Find a Vector Function That Represents the Curve of Intersection $x ^ { 2 } + 5 y ^ { 2 } + 5 z ^ { 2 } = 25$

question 20

Multiple Choice

Find a vector function that represents the curve of intersection of the two surfaces: the top half of the ellipsoid $x ^ { 2 } + 5 y ^ { 2 } + 5 z ^ { 2 } = 25$ and the parabolic cylinder $y = x ^ { 2 }$ .

• A) \(\mathrm { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 25 - t ^ { 2 } - 5 t } { 5 } } \mathbf { k }\)
• B) \(\mathbf { r } ( t ) = t \mathbf { i } - t ^ { 2 } \mathbf { j } - \sqrt { \frac { 25 - t ^ { 2 } - 5 t } { 5 } } \mathbf { k }\)
• C) \(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 5 - t ^ { 2 } - 5 t ^ { 4 } } { 5 } } \mathbf { k }\)
• D)\(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 4 } \mathbf { j } + \sqrt { \frac { 25 - t ^ { 2 } + 5 t } { 5 } } \mathbf { k }\)
• E)\(\mathbf { r } ( t ) = t \mathbf { i } + t ^ { 2 } \mathbf { j } + \sqrt { \frac { 25 + t ^ { 2 } - 5 t ^ { 4 } } { 5 } } \mathbf { k }\)

Understand the impact of simultaneous changes in supply and demand on equilibrium.

Understand the impact of changes in demand and supply on equilibrium price and quantity.

Identify the consequences of government interventions such as price ceilings and price floors.

Describe the characteristics and determinants of market equilibrium.

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