Reeves
2021-09-22
Answered

Young’s modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article “Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis” (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)). If X¯ is the sample mean Young’s modulus for a random sample of n = 16 sheets, where is the sampling distribution of X¯ centered, and what is the standard deviation of the X¯ distribution?

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Arnold Odonnell

Answered 2021-09-23
Author has **109** answers

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)

asked 2021-02-05

Using "Proof by Contraposition",sho that: if n is any odd integer and m is any even integer, then, $3{m}^{3}+2{m}^{2}$ is odd.

asked 2020-12-16

At a certain university 523 of the seniors are history majors or math majors(or both).There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history?

asked 2022-03-26

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.

asked 2020-11-16

Advanced Math

A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of$2{m}^{2}$ . At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 $\frac{A}{c}{m}^{2}$ . The nominal operating temperature of the water electrolyzer stack is $70}^{\circ$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.

(Give your answer to at least three significant digits.)

Calculate the nominal stack voltage:

Answer in V

Calculate the nominal stack current:

Answer in A

Calculate the nominal power on the water electrolyzer stack:

Answer in kW

A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of

(Give your answer to at least three significant digits.)

Calculate the nominal stack voltage:

Answer in V

Calculate the nominal stack current:

Answer in A

Calculate the nominal power on the water electrolyzer stack:

Answer in kW

asked 2021-02-03

Express the following propositions in symbolic form, and identify the principal connective:

i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics.

ii.It is not the case case that if it is sunny then i will carry an umbrella.

i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics.

ii.It is not the case case that if it is sunny then i will carry an umbrella.

asked 2021-03-08

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