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
Nadusha1986 [10]
3 years ago
6

A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form

Mathematics
1 answer:
Over [174]3 years ago
6 0

Answer:

\vec{v}= \text{ or } \approx

Step-by-step explanation:

Component form of a vector is given by \vec{v}=, where i represents change in x-value and j represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector \vec{v}=, the magnitude is ||v||=\sqrt{i^2+j^2.

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being i, one leg being j, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}

To find the other leg, i, we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}

Verify that (9\sin 10^{\circ})^2+(9\cos 10^{\circ})^2=9^2\:\checkmark

Therefore, the component form of this vector is \vec{v}=\boxed{}\approx \boxed{}

You might be interested in
Find area of triangle .. help me please!
Zinaida [17]

Answer:

12 x 6 = 72, 72 divided by 2 ( x 1/2) = 36 yd^2

Formula of a triangle:

BH x 1/2

In this case 12 is your base and 6 is your height.

3 0
2 years ago
Read 2 more answers
What is 21.2264 rounded to the nearest tenths
Marizza181 [45]

21.2264 is 21.2 rounded to the nearest tenths; the place after the decimal is there tenths place so in the hundreths place, the number 2 is less than 5 therefore rounding it to 2.

7 0
3 years ago
Read 2 more answers
I know it is a long question but please I will mark brainlist to the person who answers please help
Diano4ka-milaya [45]

Answer:

Carla lives 16 miles from the Library.

The mistake is drawng the diagram incorrectly and using the miles given in the wrong places. The <u>student's</u> diagram has Yuri in a place that's Southwest of the Library in the diagram given

Step-by-step explanation:

If Yuri lives 24 miles SOUTH of the library, the "b" side of the triangle should be 24, with the Library at the top and Yuri at the bottom left, which is the west end of the base. The base "a" of the triangle should extend 10 to the right (East in compas directions) forming the right angle. Carla lives at the sharp southeast corner of the triangle, and the Hypotenuse "c"  from her house to the Library is the distance we have to figure.

c² =a² + b²

c² = 10² + 24²

c² = 100 + 576

c² = 676

√c² = √676

c = 26       Carla lives 26 miles from the Library.

3 0
3 years ago
What is the approximate area of a circle with a diameter of 50 centimeters? use π ≈ 3.14. 87.9 square centimeters 379.9 square c
zheka24 [161]
A=πr^2
The answer is 1962.5
6 0
3 years ago
Margot is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of
OverLord2011 [107]

Answer:

f(8) = 1.1(6.25)8; f(8) = 2561137

5 0
3 years ago
Read 2 more answers
Other questions:
  • How to solve this problem step by step
    12·1 answer
  • The graph represents the function g(x). Suppose that f(x) = -x. Which is true when comparing the range of f(x) to g(x)?
    12·1 answer
  • Help . Please need done in 15 minutes
    13·1 answer
  • A runner competes in a local marathon. He places 34th which is exactly the top 40% of all runners. How many runners competed
    7·1 answer
  • If the orginal quantity is 15 and the new quantity is 19 estimate the percent change of which of these is the best esitmate for
    13·2 answers
  • Which statement is correct?
    6·1 answer
  • HELP MEEEEEE DONT COMMENT UNLESS YOU KNOWWWWWWWWWW
    12·1 answer
  • You want to frame a picture that is 5in by 7in with a 2.5 inch-wide frame.
    7·1 answer
  • You have ​$95 in your bank account. Each week you plan to deposit ​$9 from your allowance and ​$10 from your paycheck. The equat
    11·1 answer
  • You can answer the ones you want to. At least one.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!