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
Sliva [168]
3 years ago
9

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En

ter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 1). 0 ≤ t ≤ 2π. (b) Two times around counterclockwise, starting at (4, 1). 0 ≤ t ≤ 4π. (c) Halfway around counterclockwise, starting at (0, 5). 0 ≤ t ≤ π.
Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
7 0

Answer:

a) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t, b) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t, c) x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right), y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right).

Step-by-step explanation:

The equation of the circle is:

x^{2} + (y-1)^{2} = 16

After some algebraic and trigonometric handling:

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t

Where:

\frac{x}{4} = \cos t

\frac{y-1}{4} = \sin t

Finally,

x = 4\cdot \cos t

y = 1 + 4\cdot \sin t

a) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

b) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

c) x = 4\cdot \cos t'', y = 1 + 4\cdot \sin t''

Where:

4\cdot \cos t' = 0

1 + 4\cdot \sin t' = 5

The solution is t' = \frac{\pi}{2}

The parametric equations are:

x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right)

y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)

You might be interested in
Can somebody help me with this :) ??
rjkz [21]

Answer:

A. (5,9)

Step-by-step explanation:

First, you need to reflect across the line of reflection. Since the point is 7 units from the line y=2 from one side, it will be 7 units away when it is reflected. 2+7=9, so the reflected coordinates of the point are (-2,9). For the glide translation, you slide the point 7 units to the right, placing it at the final location of (5,9). Hope this helps!

8 0
3 years ago
Subtract. Express your answer in simplest form. 5/8−1/6 =
bazaltina [42]

Answer:

0.45833..... OR \frac{11}{24}

Step-by-step explanation:

The common denominator is 24.

You get: \frac{15}{24} and \frac{4}{24}

Subtracting you get: \frac{11}{24}

<em>Hope this helps!!</em>

4 0
3 years ago
Please help!! ASAP due at 3 pm!!
Maru [420]

Answer:

  • 19

Step-by-step explanation:

<u>Given function: </u>

  • f(x)=3x+4

<u>If domain is 5 the corresponding range value is:</u>

  • f(5) = 3(5) + 4 = 15 + 4 = 19
6 0
2 years ago
Write an equation in slope-intercept form of the line that passes through the givin point and is parcel to the graph of the give
Serhud [2]

The answer is X=4.

It is both parallel to x=-3 and passes through (4,2)

5 0
3 years ago
What’s the answer for 6x + 5 = 2x -15 ?
lakkis [162]

Answer:

x=-5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Check picture to answer
    11·1 answer
  • Solve for g <br> 4(g-1)+2(g+5)=36
    11·2 answers
  • Name two linear expression whose difference is 5x-4
    5·1 answer
  • The ratio of books are 9:11 what percent of the reading materials are books plzzz help
    8·1 answer
  • Find the factors of 45
    7·2 answers
  • Amelie works on her homework for 14 hour before her soccer practice and 23 hour after her soccer practice.
    7·2 answers
  • 4 cookies cost $7. At this rate, how much will 9 cookies cost?
    10·1 answer
  • What is y +9 =2(x +5) in slope intercept form?
    15·2 answers
  • Very happy if u answer my question u will make my day ​
    8·1 answer
  • 525, 650, 539, 643, 764, 539, 687<br> What is the interquartile range of these numbers
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!