Sketch a graph of the polar equation. how do I do the second one?
Express the equation in rectangular coordinates. (Use the variables x and y.) And the other one. on the next picture.
Answers
Answer:
\(y = - \frac{ \sqrt{3} }{3}x \)
\( {x}^{2} + {y}^{2} = 1\)
Step-by-step explanation:
You are correct with the graph, the angle
\( \frac{5\pi}{6} \)
should lies in the second quadrant so the polar graph will lie in the second quadrant then go to the fourth quadrant. It would be a line not a circle.
For the equation, use the tangent equation because it has y and x in it
\( \alpha = \frac{5\pi}{6} \)
\( \tan( \alpha ) = \tan( \frac{5\pi}{6} ) \)
\( \frac{y}{x} = - \frac{ \sqrt{3} }{3} \)
\(y = - \frac{ \sqrt{3} }{3} x\)
For the next picture, the graph is correct,
We know that
\( \cos {}^{2} (3t) + \sin {}^{2} ( {}^{}3t ) = 1\)
\( {x}^{2} + {y}^{2} = 1\)
Alternate Way:
\(x = \cos(3t) \)
\( \frac{ \cos {}^{ - 1} (x) }{3} = t\)
\(y = \sin(3( \frac{ \cos {}^{ - 1} (x) }{3} ) \)
\(y = \sin( \cos {}^{ - 1} (x) ) \)
Here we must imagine a triangle such that an angle has a hypotenuse 1, and a leg x, by definition the missing side is
\( \sqrt{1 - {x}^{2} } \)
by using the Pythagorean theorem.
\( \cos( \alpha ) = \frac{x}{1} \)
so
\( \sin( \alpha ) = \frac{1 - \sqrt{ {x}^{2} } }{1} \)
\(y = \sqrt{1 - {x}^{2} } \)
\( {y}^{2} = 1 - {x}^{2} \)
\( {x}^{2} + {y }^{2} = 1\)
Related Questions
Find a . the mean ; b . the deviation from the mean for each data item ; and c . the sum of the deviations in part ( b ) for the following group of data items . 155 , 156 , 162 , 164 , 168
Answers
(a) The mean of the data item from the group data is 161.
(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.
(c) The sum of the deviation is 0
What is a group data?Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.
(a) To find the mean of the data, we use the formula below.
Formula:
M = ∑x/n.......... Equation 1Where:
M = Mean = ?∑x = Sum of each data = 155+156+162+164+168 = 805n = Total number of data item = 5Substitute these values into equation 1
M = 805/5M = 161(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.
M' = x-M
For data 115,
M' = 155-161 = -6For data 156,
M' = -5For data 162,
M' = 162-161 = 1For data 164,
M' = 164-161M' = 3For data 168,
M' = 168-161M' = 7(c) The sum of the deviation is
∑M' = -6+(-5)+1+3+7∑M' = 0Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7 and the sum of the deviation of the data is 161 and 0 respectively,
Learn more about group data here: https://brainly.com/question/24298037
#SPJ1
What is the answer to these questions?
Answers
25. The degree measure of angle ABC is A. 111 2⁄3°.
26. The perimeter of triangle DEF is not provided in the given options.
27. The probability of drawing a 7 and an ace in that order is D. 4/663.
25. In the given figure, we have angle ABC = 2x + 5° and
angle CBD = x + 15°.
Since angle ABC and angle CBD are adjacent angles, their sum should be equal to 180° (forming a straight line).
Therefore, we can set up the equation:
(2x + 5°) + (x + 15°) = 180°.
Simplifying this equation, we get 3x + 20° = 180°.
Subtracting 20° from both sides gives us 3x = 160°. Dividing both sides by 3, we find x = 160° / 3.
Therefore, the degree measure of angle ABC is 2x + 5° = 2(160° / 3) + 5° = 320/3 + 5° = 335/3°. Hence, the answer is A. 111 2⁄3°.
26. In the given diagram, triangle ABC is similar to triangle DEF.
We know that corresponding sides of similar triangles are proportional. Therefore, we can set up the proportion:
AB/DE = BC/EF = AC/DF.
Substituting the given values, we have 12/DE = 12/EF = 6/8.
Simplifying this, we find DE = 8, EF = 8, and DF = 6.
