A hyperbola centered at the origin has vertices at (± √33,0) and foci at (± √59,0).

Write the equation of this hyperbola.

x^2/33 + y^2/26 = 1

Step-by-step explanation:

The formula for a hyperbola centered at the origin is:

x^2/a^2 - y^2/b^2 = 1

The vertices are located at (±a, 0), so we have that the value of a is √33

The foci are located at (±c, 0), where c^2 = a^2 + b^2

So if we have that c = √59, we can find the value of b:

59 = 33 + b^2

b^2 = 26

b = √26

So the formula for this hyperbole is:

x^2/33 + y^2/26 = 1

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: