(a)
The value of circumference of circle.
Answer to Problem 11A
The circumference of circle is
Explanation of Solution
Given information:
The diameter given is d = 6.500"
The circumference of the circle is given by
Where
To calculate the circumference of the circle,
The circumference of the circle is
Conclusion:
Thus, the circumference of the circle is
(b)
The value of circumference of circle.
Answer to Problem 11A
The circumference of circle is
Explanation of Solution
Given information:
The diameter given is d = 30.000 mm
The circumference of the circle is given by
Where
To calculate the circumference of the circle,
The circumference of the circle is
Conclusion:
Thus, the circumference of the circle is
(c)
The value of circumference of circle.
Answer to Problem 11A
The circumference of circle is
Explanation of Solution
Given information:
The radius given is r = 18.600 mm
The circumference of the circle is given by
Where
To calculate the circumference of the circle,
The circumference of the circle is
Conclusion:
Thus, the circumference of the circle is
(d)
The value of circumference of circle.
Answer to Problem 11A
The circumference of circle is
Explanation of Solution
Given information:
The radius given is r = 2.930"
The circumference of the circle is given by
Where
To calculate the circumference of the circle,
The circumference of the circle is
Conclusion:
Thus, the circumference of the circle is
(e)
The value of diameter of circle.
Answer to Problem 11A
The diameter of circle is
Explanation of Solution
Given information:
The circumference given is C = 35.000"
The circumference of the circle is given by
Where
To calculate the diameter of the circle,
The diameter of the circle is
Conclusion:
Thus, the diameter of the circle is
(f)
The value of diameter of circle.
Answer to Problem 11A
The diameter of circle is
Explanation of Solution
Given information:
The circumference given is C = 218.000 mm.
The circumference of the circle is given by
Where
To calculate the diameter of the circle,
The diameter of the circle is
Conclusion:
Thus, the diameter of the circle is
(g)
The value of radius of circle.
Answer to Problem 11A
The radius of circle is
Explanation of Solution
Given information:
The circumference given is C = 327.000 mm.
The circumference of the circle is given by
Where
To calculate the radius of the circle,
The radius of the circle is
Conclusion:
Thus, the radius of the circle is
(h)
The value of radius of circle.
Answer to Problem 11A
The radius of circle is
Explanation of Solution
Given information:
The circumference given is C = 7.680".
The circumference of the circle is given by
Where
To calculate the radius of the circle,
The radius of the circle is
Conclusion:
Thus, the radius of the circle is
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Chapter 55 Solutions
Mathematics For Machine Technology
- 6. Norms and Metrics • Show that the function || || norm on Rn. = √xT Ax, where A is a positive definite matrix, defines a . Prove that the matrix norm induced by the vector L²-norm satisfies ||A||2 ✓ max (ATA), where Amax is the largest eigenvalue.arrow_forward2. Linear Transformations • • Let T: R3 R³ be a linear transformation such that T(x, y, z) = (x + y, y + z, z + → x). Find the matrix representation of T with respect to the standard basis. Prove that a linear transformation T : VV is invertible if and only if it is bijective.arrow_forward11. Positive Definiteness Prove that a matrix A is positive definite if and only if all its eigenvalues are positive.arrow_forward
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- 8. Determinants • • Prove that the determinant of a triangular matrix is the product of its diagonal entries. Show that det(AB) = det(A)det(B) for any two square matrices A and B.arrow_forward15. Tensor Products • • Define the tensor product of two vector spaces. Compute the tensor product of (1,0) and (0, 1) in R². Discuss the role of tensors in multilinear algebra and provide an example of a second-order tensor.arrow_forward20. Numerical Methods • Describe the QR decomposition method and explain its use in solving linear systems. • Solve the following system numerically using Jacobi iteration: 10x+y+z = 12, 2x+10y+z = 13, 2x+2y+10z = 14.arrow_forward
- 1. Vector Spaces • Prove that the set of all polynomials of degree at most n forms a vector space over R. Determine its dimension. • = Let VR³ and define a subset W = {(x, y, z) Є R³ | x + y + z = 0}. Prove that W is a subspace of V and find its basis.arrow_forward24. Spectral Decomposition Explain the spectral decomposition of a symmetric matrix and its applications. • Compute the spectral decomposition of: A = 5 4arrow_forward3. Eigenvalues and Eigenvectors • Find the eigenvalues and eigenvectors of the matrix: 2 1 A = = Prove that if A is a symmetric matrix, then all its eigenvalues are real.arrow_forward
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