The perimeter of triangle DEF is the sum of its side lengths: DE + EF + DF = 8 + 8 + 6 = 22.
27.There are 4 sevens and 4 aces in a standard deck of 52 cards. Therefore, the probability of drawing a 7 first is 4/52.
After drawing a 7, there are 51 cards remaining, and only 4 aces.
Hence, the probability of drawing an ace second, given that a 7 was drawn first, is 4/51.
To find the overall probability, we multiply the individual probabilities: (4/52) * (4/51) = 16/2652 = 4/663.
Hence, the answer is D. 4/663.
For more such questions on probability
https://brainly.com/question/251701
#SPJ8
A man is four times as old as his son. In 3 years, the father will be three times as old as the son. How old is each now?
Answers
The man is 27 years old and the son is 9 years old.
We can write the son's age as 'x', and therefore write the man's age as 4x. In 3 years, both their ages will increase by 3, so the son's age is now x + 3, and the man's age is 4x + 3.
We are told that the man is now 3 times older than his son, which means his current age, 4x + 3, is the same as 3 times the son's current age, which is x + 3.
Therefore we can write an equation:
4x + 3 = 3(x + 3)
4x + 3 = 3x + 9
- 3x
x + 3 = 9
- 3
x = 6
We can now substitute this in to find their current ages:
Son's age = x + 3 = 6 + 3 = 9
Man's age = 4x + 3 = 24 + 3 = 27
I hope this helps! Let me know if you have any questions :)
experimento aleatorio con orden,remplazo y sin repeticion
Answers
A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.
How to explain the information.For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.
The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.
Learn more about the experiments at
brainly.com/question/17274244
#SPJ1
Random experiment with order, replacement and without repetition
The point (8, −15) was reflected over an axis to (−8, −15). Which axis was it reflected over? Explain. y-axis, because the x-coordinate is the opposite y-axis, because the y-coordinate is the opposite x-axis, because the x-coordinate is the opposite x-axis, because the y-coordinate is the opposite
Answers
We can infer that the point (8, -15) was reflected over the y-axis to (-8, -15) based on the change in the x-coordinate while the y-coordinate stays the same.
The y-axis reflected the point (8, -15) over to (-8, -15).
The x-coordinate changes its sign but the y-coordinate stays the same when a point is mirrored over the y-axis.
In this instance, the y-coordinate, -15, remains constant but the x-coordinate, 8, of the original point changes to -8 in the reflected point.
This shows that the y-axis is where the reflection took place.
Imagine a coordinate plane with the x-axis running horizontally and the y-axis running vertically in order to see this.
As a vertical mirror, the y-axis reflects points on either side of it.
When a point crosses the y-axis in reflection, it effectively flips to the other side of the axis while keeping its y-coordinate.
In this case, the point (8, -15) is initially situated in the positive x-direction on the right side of the y-axis.
After reflection, it becomes (-8, -15) and appears on the left side of the y-axis in the negative x-direction.
for a related inquiry on the x-coordinate.
https://brainly.com/question/28821617
#SPJ11
Answer:
The point is reflected to the Y-axis. It can be either A or B, but I mostly positive it's A.
Step-by-step explanation:
Good luck on the final module exam! I'm counting on you.
Determine the perimeter of the right triangle shown.
24 units
10 units
8 units
6 units
Answers
Answer:
A) 24 units----------------------------------
Find the legs first:
5 - (-3) = 8 units,4 - (-2) = 6 units.Find the hypotenuse using Pythagorean:
\(\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10\ units\)Find the perimeter:
P = 8 + 6 + 10 = 24 unitsCorrect choice is A.
Answer:
A) 24 units
Step-by-step explanation:
The perimeter of a triangle is the sum of its side lengths.
From inspection of the given right triangle:
Base = 8 unitsHeight = 6 unitsAs the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the length of the hypotenuse:
\(\implies c^2=a^2+b^2\)
\(\implies c^2=8^2+6^2\)
\(\implies c^2=64+36\)
\(\implies c^2=100\)
\(\implies c=\sqrt{100}\)
\(\implies c=10\)
Therefore, the perimeter of the given triangle is:
\(\implies 8+6+10=24 \; \rm units\)
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Landon sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
28 visitors purchased no costume.
