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
Irina-Kira [14]
3 years ago
10

Convert the equation r = 12 sin theta to Cartesian coordinates. Describe the resulting curve.

Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that there is a polar equation as

r=12 sin \theta

This has to be converted into cartesian.

We know the conversion is

r^2 =x^2+y^2 \\tan \theta = \frac{y}{x}

Using this we can say that

sin^2 \theta = 1-cos^2 \theta \\= 1-\frac{1}{sec^2 \theta} \\=1-\frac{1}{1+tan^2 \theta} \\=1-\frac{1}{1+\frac{y^2}{x^2} } \\=1-\frac{x^2}{x^2+y^2} \\=\frac{y^2}{y^2+y^2}

\sqrt{x^2+y^2} =12(\frac{y}{\sqrt{x^2+y^2} } \\x^2+y^2 =12y\\x^2+y^2-12y+36 = 36\\x^2+(y-6)^2 = 6^2}

Circle with centre (0,6) and radius 6.

You might be interested in
Is -15/2 a irrational number
Eduardwww [97]
No because it is equal to -7.5 I think
4 0
3 years ago
Read 2 more answers
In a call center that stays open all the time, calls arrive as a poisson process with a mean rate of 0.3 complaints per hour.(a)
DENIUS [597]

The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

Data;

  • Mean rate = 0.3
  • x = 50
  • standard deviation = ?

<h3>Poission Rule</h3>

Using poission formula,

P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431

b)

The probability the next call arrives after 2 hours.

\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488

c)

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

\lambda = 0.3 * 50 * 24 = 360

The mean = 360

The standard deviation is given as

S.D = \sigma =\sqrt{360} = 18.974\\

The probability the sum of these 50 number is less than 356 is

p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165

Learn more on poission formula here;

brainly.com/question/7879375

3 0
2 years ago
22 in<br> EESEE<br> EE<br> Area =<br> what is it
IRINA_888 [86]

Answer:

Look at my ista

Step-by-step explanation:

4 0
3 years ago
Given the graph below, which of the following statements is true?
Nesterboy [21]

To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.

To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.

<em>Of course, it passes the vertical line test, so its a function. </em>

<em>Does it pass the horizontal line test? </em><em>NO! </em><em>As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places. We therefore eliminate choices A and B. We can eliminate choice C because nowhere is it required a function to pass through the origin for it to be one-to-one. Hence, the answer is D (blue line shows this).</em>

<em>ANSWER: D</em>

6 0
2 years ago
Read 2 more answers
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new
faltersainse [42]

Answer:

The predictive value of a positive test is 18.2%.

Step-by-step explanation:

The population screened is 300.

The true prevalence value of the Lyme disease among clinic attendees is 10\% \Rightarrow 0.10.10% = 0.10.

The proportion that sensitivity is 60\% \Rightarrow 0.6060% = 0.60

The proportion of the specificity is 70\% \Rightarrow 0.70.70% = 0.70

Step 2 of 2

We have to calculate the probability value of the predictive value of positive test.

\begin{array}{c}\\\left( \begin{array}{l}\\{\rm{Positive Predictive }}\\\\{\rm{value}}\left( {PPV} \right)\\\end{array} \right) = \frac{{{\rm{Prevalence}} \times {\rm{Sensitivity}}}}{{\left( {{\rm{Prevalence}} \times {\rm{Sensitivity}}} \right) + \left( {{\rm{1 - Prevalence}} \times 1 - {\rm{Specificity}}} \right)}}\\\\ = \frac{{0.1 \times 0.60}}{{\left( {0.1 \times 0.60} \right) + \left( {1 - 0.1 \times 1 - 0.70} \right)}}\\\\ = \frac{{0.06}}{{0.33}}\\\\ = 0.181818\\\\ = 0.182{\rm{ }}\left( {{\rm{Round to 3 decimal place}}} \right)\\\end{array}  

(Positive Predictive  value, PPV) =

(Prevalence×Sensitivity)/Prevalence×Sensitivity +(1−Prevalence×1−Specificity)  

=   (0.1×0.60)/0.1×0.60  + (1−0.1×1−0.70) ​  

=    0.06 /0.33    

=   0.181818

(Positive Predictive  value, PPV) = 0.182 (3decimals)    

We have to convert the PPV into percentage,

\begin{array}{c}\\PPV = 0.182 \times 100\\\\ = 18.2\% \\\end{array}  

PPV=0.182×100

= 18.2% ​  

Therefore, the predictive positive value is 18.2%.

7 0
3 years ago
Other questions:
  • 13. In engineering notation, the number<br> 0.000452 is expressed as
    10·1 answer
  • What is the average walking rate in miles per hour if the distance(miles)=0.5. And the Time (min)= 12
    5·1 answer
  • the distance from the park to the grocery store is 0.9 mile. Ezra runs 8 tenths of that distance and walks the rest of the way.
    9·1 answer
  • Negative five teen divided by three
    8·1 answer
  • -7 is not an answer, do u mean -17? Cuz I have no ducking idea
    10·1 answer
  • If two angles are supplementary, then they are not congruent. Which diagram provides a counterexample for the statement?
    7·2 answers
  • The number 63 is how many times the number 21?
    6·2 answers
  • 3( x - 4) + 1 = 2x - 5 is it no solution or infinite solution or x = 16 or one solution
    11·1 answer
  • 1 أعط ثلاثة أمجلة
    15·1 answer
  • Francesca needs to buy 7 1/5 feet of packaging tape. There are 1 1/5 feet of tape on
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!