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FinnZ [79.3K]
2 years ago
8

Solve the following:

Mathematics
1 answer:
olga_2 [115]2 years ago
5 0

Answer:

Do in calculator simple answer

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Write the equation of a line parallel to the line y=5x+2 that goes through the point (-4, 3).
almond37 [142]

Answer:

a line parallel to the line y = 5x + 2 ---> y' = 5x + b (b ≠ 2)

y' = 5x + b goes through (-4, 3) ---> 3 = 5 × ( -4 ) + b ---> b = 23

⇒ y' = 5x + 23

5 0
2 years ago
First drop down menu: 8.5, 40, 4, 7.5, 0
sashaice [31]

1st: 0.5 x 8 = 4

2nd: 2 x 8 = 16

3rd: 0.5 x 2 = 1

4th: 2 x 2 = 4

5 0
3 years ago
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
Zak and Ryan earn $60 per week for delivering pizzas. Zak worked for x weeks and earned an additional total bonus of $25. Ryan w
Inessa05 [86]

Answer:

60x + 25 + 60y

Step-by-step explanation:

60 times x plus 60 times y plus 25

4 0
3 years ago
Read 2 more answers
6 cm<br> 16 cm<br> What is the volume of the cylinder?
jenyasd209 [6]

V = 576 pi cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = pi * (6)^2 * 16

V = pi *36*16

V = 576 pi cm^3

5 0
3 years ago
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