319 visitors purchased exactly one costume.
34 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.
Answers
The probability that the next person will purchase exactly one costume is 319/381.
How to solveThe overall count of individuals who visited includes all categories of visitors, which comprises of 28 individuals who didn't buy any costume, 319 individuals who acquired one costume, and 34 individuals who bought more than one costume, hence making a total of 381 visitors.
To determine the likelihood of an occurrence, one must divide the number of possible ways that the event could happen by the overall number of potential outcomes.
. Here, the event is a visitor purchasing exactly one costume.
So, the probability that the next visitor will purchase exactly one costume is the number of visitors who purchased exactly one costume (319) divided by the total number of visitors (381).
Therefore, the probability can be written as a fraction 319/381. This fraction cannot be simplified further.
Hence, the probability that the next person will purchase exactly one costume is 319/381.
Read more about probability here:
https://brainly.com/question/13604758
#SPJ1
E is the midpoint of DF, DE = 3x + 4 and EF = 5x - 2. Find DE, EF, and DF.
Answers
Since E is the midpoint of DF, DE and EF are two halves of DF. First, let's write down what we know.
DE = 3x + 4
EF = 5x - 2
DE = EF
DE + EF = DF
Now, let's plug our values for DE and EF into our first expression.
3x + 4 = 5x -2
Add 2 to both sides and subtract 3x from both sides.
6 = 2x
Divide both sides by 2
3 = x
Let's plug 3 in for x into DE.
DE = 3x + 4 = 3(3) + 4 = 9 + 4 = 13
DE = EF = 13
We can plug 13 in for DE and EF to get DF
DF = DE + EF = 13 + 13 = 26
Chicago has the highest sales tax in the country. Stores charge 10.25% of the price. How much is paid in sales tax on a $800 couch?
Answers
which set Paris does not show y as a function of x?
Answers
Answer:
c
Step-by-step explanation:
the x coordinations can not repeat as it does in option c so c is the answer
i need help _______________________________________________________________________
Answers
Answer:
1/2
Step-by-step explanation:
y=1/2x
1/2 is constant
Fill in the blank. In the triangle below, y=__________. Round your answer to two
decimal places.
ZD
y
Answer here
42°
35
Answers
the shortest side of a right triangle measures 7m. The lengths of the other two sides are Consecutive integers. What is the length of the other two sides?
Answers
The lengths of the other two sides of the right triangle are 24m and 25m, respectively.
Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we have the equation:
\(7^2 + x^2 = (x + 1)^2\)
Expanding and simplifying this equation, we get:
\(49 + x^2 = x^2 + 2x + 1\)
Now, we can cancel out \(x^2\) from both sides of the equation:
49 = 2x + 1
Next, we can isolate 2x:
2x = 49 - 1
2x = 48
Dividing both sides by 2, we find:
x = 24
Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.
Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.
For more question on lengths visit:
https://brainly.com/question/28322552
#SPJ8
Ms. Fitzsimmons wanted to buy two of the same jackets in different colors online. The online store
charged a one-time flat rate of $7.99 for shipping. Her grand total was $62.27. What is the cost of
one jacket?
The cost of one jacket is $
Answers
Answer:
the cost of one jacket is $27.14
I WILL GIVE THE BRAINIEST
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Answers
An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
How to write an equation to determine the number of students that went on this trip?In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;
Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;
\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
Read more on solution and equation here: brainly.com/question/25858757
#SPJ1
Complete Question:
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.
Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
(ASAP!!) Given that point M is the midpoint of TS and UR which of the following triangle congruence methods could be used to prove TUM SRM? T R M U S Do O ASA 0 O AAA O 0 O Qo O SAS 0 O SSS
Answers
Answer: SAS or Side-Angle-Side
Step-by-step explanation: Two triangles are congruent if they have the same exactly 3 sides and same exactly 3 angles.
There are methods to help prove congruence.
For example:
ASA or Angle-Side-Angle: when two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle; SAS or Side-Angle-Side: when two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle;SSS or Side-Side-Side: if three sides of one triangel are congruent to the three sides of the other triangle, they are congruent;The triangles TUM and SRM are congruent because:
Lines RU and TS intersect at point M forming two pair of opposite angles, which are vertical and therefore, the same.
