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In Freeport, Illinois, Empire Street runs east to west and route 26 runs north to south.

Zippy’s Pizza parlor is located on route 26, 3 miles south of Empire street.

Zippy’s advertises that it delivers within a 4 mile radius.



-Write an equation that represents the radius of delivery for Zippy’s Pizza. Assume that Zippy’s is located at the origin.
-How far east and west from route 26 can you live on Empire street and still receive Zippy’s Pizza delivery?
-Little Cubs Field is located 2 miles west and 4 miles north of Zippy’s. How far is Little Cubs Field from Zippy’s?
-How far is Little Cubs Field from the radius of delivery?

Respuesta :

The area of delivery of Zippy's Pizza given by a radius of delivery is a

circular area.

  • First Question: x² + y² = 4²
  • Second Question: √5 miles to the west and √5 to the east from route 26
  • Third Question; The distance between Little Cub's Field and Zippy is 2·√5 miles
  • Fourth Question: The distance between Little Cubs Field and the radius of delivery is 2·(2 - √5) miles.

Reasons:

Direction of Empire Street = East to west

Direction of route 26 = North to south

Location of Zippy's Pizza parlor on route 26 = 3 miles south of Empire street

The radius of the area Zippy makes delivery = 4 miles

Question One:

Required: Equation for the radius of delivery

Solution:

The equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

Where the center of the circle is at the origin, we have;

(h, k) = (0, 0)

Therefore, the equation that represents the radius of delivery for Zippy's Pizza is  is; (x - 0)² + (y - 0)² = r²

x² + y² = r²

The radius r = 4, the equation is therefore;

  • x² + y² = 4²

Second Question;

The equation that represents Empire street with Zippy's Pizza at the origin is y = 3

Therefore at the maximum distance east and west, along Empire street, we have;

x² + 3² = 4²

x² = 4² - 3² = 5

x = ±√5

The distance east and west along Empire street where one can still receive pizza are; √5 miles west and √5 east from Route 26

The maximum distances from route 26 a person can live on Empire street and receive pizza are;

  • √5 miles to the west and √5 to the east from route 26

Question Three;

The location of Little Cubs Field = 2 miles west and 4 miles north from Zippy's

The coordinates of Little Cubs Field relative to Zippy at the origin is therefore;

Little Cubs Field coordinates = (-2, 4)

The distance between Little Cub's Field and Zippy, d = √((-2)² + 4²) = 2·√5 miles

Question Four;

The distance between Little Cubs Field and the radius of delivery is given as follows;

D = d - r = 4 - 2·√5

The distance between Little Cubs Field and the radius of delivery is D = 2·(2 - √5) miles.

Learn more here:

https://brainly.com/question/6780708

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