Precalc Sheet Practice Flashcards

Comprehensive practice vocabulary flashcards covering Precalculus concepts including parametric equations, vector properties, linear transformations, and system states based on the provided review sheet.

Horizontal and Vertical Radii

The horizontal radius is $16$ inches and the vertical radius is $8$.

Horizontal Parabola Equation

$$x = 2y^2 + 16y + 35$$

Circumference Measurement

$$18.856\,ft$$

Linear Transformation N

Only N could be a linear transformation function because it must satisfy additive and scaling properties.

Transformation h

Produces a rotation of vectors by $1$ radian clockwise about the origin.

Inverse Relationship of A and B

A and B must be inverses of each other if their linear transformation effects are reversed.

Column Vector Solutions

A column vector that contains the solutions to the system of equations.

Transition Probability (State 1 to State 2)

The probability that an object in state 1 at step $n = 0$ will be in state 2 at step $n = 3$ is $\frac{1}{3}$. (Incorrect value corrected to transcript: 1/3)

Steady State of State 1 and State 2

The steady state of State 1 is $50\%$ and the steady state of State 2 is $50\%$.

Long-run System Distribution

Because the vector remains unchanged, the system has about $30\%$ in one state and $70\%$ in the other.

Hyperbola Parametric Equations

$x(t) = 2 + \sec(t)$ and $y(t) = 1 - 3\tan(t)$.

Real Zero t_0 Function property

If $t_0$ is a real zero, then $y(t_0)$ gives the y-coordinate of a y-intercept of the graph.

Periods of g relative to f

Because the periods of the functions $x_2(t)$ and $y_2(t)$ that define g are half the periods of the functions $x_1(t)$ and $y_1(t)$ that define f, the graph of g traverses the graph of f twice for $0 \le t \le 2\pi$.

Additive Transformation of a Circle

The transformation of the graph of the circle does not change the radius but it does change the location of the center because the transformation is additive, not multiplicative.

Ellipse

A geometric shape specifically described as an ellipse that is not a circle.

Particle Position Farthest Left

The particle is farthest left at time $t = \pi$ seconds.

Particle 2 Path Direction

The path of particle 2 is clockwise about the top half of the circle.

Intervals Left of the y-axis

The particle is to the left of the y-axis on the intervals $0 \le t < 1.524$ and $3.584 < t < 4.833$.

Velocity at T=1 Second

The particle is moving right toward the y-axis because the x-component of position is negative and the component of velocity is positive.

Parallel Vector Condition

The components of one vector must be nonzero multiples of the components of the other vector.

Vector -2v Relationship

$-2v$ is parallel to v, has twice the magnitude of v, and is in the opposite direction of v.

Dot Product Calculation

The dot product of $u$ and $v$ is calculated as $(5)(3) + (-1)(-2)$.

Vector Magnitude and Direction (5)

The magnitude is $5$ and the head of the vector points up and to the right.