Answers
Explanation: 16x+97/9-12/5x-98/9
Related Questions
a radio station broadcasts a signal over an area with a 120-mile diameter. the population density of the area is 100 people per square mile. how many people are within receiving distance of the broadcast signal?
Answers
The radio station can reach around 1,030,400 people within its coverage area.
Using the equation, calculate the size of the circular circle that the radio station signal can cover.
A = πD²/4 is the area and D is the diameter. using the pi-number 3.14.
r = 120 / 2 = 60 miles
The density of the area: 100 people per sq. mile
A = r² π = 60² · 3.14 = 3600 · 3.14 = 11,304 sq. miles
11,304 · 100 = 1,030,400
or
A = (3.14)(120 mi) (120 mi)
² / 4 \s A = 11304 mi²
being aware that 100 individuals reside in each square mile.
total population receiving the signal =11304 mi² x (100 people / 1 mi²)
= 1,130,400
Know more about population density
https://brainly.com/question/13902749
#SPJ4
If a committee of 6 people had to be chosen at random, what is the probability that out 9 males and 7 females, exactly 3 males and 3 females are chosen?
Answers
The probability that out 9 males and 7 females, exactly 3 males and 3 females are chosen is 0.3671
How to solve the combination problemThe problem tp solve is selection of 6 people which are made up of 3 males and 3 females from 9 males and 7 females
number of ways to choose exactly 3 male and 3 female
= number of ways of selecting males * number of ways of selecting females
number of ways of selecting males
= 9 combination 3
= ⁹C₃
= 9! / (3! * (9 - 3)!)
= 84 ways
number of ways of selecting females
= 7 combination 3
= ⁷C₃
= 35 ways
number of ways = 35 * 84 = 2940 ways
number of ways to choose 6 people from 16 persons (9 male + 7 female)
= 16 combination 6
= ¹⁶C₆
= 8008 ways
The probability
= 2940 / 8008
= 0.3671
Learn more about combination here:
https://brainly.com/question/29338074
#SPJ1
Systematic sampling and cluster sampling are examples of which type of sampling method used in human research
Answers
Systematic sampling and cluster sampling are examples of probability sampling methods used in human research. These methods are employed to ensure that each participant in the population has a known, non-zero chance of being selected, which helps in obtaining representative samples and drawing more accurate conclusions.
Systematic sampling and cluster sampling are both examples of probability sampling methods used in human research.
Probability sampling methods involve randomly selecting participants from a larger population, giving each individual an equal chance of being selected.
Systematic sampling involves selecting every nth participant from a list of the population, while cluster sampling involves dividing the population into clusters or groups and then randomly selecting entire clusters to include in the study.
These methods are considered to be more representative and unbiased than non-probability sampling methods, which do not involve random selection and may not accurately reflect the characteristics of the population.
For similar question on probability.
https://brainly.com/question/12344616
#SPJ11
What describes the correct way to convert minutes to an hour
Answers
Answer:
Yo mean correct way??
yo can divide minute by 60 to convert minute into hour
For example
To convert 10 minute into hour. then we should divide 10 by 60. 10/60
Answer:
In any conversion you have to establish ratios (or rates) for the different units being converted.
The process will be performed by a series of multiplications that will cancel out the "unwanted" units.
multiplication by one (1) does not change the value in an equation.
you have to multiply by a "series of ones" that take into account the units being converted..
for example
1 minute/60 seconds or 1 inch = 2.54 cm or 1 day = 24 hours
in your problem you have minutes... lets say you have 100 minutes
100 minutes * 1 hour minutes cancel and you have 100/60 = 1 \(\frac{2}{3}\) hrs
60 minutes
Step-by-step explanation:
The main rotor of a helicopter is spinning at a
constant rate. The rotor makes 80 revolutions every
12 seconds. At what rate, in revolutions per minute.
is the rotor spinning?
Answers
Answer:6.7
Step-by-step explanation: Just divide 80 by 12 you get 6.6 so round up
What is the value of x?
B
170
O x = 55°
O x = 60°
O x = 70°
X
С
O x = 110°
A
Answers
wo cards are dealt from an ordinary deck of 52 cards. this means that two cards are sampled uniformly at random without replacement. (a) what is the probability that both cards are aces and one of them is the ace of spades?
Answers
The probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.
The probability of being dealt two aces and one of them being the ace of spades is 1/221. This is because the chance of the first card being the ace of spades is 1/52 and the chance of the second card being an ace, given that the first card is an ace, is 3/51. Thus, the probability of both cards being aces and one of them being the ace of spades is 1/221.
Mathematically, this can be expressed as P(Ace of Spades, Ace) = P(Ace of Spades) x P(Ace|Ace of Spades) = (1/52) x (3/51) = 1/221.
