Shannon rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 13.

Response:

Volume of the trapezoidal prism = 15x^2 cubic units

Detailed explanation:

First, let’s calculate the area of the trapezoidal bases.

The lengths of the parallel sides are x and 2x, averaging to 1.5x.

The height stands at x

Consequently, area of the trapezoidal base comes out to be 1.5x * x = 1.5x^2

The volume of this prism is computed as area of the base multiplied by height

(the length is not a factor, but height certainly is)

Thus, 1.5x^2 * 10 yields 15x^2

An inverse function will also qualify as a function if the original is a One-to-One function. This means that each y value corresponds to exactly one x value, thus ensuring that the inverse remains a function.

The function shown in option C meets this criteria, as all x values and y values are distinct. Therefore, the inverse of the function in option C will also be a functional relation.

In contrast, other options have repeated y values, indicating they do not exhibit the one-to-one characteristic.

Hence, the correct answer is option C

The result is calculated as 10 multiplied by 8 multiplied by 5, which equals 400.

To determine the time interval δt, we must subtract the starting time from the ending time. In this scenario, the first value in the coordinates signifies time:

δt=50 - 0
δt= 50s

The time interval is 50s.

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) ]