two cars leave town at the same time. one travels west at 56 mph, and the other travels south at 42 mph. after one hour, how far apart are the cars?
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To find the distance between the two cars after one hour, we can use the Pythagorean theorem.
Since the cars are traveling at right angles (west and south), we can consider their paths as the legs of a right triangle, and the distance between them as the hypotenuse.
Let's call the distance traveled by the car traveling west as "d1" and the distance traveled by the car traveling south as "d2".
To find d1, we can multiply the speed of the car traveling west (56 mph) by the time traveled (1 hour):
d1 = 56 mph * 1 hour = 56 miles
To find d2, we can multiply the speed of the car traveling south (42 mph) by the time traveled (1 hour):
d2 = 42 mph * 1 hour = 42 miles
Now, we can use the Pythagorean theorem to calculate the distance between the two cars (the hypotenuse):
distance^2 = d1^2 + d2^2
Plugging in our values, we have:
distance^2 = 56^2 + 42^2
distance^2 = 3136 + 1764
distance^2 = 4900
To find the distance between the cars, we need to take the square root of both sides:
distance = √4900
distance = 70 miles
Therefore, after one hour, the two cars are approximately 70 miles apart.
To find the distance between the two cars after one hour, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the triangle represent the distances traveled by each car in one hour. The westward car travels at 56 mph for one hour, covering a distance of 56 miles. The southward car travels at 42 mph for one hour, covering a distance of 42 miles.
Therefore, we have a right triangle with one side measuring 56 miles and the other side measuring 42 miles.
Using the Pythagorean theorem, we can calculate the hypotenuse, which represents the distance between the two cars after one hour.
The formula is given by:
c^2 = a^2 + b^2
where c is the hypotenuse (distance between the two cars), a is the distance traveled by the westward car, and b is the distance traveled by the southward car.
Plugging in the values, we get:
c^2 = 56^2 + 42^2
c^2 = 3136 + 1764
c^2 = 4900
Taking the square root of both sides, we get:
c = sqrt(4900) ≈ 70.0
Therefore, the distance between the two cars after one hour is approximately 70 miles.
Use the Pythagorean Theorem to find the diagonal (hypotenuse of right triangle).
a^2 + b^2 = c^2
56^2 + 42^2 = c^2