This means that the probability of being dealt two aces and one of them being the ace of spades is 1 in 221, or 0.45%.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Supposa 39 women used a skin crean for 22 weeks. At the ond of the period, a denmalologst judged whecher nach woman axhbted skin improvemert. The I N I N I I I N N I G results are shown to the tight (where I = improved skin and N= no improverment). Conplele parts a and b I I I I INNIN I IN INNTNTNTNT INNINININ a. Do the dala provide suflicient evisence bo condude that the cream wil improve the skin of more than 50% of women? Test using a = 0.01. What are the typotheses for this teat? B. H;p=0.50,H
α
,p>0.50 A. H
j
:p=0.50,H
a
p
=0.50 D. H
2
=p
=0.50,H
a
=p=0.50 C H
j
p=0.50;H
j
p<0.50 Find the rejection region for the test Choote the correct antwer below. B. x<−2.33 or 2>2.33. A. 2>233 D. x<233 C. 2⩾2375 ค. 1<−2.675 or 2≥2.675 E. 2<2576 Cuiculaie the value of the iest matahe: 1 * (Coond wo two decinar places es needed.) A. Do not reject the null hypothesis because tho test statistic is not in the rejection region. B. Reject the null hypothesis because the test statistic is in the rejection region. C. Reject the null hypothesis because the test statistic is not in the rejection region. D. Do not reject the null hypothesis because the test statistic is in the rejection region. b. Find and interpret the p-value of the test. The p-value is (Round to four decimal places as needed.) Interpret this value. A. Assuming p=0.50, the p-value is the probabilty that
p
^
is greater than 0.50 for a nandom sample of 39 observations. B. Assuming p=0.50, the p-value is the probability that
p
^
is greater than the observed vakue for a random sample of 39 observations. c. Assuming p is the observed value, the p-value is the probability that
p
^
is greater than that valun for a fandom sample of 39 observations. D. Assuring p is the observed value, the p-value is the probabllity that
p
^
is greater than 0.50 for a random sample of 39 observations:
Answers
a. The data does not provide sufficient evidence to conclude that the cream will improve the skin of more than 50% of women at a significance level of 0.01. b. The rejection region for the test is x ≥ 2.33 or x ≤ -2.33.
The hypotheses for this test are H0: p ≤ 0.50 (the proportion of women with improved skin is less than or equal to 50%) and Ha: p > 0.50 (the proportion of women with improved skin is greater than 50%). To calculate the test statistic, we need to determine the observed proportion of women with improved skin (p). From the given data, we see that out of 39 women, there are 19 who showed improvement. Therefore, p = 19/39 ≈ 0.487.
Since the test statistic falls within the non-rejection region (-2.33 < x < 2.33), we do not reject the null hypothesis. This means that there is not enough evidence to conclude that the cream will improve the skin of more than 50% of women.
b. The rejection region for the test is x ≥ 2.33 or x ≤ -2.33. This means that if the test statistic falls outside this range, we would reject the null hypothesis.
The p-value of the test, which represents the probability of observing a sample proportion as extreme as or more extreme than the observed proportion under the null hypothesis, is approximately 0.3234. This value indicates that assuming the null hypothesis is true (i.e., p = 0.50), the probability of obtaining a sample proportion as far away from 0.50 or more extreme in favor of the alternative hypothesis is 0.3234. Since the p-value is greater than the chosen significance level of 0.01, we do not have enough evidence to reject the null hypothesis.
Learn more about null hypothesis here: brainly.com/question/31816995
#SPJ11
. How many days will it take for $9500 to earn $800 at 8.25% p.a.?
Answers
It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.
To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:
Interest = Principal * Rate * Time
In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.
Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).
$800 = $9500 * 0.0825 * (t / 365)
Simplifying the equation:
800 = 9500 * 0.0825 * (t / 365)
Divide both sides by (9500 * 0.0825):
800 / (9500 * 0.0825) = t / 365
Simplify the left side:
800 / (9500 * 0.0825) ≈ 0.1083
Now, solve for t by multiplying both sides by 365:
0.1083 * 365 ≈ t
t ≈ 39.532
Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.
for such more question on annual interest rate
https://brainly.com/question/29451175
#SPJ8
Gardial GreenLights, a manufacturer of energy-efficient lighting solutions, has had such success with its new products that it is planning to substantially expand its manufacturing capacity with a $20 million investment in new machinery. Gardial plans to maintain its current 50% debt-to-total-assets ratio for its capital structure and to maintain its dividend policy in which at the end of each year it distributes 25% of the year's net income. This year's net income was $8 million. How much external equity must Gardial seek now to expand as planned
Answers
To expand its manufacturing capacity with a $20 million investment in new machinery while maintaining its current capital structure and dividend policy, Gardial GreenLights must seek external equity of $8 million.
