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xeze [42]
3 years ago
7

I Need Help

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
4 0

Answer:

c. : 4 times

Step-by-step explanation:

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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
1 year ago
The price of a leather coat is $150.00 plus 8% sales tax. What is the sales tax on the leather coat?
olasank [31]

Answer:

$12

Step-by-step explanation:

To find this, you just need to find 8 percent of 150. You can do this by multiplying 150 by .08, or multiplying 150 by 8/100.

5 0
2 years ago
Suppose two parallel lines are cut by a transversal. What angle relationships describe congruent angles in this context?
stiv31 [10]

Answer:

im pretty sure its the 3rd one.

Step-by-step explanation

6 0
3 years ago
Read 2 more answers
4. How many days of selling bicycles is involved in the study?<br>b. 40<br>c. 35<br>d. 10<br>a. 45​
Katarina [22]
Is there any other information that you can give us?
5 0
3 years ago
A clown is shot out of cannon with a velocity of 200 feet per second at an angle of 24°
Nadusha1986 [10]

Answer:

Vertical component of velocity is 81.35 ft/sec.

Horizontal component of velocity is  182.6 ft/sec.

Step-by-step explanation:

Horizontal component of velocity is defined as:

v_{x} = v\times cos\theta

Vertical component of velocity is defined as:

v_{y} = v\times sin\theta

Where v_{x} , v_{y} are the horizontal and vertical components of velocity.

v is the actual velocity and

\theta is the angle with horizontal axis at which the object was thrown.

Here, we are provided with the following:

v = 200 ft/sec

\theta = 24^\circ

v_{x} = 200 \times cos24^\circ\\\Rightarrow 200 \times 0.913\\\Rightarrow v_{x} = 182.6 ft/sec

v_{y} = 200 \times sin24^\circ\\\Rightarrow 200 \times 0.407\\\Rightarrow v_{y} = 81.35 ft/sec

So, Vertical component of velocity is 81.35 ft/sec.

Horizontal component of velocity is  182.6 ft/sec.

3 0
3 years ago
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