to produce a cup of standard Columbian coffee and the cost to produce a cup of hot chocolate. Matrix P contains the selling prices to the customer. Coffee Chocolate C = $ 0.90 $ 0.84 $ 1.26 $ 1.15 $ 1.64 $ 1.50 Small Medium Large Coffee Chocolate P = $3 .05 $2 .25 $ 3.65 $3 .05 $ 4.15 $3 .65 Small Medium Large a. Compute P − C and interpret its meaning. b. If the tax rate in a certain city is 7 % , use scalar multiplication to find a matrix F that gives the final price to the customer (including sales tax) for both beverages for each size. Round each entry to the nearest cent.
In matrix C , a coffee shop records the cost to produce a cup of standard Columbian coffee and the cost to produce a cup of hot chocolate. Matrix P contains the selling prices to the customer. Coffee Chocolate C = $ 0.90 $ 0.84 $ 1.26 $ 1.15 $ 1.64 $ 1.50 Small Medium Large Coffee Chocolate P = $3 .05 $2 .25 $ 3.65 $3 .05 $ 4.15 $3 .65 Small Medium Large a. Compute P − C and interpret its meaning. b. If the tax rate in a certain city is 7 % , use scalar multiplication to find a matrix F that gives the final price to the customer (including sales tax) for both beverages for each size. Round each entry to the nearest cent.
Solution Summary: The author calculates the difference between matrices C and P, which is the selling price to the customer and the cost to produce a cup of standard Columbian coffee.
In matrix
C
, a coffee shop records the cost to produce a cup of standard Columbian coffee and the cost to produce a cup of hot chocolate. Matrix
P
contains the selling prices to the customer.
Coffee
Chocolate
C
=
$
0.90
$
0.84
$
1.26
$
1.15
$
1.64
$
1.50
Small
Medium
Large
Coffee
Chocolate
P
=
$3
.05
$2
.25
$
3.65
$3
.05
$
4.15
$3
.65
Small
Medium
Large
a. Compute
P
−
C
and interpret its meaning.
b. If the tax rate in a certain city is
7
%
, use scalar multiplication to find a matrix
F
that gives the final price to the customer (including sales tax) for both beverages for each size. Round each entry to the nearest cent.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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