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djverab [1.8K]
3 years ago
15

Simplify the given expression below: (4+2i)-(1–7i)

Mathematics
1 answer:
emmasim [6.3K]3 years ago
4 0

Answer:

3 + 9i

Step-by-step explanation:

(4 + 2i) - (1 - 7i)

distribute the (-)

(4 + 2i) - 1 + 7i

combine like terms

3 + 9i

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Solve/answer the question and help me understand this question please
faltersainse [42]

Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

<h3>understanding the direction</h3>

In navigation problems, direction angles are specified a couple of different ways. A <em>bearing</em> is usually an angle in the range [0°, 360°), <em>measured clockwise from north</em>. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

<h3>the two vectors</h3>

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

  • magnitude∠direction
  • magnitude <em>cis</em> direction

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

<h3>vector sum</h3>

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

<em>Additional comment</em>

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

7 0
2 years ago
What is 712 divided in 8 in long division
yuradex [85]

Answer:

89

Step-by-step explanation:

8 0
3 years ago
Which of the following could be the lengths of the sides of a 45°-45°-90° triangle?
Sunny_sXe [5.5K]
Answer would be <span>6.
i've done this one before.</span>
7 0
3 years ago
The length of your classroom is about 3.5 x 10^2 inches. If the hallway is ten times as long as the classroom, what is the lengt
tatuchka [14]

Answer:

3.5x10^3

Step-by-step explanation:

3.5x10^2 = 350

350x10 = 3500

3500 = 3.5x10^3

8 0
3 years ago
Which pair of triangles below shows the AAS Postulate. Explain
BabaBlast [244]

Answer:

<u>We can conclude that Δ XYZ ≅ Δ RST by AAS postulate</u>

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by AAS postulate because:

1. Their non-included sides YZ and ST are equal (10 units = 10 units).

2. Their angles ∠Y and ∠S are equal.

3. Their angles ∠X and ∠R are equal.

4.Their non-included sides XZ and RT are equal.

<u>Now, we can conclude that Δ XYZ ≅ Δ RST by AAS postulate.</u>

8 0
3 years ago
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