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
The table above shows the weekly salaries and commission of ten salespeople. What is the interquartile range of the data? Usa te
egoroff_w [7]

Answer: A) 150

You put all the numbers in numerical order, than you get the middle number of both halves which will be 300 and 450, so you find the difference of that which is 150

8 0
3 years ago
Gina looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one
Alja [10]
No. A square has equal sides that are perpendicular and parallel. I'm guessing this room resembles some other figure.
8 0
3 years ago
Read 2 more answers
Find the smallest possible interger value n for which 99n is a multiple of 24
motikmotik
I would guess that you would need to find the Least Common Multiple (LCM) of 99 and 24 first. 

After listing out all of the multiples, you would have 792 be the LCM of 99 and 24. But since we need to find the integer value of n, in 99n (which means 99 x n), then we need to divide 792 by 99, which would be 8.

n = 8 
3 0
3 years ago
Read 2 more answers
A 2-column table with 5 rows. Column 1 is labeled Decimal with entries 0.1 6 repeating, 0.3 repeating, 0.5, x, 0.8 3 repeating.
Sindrei [870]

Answer:

A 2-column table with 5 rows. Column 1 is labeled Decimal with entries 0.1 6 repeating, 0.3 repeating, 0.5, x, 0.8 3 repeating. Column 2 is labeled Fraction with entries one-sixth, two-sixths, three-sixths, four-sixths, five-sixths.

Which best shows how the table can be used to determine the missing value x?

2(two-sixths) equals four-sixths, so 2(0.5) = 1, and x = 1.

4(1-sixth) equals four-sixths, so 4(0.16) = 0.64, and x = 0.64.

Three-sixths plus one-sixth equals four-sixths, so 0.5 + 0.16 = 0.6, and x = 0.6.

Five-sixths plus one-sixth equals four-sixths, so 0.83 + 0.16 = 0.99, and x = 0.9

4 0
3 years ago
9 gal/s=______at/min
Mnenie [13.5K]
9 gal............................................................1second
?how many gallons......................................60 seconds(1min)

to find out you do 9*60=540 gallons per minute
6 0
3 years ago
Read 2 more answers
Other questions:
  • Which expression has the same sum as the one below?
    14·2 answers
  • Please help 20 points
    15·1 answer
  • Subtract – 7x + 6 from – 2x^2 + 9x-2
    12·1 answer
  • The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the
    7·1 answer
  • What is 9×9+8-8÷10<br><br>Please And Thank You
    13·2 answers
  • Which line of poetry is marked correctly with weak and strong beats?
    6·1 answer
  • How. Many 5s is in 200989
    14·2 answers
  • Suppose A and B represent mutually exclusive events.
    8·1 answer
  • Please help me find the function rule, i dont know what to do!! I will give big brain
    5·1 answer
  • List three keywords that refer to multiplication ?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!