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(a) In high-dimensional geometry, given vectors of compatible dimensions are combined to produce a number called the dot product. For vectors with 31 components, like U and V here, the definition of their dot product is UV- Evaluate the dot product: UV= D UV

(a) In high-dimensional geometry, given vectors of compatible dimensions are combined to produce a number called the dot product. For vectors with 31 components, like U and V here, the definition of their dot product is UV- Evaluate the dot product: UV= D UV

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter7: Triangles
Section: Chapter Questions
Problem 1RP: We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to...
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Scroll to the bottom of this question to see a table defining two vectors, U and V, each with 31 components. (Note: The table has been carefully prepared to make it easy to copy-paste into a spreadsheet. Computer assistance is recommended in this problem.) 30 (a) In high-dimensional geometry, given vectors of compatible dimensions are combined to produce a number called the dot product. For vectors with 31 components, like U and V here, the definition of their dot product is U.V-U.VI. Evaluate the dot product: U. V= Now consider the generic integral I = u(x₁) = U₁, v(2₁) = V₁ link the numbers given in the table with the values of u and at the equally-spaced nodes ₁0+iAz, where Az = b-a 30 (b) Suppose I is defined using a = 0 and b = 1. Find the approximations for I indicated below. The right-endpoint Riemann sum with n = 30 subintervals: Ra The Trapezoidal approximation with = 30 subintervals: To (c) Suppose I is defined using a 1 and 6-6. Find the approximations for I indicated below. The Trapezoidal approximation with n= 15 subintervals: T₁s = The approximation from Simpson's Rule with n=10 subintervals: 510 = 0 Here are the definitions for U = (Ue,U₁,...,U30) and V = (V, V₁,..., V₁0). 4 1 2 3 4 7 -1 -1 8 6 -3 -3 7 4 5 27 5 6 # 6 -3 6 7 7 6 8 7 3 9 10 -[u(z)u(z) dir, where the key equations 7 11 11 2 9 12 -50 13 8 5 14 69 15 -20 16 3 -3 17 8 -3 18 7 -1 19 9 -1 20 3 1 21 -2 3 22 7 6 23 -2 3 24 2 7 25 7 -1 26 -4 2 27 -5 9 28 3 7 29 0 -1 30 4 -1 Ⓡ #
Transcribed Image Text:Scroll to the bottom of this question to see a table defining two vectors, U and V, each with 31 components. (Note: The table has been carefully prepared to make it easy to copy-paste into a spreadsheet. Computer assistance is recommended in this problem.) 30 (a) In high-dimensional geometry, given vectors of compatible dimensions are combined to produce a number called the dot product. For vectors with 31 components, like U and V here, the definition of their dot product is U.V-U.VI. Evaluate the dot product: U. V= Now consider the generic integral I = u(x₁) = U₁, v(2₁) = V₁ link the numbers given in the table with the values of u and at the equally-spaced nodes ₁0+iAz, where Az = b-a 30 (b) Suppose I is defined using a = 0 and b = 1. Find the approximations for I indicated below. The right-endpoint Riemann sum with n = 30 subintervals: Ra The Trapezoidal approximation with = 30 subintervals: To (c) Suppose I is defined using a 1 and 6-6. Find the approximations for I indicated below. The Trapezoidal approximation with n= 15 subintervals: T₁s = The approximation from Simpson's Rule with n=10 subintervals: 510 = 0 Here are the definitions for U = (Ue,U₁,...,U30) and V = (V, V₁,..., V₁0). 4 1 2 3 4 7 -1 -1 8 6 -3 -3 7 4 5 27 5 6 # 6 -3 6 7 7 6 8 7 3 9 10 -[u(z)u(z) dir, where the key equations 7 11 11 2 9 12 -50 13 8 5 14 69 15 -20 16 3 -3 17 8 -3 18 7 -1 19 9 -1 20 3 1 21 -2 3 22 7 6 23 -2 3 24 2 7 25 7 -1 26 -4 2 27 -5 9 28 3 7 29 0 -1 30 4 -1 Ⓡ #
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