The capital structure of Gardial GreenLights is characterized by a 50% debt-to-total-assets ratio. Since the company plans to maintain this ratio, the remaining 50% of the assets must be financed through equity. The investment in new machinery is $20 million, which represents 50% of the total assets needed for expansion. Therefore, the total assets required for expansion would be $40 million (20 million divided by 0.5). To determine the amount of external equity needed, we subtract the company's existing equity from the total assets required. Given that the company's dividend policy entails distributing 25% of the year's net income, we can calculate the retained earnings. This year's net income was $8 million, and 25% of that ($2 million) would be distributed as dividends. Therefore, the retained earnings amount to $6 million ($8 million - $2 million). Since external equity is the difference between the total assets required and retained earnings, Gardial GreenLights must seek external equity of $34 million ($40 million - $6 million) to finance its expansion plans.
Learn more about equity here:
https://brainly.com/question/31458166
#SPJ11
i’ll give a cookie to whoever answers
(multiple choice.)
which of the following best describes the pattern 2, 4, 8, 16.....?
a.) n, 2n, 3n, 4n
b.) n, 2n, 4n, 8n
c.) n, n^2, n^4, n^8
d.) n, n + 2, n + 4, n + 8
Answers
Answer:
I think D
Step-by-step explanation:
help i'll mark youuuuuuuuuuuuuu
Answers
Answer:
A. 525 feet
Step-by-step explanation:
If every hour their altitude increased by 135 then their would be an increase of 675 (135 × 5) after 5 hours. To find their altitude 5 hours earlier then you would subtract 675 from their current altitude. 1,200-675=525 feet
Using synthetic division, if 2 is the zero of x³ -7x+6p (x)
Answers
Answer:THe answer is 98.78x
Step-by-step explanation:
2r34 means 567
a box contains 16 green marbles and 12 white marbles. if the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
The probability of choosing another white marble is:11/27 = 0.4074 (rounded to four decimal places).This can be calculated by dividing the number of white marbles left in the box by the total number of marbles left in the box.
Since the first marble chosen there are now 11 white marbles and 15 total marbles remaining in the box.
The probability of choosing another white marble, use the following fraction:
(Number of white marbles remaining) / (Total marbles remaining)
Probability = 11/15
To express this as a decimal rounded to four decimal places:
Probability = 11 ÷ 15 ≈ 0.7333
So, the probability of choosing another white marble is 11/15 or 0.7333.
learn more about probability here: brainly.com/question/30034780
#SPJ11
34
Question 6 Multiple Choice Worth i pones)
(03.02 MC)
The vertices of AABC are A (1,5), B (3,9), and C (5,3). The vertices of ADEF are D (-3, 3), E (-2,5), and F (-1. 2). Which conclusion is true about the triangles?
The ratio of their corresponding sides
,
They are congruent by the definition of congruence in terms of rigid motions.
The ratio of their corresponding angles is 1:3.
They are similar by the definition of similarity in terms of a dilation.
Answers
Answer:
They are similar by the definition of similarity in terms of a dilation
Step-by-step explanation:
The given vertices of triangle ΔABC are;
A(1, 5), B(3, 9), and C(5, 3)
The vertices of triangle ΔDEF are;
D(-3, 3), E(-2, 5), and F(-1, 2)
Therefore, we get;
The length of segment, \(\overline{AB}\) = √((9 - 5)² + (3 - 1)²) = 2·√5
The length of segment, \(\overline{BC}\) = √((9 - 3)² + (3 - 5)²) = 2·√10
The length of segment, \(\overline{AC}\) = √((5 - 3)² + (1 - 5)²) = 2·√5
The length of segment, \(\overline{DE}\) = √((5 - 3)² + (-2 - (-3))²) = √5
The length of segment, \(\overline{EF}\) = √((2 - 5)² + (-1 - (-2))²) = √10
The length of segment, \(\overline{DF}\) = √((2 - 3)² + (-1 - (-3))²) = √5
∴ \(\overline{AB}\)/\(\overline{DE}\) = 2·√5/(√5) = 2
\(\overline{BC}\)/\(\overline{EF}\) = 2·√10/(√10) = 2
\(\overline{AC}\)/\(\overline{DF}\) = 2·√5/(√5) = 2
The ratio of their corresponding sides are equal and therefore;
ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.
please help asap if you help i'll give brainilist. Two pieces of metal measure one and one sixth yards and three twelfths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed?
four and one quarter yards
four and one sixth yards
one and one quarter yards
one and ten eighteenths yards
Answers
Answer:
Step-by-step explanation:
four and one quarter yards. explanation: add 1 1/6 + 3/12 = 1 5/12. now, multiply that by 3.
