The background of a printed company logo is in the shape of an ellipse with height 30 inches and width 34 inches. Find an equation for the ellipse and use it to find the vertical width, in inches, of the logo background at a distance of 6 inches horizontally from the center. (Round your answer to the nearest hundredth if necessary.)

The equation of an ellipse is and the vertical width of ellipse at x = 6 inch from centre of ellipse is 28.06 inch.

Step-by-step explanation:

We know that, the equation of an ellipse with horizontal major axis with centre at (0,0):

    ------------------------------------(1)

According to the question,

inch⇒

inch⇒

After putting the value of and in the equation(1), we get

The equation of an ellipse is

⇒

⇒-----------------------------(2)

At inch from centre(0,0) of ellipse,

⇒ inch

Therefore, the total vertical width of ellipse at x = 6 inch from centre of ellipse = = 28.06 inch

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk