Gas mileage depends in part on the speed of the car. The gas mileage of a luxury car is given by L ( x ) = − 0.015 x 2 + 1.44 x − 21 , where 25 ≤ x ≤ 70 represents the speed in miles per hour and L ( x ) is given in miles per gallon. a .At what speed will the car get the maximum gas mileage? b .What is the maximum gas mileage? Round to the nearest whole unit.
Gas mileage depends in part on the speed of the car. The gas mileage of a luxury car is given by L ( x ) = − 0.015 x 2 + 1.44 x − 21 , where 25 ≤ x ≤ 70 represents the speed in miles per hour and L ( x ) is given in miles per gallon. a .At what speed will the car get the maximum gas mileage? b .What is the maximum gas mileage? Round to the nearest whole unit.
Solution Summary: The author calculates the speed at which the car will get maximum car mileage by using the ti-83 calculator.
Gas mileage depends in part on the speed of the car. The gas mileage of a luxury car is given by
L
(
x
)
=
−
0.015
x
2
+
1.44
x
−
21
, where
25
≤
x
≤
70
represents the speed in miles per hour and
L
(
x
)
is given in miles per gallon.
a.At what speed will the car get the maximum gas mileage?
b.What is the maximum gas mileage? Round to the nearest whole unit.
Let W={(0, a, 0) | a Є R}.
(a) List four elements from W.
(b) Determine whether W is a subspace of R³, and prove that your answer is
correct.
For this problem, refer to the network as shown in Figure 1, answer the following
questions.
B
A
C
FIGURE 1. For Problem (7).
Let x₁ be the number of users at website A.
Let x2 be the number of users at website B.
Let x3 be the number of users at website C.
Assume that there are a total of 900 users at these three websites. This gives us
the following system of linear equations:
x1 = x2 + 1x3
x2 = x1 + x3
x3 = x2
= 900
x1 + x2 + x3 =
(a) Put this system into a standard form (with all variables on the left side and
with the constants on the right), and convert that system into an augmented
matrix, and then...
(b) Use elementary row operations to put the augmented matrix into reduced row
echelon form, and then...
(c) Write down the solution space for this system of equations, and then...
(d) Identify which website(s) would be ranked most highly by PageRank.
4
2
Let C =
-6 -3
(a) Find det(C).
(b) Use your answer for (a) to determine whether C is invertible.
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.
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY