A new highway was built outside of tri town to relieve traffic on Route 1. How many miles are saved by traveling on the new high
1 answer:
By applying the Pythagorean Theorem, the number of miles saved is: 4 miles.
<h3>What is the Pythagorean Theorem?</h3>If c is the hypotenuse of a right triangle, and the lengths of the two legs are a and b respectively, the Pythagorean Theorem states that, c = √(a² + b²).
The diagram showing the new highway is attached below.
The diagram represents a right triangle. SO, apply the Pythagorean Theorem to find how long it is to travel on the new highway from point A to B.
Thus:
AB is the hypotenuse of the right triangle.
AB = √(AC² + BC²)
Plug in the values
AB = √(12² + 5²)
AB = 13 miles.
Moving from A to B without the highway = AC + BC = 12 + 5 = 17 miles.
Miles saved travelling on the new highway = 17 - 13 = 4 miles.
Therefore, by applying the Pythagorean Theorem, the number of miles saved is: 4 miles.
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Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
<u>Now let's calculate the area</u>
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
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AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| =
|AB X AC| =
|AB X AC| = 13.15
Area = 13.15 square units.
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<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.
The information about the rational numbers and integers shows that the correct option is C.
<h3>How to explain the information?</h3>It should be noted that rational numbers are numbers where we can write as a fraction of two integers. Any rational number is in the form a/b where a,b are integers and b is nonzero.
Terminating decimals can be written as a rational number. Something like 3.1 is equivalent to 31/10.
Of the four answer choices, only choice C is correct.
Choice A has the value '3' as a rational number, but it doesn't have it in the set of integers as well. So that's why choice A is incorrect.
Choice B has -3.4 in the set of integers, which is not correct. Integers do not have any decimal portion. The same applies to choice D also. We can rule choices B and D out.
Therefore, the correct option is C.
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