1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artist 52 [7]
3 years ago
12

Drag each tile to the correct box. Vector t, with a magnitude of 4 meters/second and a direction angle of 60°, represents a swim

mer’s motion. Arrange the vectors in ascending order of the magnitudes of their vector sums with the vector t.

Mathematics
1 answer:
astraxan [27]3 years ago
4 0

Answer:

From top to bottom, the boxes shown are number 3, 5, 6, 2, 4, 1 when put in ascending order.

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet tell you the magnitude of the sum. For a problem such as this, it is even more convenient to let the calculator give you all the answers at once.

The TI-84 image shows the calculation for a list of vectors being added to 4∠60°. The magnitudes of the sums (rounded to 2 decimal places—enough accuracy to put them in order) are ...

... ║4∠60° + 3∠120°║≈6.08

... ║4∠60° + 4.5∠135°║≈6.75

... ║4∠60° + 4∠45°║≈7.93

... ║4∠60° + 6∠210°║≈3.23

... ║4∠60° + 5∠330°║≈6.40

... ║4∠60° + 7∠240°║≈ 3

_____

In the calculator working, the variable D has the value π/180. It converts degrees to radians so the calculation will work properly. The abs( ) function gives the magnitude of a complex number.

On this calculator, it is convenient to treat vectors as complex numbers. Other calculators can deal with vectors directly

_____

<em>Doing it by hand</em>

Perhaps the most straigtforward way to add vectors is to convert them to a representation in rectangular coordinates. For some magnitude M and angle A, the rectangular coordinates are (M·cos(A), M·sin(A)). For this problem, you would convert each of the vectors in the boxes to rectangular coordinates, and add the rectangular coordinates of vector t.

For example, the first vector would be ...

3∠120° ⇒(3·cos(120°), 3·sin(120°)) ≈ (-1.500, 2.598)

Adding this to 4∠60° ⇒ (4·cos(60°), 4°sin(60°)) ≈ (2.000, 3.464) gives

... 3∠120° + 4∠60° ≈ (0.5, 6.062)

The magnitude of this is given by the Pythagorean theorem:

... M = √(0.5² +6.062²) ≈ 6.08

___

<em>Using the law of cosines</em>

The law of cosines can also be used to find the magnitude of the sum. When using this method, it is often helpful to draw a diagram to help you find the angle between the vectors.

When 3∠120° is added to the end of 4∠60°, the angle between them is 120°. Then the law of cosines tells you the magnitude of the sum is ...

... M² = 4² + 3² -2·4·3·cos(120°) = 25-24·cos(120°) = 37

... M = √37 ≈ 6.08 . . . . as in the other calculations.

You might be interested in
Is this a function ?
Sergio039 [100]

Answer:

it is a function

Step-by-step explanation:

the input is not repeated

6 0
3 years ago
4(c + d) -3c + 5d when c=1.5 and d= -6.2
patriot [66]

Answer:

-54.3

Step-by-step explanation:

4(1.5−6.2)−4.5−31

=(4)(−4.7)−4.5−31

=−18.8−4.5−31

=−23.3−31

=−54.3

7 0
3 years ago
Ms.Omar runs the school tennis club. She has a bin of tennis balls and rackets. For every 5 tennis balls in the bin, there are 3
stepan [7]

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> number of tennis balls

y ----> number of tennis rackets

we know that

To find out the ratio of tennis balls to tennis rackets, divide the number of tennis ball by the number of tennis rackets

In this problem we have

\frac{x}{y}=\frac{5}{3}

so

x=\frac{5}{3}y

That means

The number of tennis balls is three-fifths times the number of tennis rackets

see the attached figure to better understand the problem

8 0
3 years ago
Create a system of equations whose solution is <br> (−4, 7)<br> .
saveliy_v [14]
So 7 is greater I am not smart I am just trying to answers some question
5 0
3 years ago
Write 8 as a product of primes.<br> Use index notation
dimaraw [331]

Answer:

2³

Step-by-step explanation:

8 = 2 × 2 × 2 = 2³

4 0
2 years ago
Other questions:
  • Help me................
    15·1 answer
  • Gary jogs 2/3 of a mile in 1/3 of an hour. how many mipes can he jog in 1 hour?
    6·1 answer
  • I need help with 3-6
    10·1 answer
  • Pat has a lawn mowing business and has been experimenting with different prices in order to earn the most money. Some of the pri
    5·1 answer
  • A right triangle has a hypotenuse that is 15 inches long and one leg that 9 inches long what is the perimeter of the triangle
    8·1 answer
  • A.3/4-3/10<br><br> Do this for me please and this <br><br> B.3 1/2- 1 1/3
    8·1 answer
  • PLEASE HELP
    12·1 answer
  • What would the distance between the ordered pairs (-2,3) and (4,-6) be?
    5·1 answer
  • F(x) = x^2 - 4, X is greater/less than 0<br><br> (a) Find the inverse function of f.<br> F^-1(x) =
    5·1 answer
  • There are 4 aces and 4 kings in a standard deck of playing cards. you pick one random card at random. What is the probability of
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!