The table represents the equation y = 2 – 4x. A 2-column table with 5 rows. The first column is labeled x with entries negative

Answer:

E(t) = [ 4cos(t), 2 sin(t) ]

Step-by-step explanation:

The equation for the ellipse can be represented as:

 (x² ÷ a² ) + (y² ÷ b² ) = 1    Here, a and b symbolize the semi-major and semi-minor axes.

In this specific instance, we have    x²/16 + y²/ 4 = 1

This expression indicates that it follows the form of (x/a)² + (y/b)² =1

Specifically in our case,    x²/16  + y²/4 = 1, which resembles                 sin²α + cos²α = 1.

By setting x = 4 cos(t), we can proceed to calculate y.

Utilizing the equation x²/16  + y²/4 = 1, we find that:

x²/16  + y²/4 = 1   ⇒    (x²  +  4y²) ÷ 16  = 1

Solving for y yields: (x²  +  4y²)  = 16    ⇒  y²  = ( 16 - x²) ÷4

Substituting x = 4 cos(t) gives us y²  =  (16 - 16cos²(t)) ÷ 4, leading to y = √4 (1 - cos²(t)).

Consequently, we have y = 2 sin(t).

Thus, the vector parameterization of the ellipse can be stated as:

E(t) = [ 4cos(t), 2 sin(t) ]

Hello! I'm here to assist you! To calculate interest, we apply the formula prt, which involves multiplying the principal (the amount of money initially), the rate (the interest rate), and the time (typically in years). Here are the results:

$252 at 8% over 2 years yields $40.32
$400 at 2% for a duration of 6 months results in $4
$5,000 at 3.5% for 1 year gives $175
$6,240 at 10% for 9 months amounts to $468

For period calculations, we convert months into decimals: 6 months equals 0.5 years, and 9 months equals 0.75 years. Simply multiply the principal amount by the percentage in decimal form and by the time, and that’s it!