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
Sladkaya [172]
2 years ago
14

Let v1=(1, 6) and v2=(5, -3)

Mathematics
1 answer:
astraxan [27]2 years ago
3 0

Answer:

See Explanation;

Step-by-step explanation:

The given vectors are;

v_1=\:\: and v_2=\:\:

a) To add or subtract two vectors, we add or subtract their corresponding components

v_1+v_2=\:\:+\:\:

v_1+v_2=\:\:

v_1+v_2=\:\:

v_1-v_2=\:\:-\:\:

v_1-v_2=\:\:

v_1-v_2=\:\:

v_2-v_1=\:\:-\:\:

v_2-v_1=\:\:

v_2-v_1=\:\:

b) See attachment for graphs(1,6

You might be interested in
A. Find the amplitude.
Feliz [49]

Answers:

  • a) Amplitude = 2
  • b) Period = pi
  • c) Vertical shift = -2, which means it has been shifted down 2 units.
  • d) Horizontal shift = 3pi/8, this shifting is to the right.
  • e) There is <u>  one  </u> cycle between 0 and 2pi.
  • f) The equation of the graph is y = 2*sin(2(x-3pi/8))-2

========================================================

Explanations:

Part (a)

The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.

Note: Amplitude is always positive as it measures a distance.

---------------------

Part (b)

For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.

The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8

So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi

The graph repeats itself every pi units, so the period is pi.

---------------------

Part (c)

The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.

---------------------

Part (d)

This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.

The parent sine function y = sin(x) goes through the origin (0,0)

However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)

This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2

This must mean we need to shift the sine graph 3pi/8 units to the right.

---------------------

Part (e)

Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).

So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.

Overall, one full cycle is between 0 and 2pi.

---------------------

Part (f)

Again I'm going to use sine instead of cosine. Refer back to part (d).

The general sine curve equation is

y = A*sin(B(x-C))+D

where

  • |A| = amplitude
  • B handles the period, specifically T = 2pi/B where T is the period. We can solve for B to get B = 2pi/T
  • C = horizontal phase shift
  • D = vertical shift, and ties together with the midline equation

In this case, we found that

  • |A| = 2
  • T = pi leads to B = 2pi/T = 2pi/pi = 2
  • C = 3pi/8
  • D = -2

So,

y = A*sin(B(x-C))+D

will update to

y = 2*sin(2(x-3pi/8))-2

which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).

6 0
2 years ago
Which equation can be used to find one-tenth of 119.9
mel-nik [20]
To find one tenth of 119.9 just divide 119.9 by 10
3 0
2 years ago
At time t ≥ 0, the velocity of a body moving along the s-axis is v = t² -5t +4. When is the body moving backwards
katovenus [111]

Answer:

A

Step-by-step explanation:

The velocity of a moving body is given by the equation:

v=t^2-5t+4 ,\, t\geq0

Is the velocity is <em>positive </em>(v>0), then our object will be moving <em>forwards</em>.

And if the velocity is negative (v<0), then our object will be moving <em>backwards</em>.

We want to find between which interval(s) is the object moving backwards. Hence, the second condition. Therefore:

v

By substitution:

t^2-5t+4

Solve. To do so, we can first solve for <em>t</em> and then test values. By factoring:

(t-4)(t-1)=0

Zero Product Property:

t=1, \text{ and } t=4

Now, by testing values for t<1, 1<t<4, and t>4, we see that:

v(0)=4>0,\, v(2)=-20

So, the (only) interval for which <em>v</em> is <0 is the second interval: 1<t<4.

Hence, our answer is A.

7 0
3 years ago
Mr. Addis drove 136 miles on 8 gallons if gas. What is the unit rate?
barxatty [35]

Answer:

17 i think

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
I need help..... please
Bogdan [553]

Answer:

Step-by-step explanation:

I would say Town residents

5 0
2 years ago
Other questions:
  • Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle? 108° 127° 1
    11·2 answers
  • Cards numbered 1 through 15 are mixed up and placed in a bag. Malik chooses one of the cards without looking. What is the probab
    5·2 answers
  • Stacey Steady pays $19.95 per month for her fitness center membership. If she works out twice a week for a year, how much does s
    5·2 answers
  • Factors of x2 – 3x + 2 are<br>hy​
    13·1 answer
  • Find the inverse of each function<br><br> 1. f(x) = 4/(x+2) - 2<br><br> 2. f(x)= -2x^5 - 3
    9·2 answers
  • Angie is on a road trip, and is reading a map that has a scale of 1 in: 40 miles. Her trip measures 5.5 inches on the map. What
    6·1 answer
  • D =
    11·1 answer
  • Walter bought 500 marbles at the swap meet. Two-fifths of them
    9·1 answer
  • Is 6,9, 12 a right triangle, acute triangle or obtuse triangle???
    13·1 answer
  • Jim opens a savings account with $22,500. his account pays 3.5% interest compounded daily. at the end of 5.5 years, jim closes t
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!