Graph the Hyperbola $3 y ^ { 2 } - 11 x ^ { 2 } = 1$

question 14

Multiple Choice

Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. $3 y ^ { 2 } - 11 x ^ { 2 } = 1$

• A) vertices: \(\left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right)\) ; Foci: \(\left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right)\) ; Length of transverse axis: \(\frac { 2 \sqrt { 11 } } { 11 }\) ; Length of conjugate axis: \(\frac { 2 \sqrt { 3 } } { 3 }\) ; Eccentricity: \(\frac { \sqrt { 154 } } { 11 }\) ; Asymptotes: \(y = \pm \frac { \sqrt { 33 } } { 11 } x\) .
• B) vertices: \(\left( \pm \frac { \sqrt { 11 } } { 11 } , 0 \right)\) ; Foci: \(\left( \pm \frac { \sqrt { 462 } } { 33 } , 0 \right)\) ; Length of transverse axis: \(\frac { 2 \sqrt { 3 } } { 3 }\) ; Length of conjugate axis: \(\frac { 2 \sqrt { 11 } } { 11 }\) ; Eccentricity: \(\frac { \sqrt { 154 } } { 11 }\) ; Asymptotes: \(y = \pm \frac { \sqrt { 33 } } { 3 } x\) .
• C) vertices: \(\left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right)\) ; Foci: \(\left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right)\) ; Length of transverse axis: \(\frac { 2 \sqrt { 3 } } { 3 }\) ; Length of conjugate axis: \(\frac { 2 \sqrt { 11 } } { 11 }\) ; Eccentricity: \(\frac { \sqrt { 154 } } { 11 }\) ; Asymptotes: \(y = \pm \frac { \sqrt { 33 } } { 3 } x\) .
• D) vertices: \(\left( \pm \frac { \sqrt { 3 } } { 6 } , 0 \right)\) ; Foci: \(\left( \pm \frac { 2 \sqrt { 3 } } { 3 } , 0 \right)\) ; Length of transverse axis: \(\frac { \sqrt { 3 } } { 3 }\) ; Length of conjugate axis: \(2\) ; Eccentricity: \(2\) ; Asymptotes: \(y = \pm \frac { \sqrt { 3 } } { 3 } x\) .
• E) vertices: \(\left( 0 , \pm \frac { \sqrt { 3 } } { 3 } \right)\) ; Foci: \(\left( 0 , \pm \frac { \sqrt { 462 } } { 33 } \right)\) ; Length of transverse axis: \(\frac { 2 \sqrt { 3 } } { 3 }\) ; Length of conjugate axis: \(\frac { 2 \sqrt { 11 } } { 11 }\) ; Eccentricity: \(\frac { \sqrt { 154 } } { 11 }\) ; Asymptotes: \(y = \pm \frac { \sqrt { 33 } } { 11 } x\) .

Determine the impact of changes in current asset and liability accounts on cash flows.

Explain the significance and calculation of free cash flow.

Understand the adjustments needed to reconcile net income with net cash provided by operating activities.

Recognize ethical considerations in financial management and reporting.

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Definitions:

Base Price

The initial cost of a good or service before any discounts, additional fees, or taxes are applied.

Percentage Discount

A reduction from the original price of a product or service expressed as a percentage of the original price.

Quantity Discount

A price reduction offered to buyers for purchasing large volumes, encouraging bulk purchases.

Optimal Number

The ideal or most efficient quantity or amount that achieves the best outcome under given constraints.