A new model is to be built to serve the towns of Sunnyvale and Gloomington, who’s centers are 6 miles apart. The developers want to locate the mall not more than 3 miles from the center of Sunnyvale and also not more than 5 miles from the center of Gloomington. Drawl a simple map showing Sunnyvale, Gloomington, and all potential locations for the new mall, based on the given information. Be sure to show the scale of your map. Explain how you determine do the possible locations for the mall.

Question

25-10-2022
Mathematics

Answered

A new model is to be built to serve the towns of Sunnyvale and Gloomington, who’s centers are 6 miles apart. The developers want to locate the mall not more than 3 miles from the center of Sunnyvale and also not more than 5 miles from the center of Gloomington. Drawl a simple map showing Sunnyvale, Gloomington, and all potential locations for the new mall, based on the given information. Be sure to show the scale of your map. Explain how you determine do the possible locations for the mall.

Answer :

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DavideJ196361 DavideJ196361 · Answer 1 · 2022-10-25T08:02:20-04:00

See explanation below

Explanation:

We are told the centres of the two towns are 6miles apart.

This means the distance between Sunnyvale and Gloomington = 6 miles.

We will draw a line with a distance of 6cm to indicate their distance apart.

The two end points of the line will indicate the location of Sunnyvale and Gloomington respectively.

For the developers to locate the mall not more than 3 miles from the center of Sunnyvale, we will draw a circle which has radius of 3cm. This way the mall doesn't exceed 3 miles from Sunnyvale.

For the developers to locate the mall not more than 5 miles from the center of Gloomington, we will draw a circle which has radius of 5cm. This way the mall doesn't exceed 5 miles from Gloomington.

The scale of the drawing will be 1cm represent 1 mile

You can use a compass(drawing tool) to draw the circles. adjusting the legs to suit the measurement of each radius.

The area under the each of the circles are all the possible locations of the map. The location of the new mall cannot go beyond the area under circles but can be within it.