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(a)
The dimension over wires of the American national thread under given scenario.
Answer to Problem 32A
Dimension over wires of the American national thread
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
Where,
Also, it is given that
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
Here, we have been given
Putting above values in standard formula, we get-
Hence, dimension over wires of the American national thread
(b)
To calculate the dimension over wires of the American national thread under given scenario.
Answer to Problem 32A
Dimension over wires of the American national thread
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
Where,
Also, it is given that
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
Here, we have been given
Putting above values in standard formula, we get-
Hence, dimension over wires of the American national thread
(c)
To evaluate the dimension over wires of the American national thread.
Answer to Problem 32A
Dimension over wires of the American national thread
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
Where,
Also, it is given that
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
Here, we have been given
Putting above values in standard formula, we get-
Hence, dimension over wires of the American national thread
(d)
To evaluate the dimension over wires of the American national thread.
Answer to Problem 32A
Dimension over wires of the American national thread
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
Where,
Also, it is given that
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
Here, we have been given
Putting above values in standard formula, we get-
Hence, dimension over wires of the American national thread
(e)
To find the dimension over wires of the American national thread for the given parameters.
Answer to Problem 32A
Dimension over wires of the American national thread
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
Where,
Also, it is given that
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
Here, we have been given
Putting above values in standard formula, we get-
Hence, dimension over wires of the American national thread
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Chapter 16 Solutions
Mathematics For Machine Technology
- Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....arrow_forwardiii) i=5 x² = Σ i=1 (Yi — mi)² σ 2 By minimising oc², derive the formulae for the best values of the model for a 1 degree polynomial (2 parameters).arrow_forwardRefer to page 311 for a sequence of functions defined on a given interval. Instructions: • Analyze whether the sequence converges pointwise and/or uniformly on the given interval. • Discuss the implications of uniform convergence for integration and differentiation of the sequence. • Provide counterexamples if any condition fails. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forward
- Refer to page 310 for a matrix and its associated system of differential equations. Instructions: • Find the eigenvalues of the given matrix and classify the stability of the system (e.g., stable, • unstable, saddle point). Discuss the geometric interpretation of eigenvalues in the context of system behavior. • Provide conditions under which the system exhibits periodic solutions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 313 for a nonlinear differential equation and its linear approximation. Instructions: • Linearize the given nonlinear system around the equilibrium points. • Analyze the stability of each equilibrium using the Jacobian matrix and its eigenvalues. • Discuss the limitations of linearization for determining global behavior. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 314 for a matrix and its decomposed form. Instructions: • Verify the given singular value decomposition of the matrix. • • Discuss the geometric interpretation of the left and right singular vectors. Use the SVD to analyze the matrix's rank and nullity. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZ F/view?usp=sharing]arrow_forward
- Refer to page 312 for a set of mappings between two groups G and H. Instructions: • • Verify which of the provided mappings are homomorphisms. Determine the kernel and image of valid homomorphisms and discuss their properties. • State whether the groups are isomorphic, justifying your conclusion. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forward12:25 AM Sun Dec 22 uestion 6- Week 8: QuX Assume that a company X + → C ezto.mheducation.com Week 8: Quiz i Saved 6 4 points Help Save & Exit Submit Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment is closest to: Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided. 00:33:45 Multiple Choice О $6,984. $11,859. $22,919. ○ $9,469, Mc Graw Hill 2 100-arrow_forwardNo chatgpt pls will upvotearrow_forward
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