Write the equation of the ellipse with center at (21), one vertex at (2-4), and one focus at (2,-2)

Step-by-step explanation:

The equation of an ellipse outside the origin is as follows

The above is for an ellipse centered on (h, k). in this case the center is in (2,1) so and

So far we have:

Now we find a and b, Where b is the semi-major axis and the minor semi-axis.

If the center is at (2, 1) and one focus is at (2,-2) this means there are 3 units of distance between the center and the focus. This quantity will be called c.

Now, of one vertex is at (2,-4) this means there are 5 units of distance between the center and the vertex, this is the semi major axis of the ellipse

⇒

and to find a:

clearing for a:

Substituting in the equation of the ellipse

wich is the second of the options.

answer:

1. 0.04

2. 0.15

step-by-step explanation:

i just finished that assignment for properties of probability distributions.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: