If a scale distance of 3.5 inches on a map represent an actual distance of 175 km what actual distance does a scale distance of
1 answer:
Considering the definition of map and scale, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
<h3>Definition of map and scale</h3>A map is a representation of a place, at a size smaller than the real size.
The scale of a cartographic representation is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. That is, the scale is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.
One way to represent the scale is by a fraction, which indicates the proportion between the distance on a map and its corresponding distance in reality:
In this case, you know that a scale distance of 3.5 inches on a map represent an actual distance of 175 km.
To know the real distance that represents a scale distance of 5.7 inches, as the scale ratio is the same as in the previous case, it is expressed:
Solving:
×distance in reality= 5.7 inches
distance in reality=
<u><em>distance in reality= 269.59 km</em></u>
In summary, an actual distance of 269.59 km represent a scale distance of 5.7 inches .
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Answer:
The largest possible volume of the box is 2000000 cubic meters.
Step-by-step explanation:
The volume (), in cubic centimeters, and surface area (
), in square centimeters, of the box with a square base are described below:
(1)
(2)
Where:
- Side length of the base, in centimeters.
- Height of the box, in centimeters.
By (2), we clear within the formula:
And we apply in (1) and simplify the resulting expression:
(3)
Then, we find the first and second derivatives of this expression:
(4)
(5)
If and
, then we find the critical value of the side length of the base is:
Then, we evaluate this result in the expression of the second derivative:
By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:
The largest possible volume of the box is 2000000 cubic meters.