Being midpoint, point M divides RU into two equal segments: UM = MR. The same happens to TS: TM = MS.
Two sides and the included angle of one triangle is congruent to the corresponding parts of the other triangle, which means ΔTUM and ΔSRM are congruent and proved by SAS method.
Misty’s surgery lasted 214 hours. Convert the time to seconds.
Answers
Answer:
770,400
Step-by-step explanation:
770,400 seconds
1 2/5 fraction that have the same value
Answers
Answer:
7/5
Step-by-step explanation:
1 2/5, a mixed number, is equivalent to 7/5.
Solve 6/7 = y - 3/7. WHAT IS Y?
Answers
Answer:
y = 9/7
Step-by-step explanation:
There's another silence as Steve looks toward the crowd and then toward Tommy. He wears a tight grin.
STEVE
Based on the clues in this passage, what will most likely happen next?
• The neighbors will stop doubting Tommy.
Well, I guess what we'd better do then is to run a check on the neighborhood and see which ones of us are really human.
• The neighbors will stop taking Steve seriously.
• The neighbors will continue to joke about the situation.
There's laughter at this, but it's a laughter that comes
from a desperate attempt to lighten the atmosphere. It's a • The neighbors will begin checking to see who is release kind of laugh.
really human.
36. GROUP SHOT - THE PEOPLE 36.
As they look at one another in the middle of their laughter.
-The Monsters Are Due on Maple Street,
Rod Serling
Answers
Answer:
5
Step-by-step explanation:
Could it be zero? 4(x+2)=10
2. 12-8x=3(x+4)
Answers
Answer:
1) x=0.5
2 x=0
Step-by-step explanation:
Question No. 1
4(x+2)=10
4x+8=10
4x=2
x=0.5
Question No. 2
12-8x=3(x+4)
12-8x=3x+12
8x-3x=12-12
5x=0
x=0
If Charlotte is 2.5cm from Raleigh, how much km is it from Charlotte to Raleigh?
Answers
In this map 1 cm is equal to 75 km
Charlotte is 2.5 cm from Raleigh
then 2.5 = 2 + 0.5 = 2 + (1/2)
then multiply 75 by 2 and divide 75/2
Thereafter unite both results
75x2= 150, 75/2= 37.5
then 150 + 37.5= 187.5 km
there are 187.5 km between both cities.
in January the depth of a lake was 943 feet in August the depth of the lake was 754.4 what is the percentage decrease of the depth of the lake from January to August
Answers
The percentage decrease of the depth of the lake from January to August is 20%.
What is percentage decrease?The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.
Given,
The depth of lake in January = 943 feet
The depth of lake in August = 754.4 feet
The difference is = (943-754.4) feet
= 186.6 feet
So, the percentage decrease of the depth of the lake from January to August will be = (186.6 ÷ 943) × 100
= 20%
Therefore, the answer is 20%.
To know more about percentage decrease refer to:
https://brainly.com/question/13631568
#SPJ1
5/9 (t +3) =40
PLSSS HELP MEEE
Answers
Answer:
Step-by-step explanation:
Ok so T = 69
if G is midpoint of FH, find FG
Answers
Mike spins a spinner and flips a coin. What
is the probability of getting E on the spinner
and the coin landing on heads?
Answers
=3/8*1/2
=3/16
Are they like terms? 3x & -x
Answers
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Answers
99 minutes * 0.43 = 42.57 minutes
Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
what is 4(1/2+3/4)+(-2)
Answers
Answer:
3
Step-by-step explanation:
4(1/2+3/4)+(-2)
4 x 5/4 - 2
5 - 2
3
i hope this helps :)
Answer:
your answer is 3
Step-by-step explanation:
Kim is in the tenth grade and takes a standardized science test. Use his test scores below to answer the question that follows. raw score 72 percentile 88 stanine 8 grade equivalent 12.1
Kim's test scores indicate that: he scored as well as or better than 72 of the test takers. 28% of the test takers scored better than he did. he would perform adequately in a twelfth grade science class. he scored as well as or better than 88% of the test takers. he answered 72% of the questions correctly.
Answers
Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.
His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.
Learn more about tests:
https://brainly.com/question/1265793
#SPJ4