Find the Curvature K of the Curve $\mathbf { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + \frac { 7 t ^ { 3 } } { 4 } \mathbf { k } \text { at the point } P ( 2,20,14 )$

question 25

Multiple Choice

Find the curvature K of the curve $\mathbf { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + \frac { 7 t ^ { 3 } } { 4 } \mathbf { k } \text { at the point } P ( 2,20,14 )$ Round your answer to three decimal places.

• A)7.286
• B)9.952
• C)0.021
• D)0.014
• E)0.009

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Definitions:

Ledger Balance

The total balance of all accounts in a ledger at a particular point in time, reflecting the current financial position.

Trial Balance

An accounting table that consolidates all ledger balances into equivalent columns for debit and credit accounts.

T Accounts

T accounts are a visual representation used in accounting to depict ledgers, showing debits on the left and credits on the right.

Financial Statements

Reports that summarize the financial health, performance, and cash flows of a business for a specific period, typically including the balance sheet, income statement, and cash flow statement.