The following definition is discussed in advanced mathematics courses.

Evaluate

Anish Buchanan
2021-10-05
Answered

The following definition is discussed in advanced mathematics courses.

Evaluate

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ensojadasH

Answered 2021-10-06
Author has **100** answers

Since

Since

Since

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The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $

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A car travels at 108 kph from A to B for t seconds, applies the brakes for 4 seconds between B and C to give the car a constant deceleration and a speed of 72 kph at C, and finally travels at this speed from C to D, also for t seconds. If the total horizontal distance from A to D is 3100 m, determine the distance between A and B.

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In the equation above, j and k are constants. If the equation is true for all positive real values of x and y, what is the value of

A)3

B)4

C)5

D)6

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Use the table to determine the total of the service charge. Sally Hudson's service charges: basic charge, 9 bills paid, lost card replacement, and 6 ATM transactions, 3 national and 3 out of network.

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The yield strength of CP titanium welds was measured for welds cooled at rates of \(10^{\circ}C/s,15^{\circ}C/s\ \text{and}\ 28^{\circ}C/s\). The results are presented in the following table. (Based on the article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds,” D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s.)

\(\begin{array}{}
\hline
\text{Cooling Rate}&\text{Yield Strenghts}\\
\hline
10&71.00&75.00&79.67&81.00&75.50&72.50&73.50&78.50\\
15&63.00&68.00&73.00&76.00&79.67&81.00\\
28&68.65&73.70&78.40&84.40&91.20&87.15&77.20&80.70&84.85&88\\
\hline
\end{array}\)

a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the yield strength of CP titanium welds varies with the cooling rate?

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Using the Mathematical Induction to prove that: ${3}^{2n}-1$ is divisible by 4, whenever n is a positive integer.

asked 2022-05-20

1a.

Show from first principles, i.e., by using the definition of linear independence,

that if μ = x + iy, y ̸= 0 is an eigenvalue of a real matrix

A with associated eigenvector v = u + iw, then the two real solutions

Y(t) = eat(u cos bt − wsin bt)

and

Z(t) = eat(u sin bt + wcos bt)

are linearly independent solutions of ˙X = AX.

1b.

Use (a) to solve the system (see image)