Using the arithmetic operations the total yards of metal is needed 4(1/4).
What is arithmetic operation?The study and application of numbers in all other branches of mathematics is the focus of the branch of mathematics known as arithmetic operations. In essence, it consists of addition, subtraction, multiplication, and division operations.
According to the given:
First pieces of metal = 1 (1/6)
= 7/6
Then Second pieces of metal = 3/12
Adding both the pieces, we have
=7/6 + 3/12
= (14 + 3)12
= 17/12.
now multiply that by 3.
We get,
= (17/12)3
= 17/4
= 4(1/4)
Using the arithmetic operations the total yards of metal is needed 4(1/4).
To know more about arithmetic operations visit:
brainly.com/question/20595275
#SPJ2
Which do you think is easier to understand and why do you think so, multiplying radicals or multiplying polynomials?
Answers
I believe that its easier to understand the multiplication of a radical than that of a polynomial.
How to illustrate the information?In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.
A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:
= 3✓2 × 4✓2
= 12✓4
= 12 × 2
= 24
The multiplication of a radical is easier.
Learn more about polynomial on:
https://brainly.com/question/2833285
#SPJ1
TRUE/FALSE. inverse functions must be one to one, meaning a horizontal line should not cross more than once on a graphed function
Answers
Select all the correct answers.
The table shows points on the graph of the function f (x) = 3 sin (x- pi/2) + 1
Answers
Answer:
B,C and E
Step-by-step explanation:
The period can be calculated by dividing 2pi by the coefficfient of the x, so in this case 1. And we'll get 2pi/1 = 2pi.
The function clearly has a minimum of -2, you can see that from the table.
Same thing for the maximum = 4.
Answer:
See Photo
Step-by-step explanation:
Plato/Edmentum
and, New innings hidjsjs. dbsjsjjz djskskkdjd
Answers
Answer:
THANK YOU?
Step-by-step explanation:
DNSNJSMSNNFJD
Please, give me brainliest
10+2r=8 need the answer now
Answers
Simplifying
10 = 2r + -8
Reorder the terms:
10 = -8 + 2r
Solving
10 = -8 + 2r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-2r' to each side of the equation.
10 + -2r = -8 + 2r + -2r
Combine like terms: 2r + -2r = 0
10 + -2r = -8 + 0
10 + -2r = -8
Add '-10' to each side of the equation.
10 + -10 + -2r = -8 + -10
Combine like terms: 10 + -10 = 0
0 + -2r = -8 + -10
-2r = -8 + -10
Combine like terms: -8 + -10 = -18
-2r = -18
Divide each side by '-2'.
r = 9
Simplifying
r = 9
Answer:
r = -1
Step-by-step explanation:
subtract 10 from both sides
2r = -2
divide both sides by 2
r = -1
Demand history for the past three years is shown below, along with the seasonal indices for each quarter.
Year Quarter Demand Seasonal Index
Year 1 Q1 319 0.762
Q2 344 0.836
Q3 523 1.309
Q4 435 1.103
Year 2 Q1 327 0.762
Q2 341 0.836
Q3 537 1.309
Q4 506 1.103
Year 3 Q1 307 0.762
Q2 349 0.836
Q3 577 1.309
Q4 438 1.103
Use exponential smoothing with alpha (α) = 0.35 and an initial forecast of 417 along with seasonality to calculate the Year 4, Q1 forecast.
Answers
The Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
Exponential smoothing is a forecasting technique that takes into account both the historical demand and the trend of the data. It is calculated using the formula:
Forecast = α * (Demand / Seasonal Index) + (1 - α) * Previous Forecast
Initial forecast (Previous Forecast) = 417
α (Smoothing parameter) = 0.35
Demand for Year 4, Q1 = 307
Seasonal Index for Q1 = 0.762
Using the formula, we can calculate the Year 4, Q1 forecast:
Forecast = 0.35 * (307 / 0.762) + (1 - 0.35) * 417
= 335.88
Therefore, the Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
The forecasted demand for Year 4, Q1 using exponential smoothing is 335.88.
To know more about exponential smoothing , visit
https://brainly.com/question/15061467
#SPJ11
This is for my final grade before spring break please help me asap nowwww
Answers
Answer: B, Two solutions
Step-by-step explanation:
Answer:
can you take a clear pic pls
i thing that would help me solve the answer
Step-by-step explanation:
You want to reduce your daily calorie consumption by about 9%. You currently consume about 2100 calories per day. Use mental math to estimate the number of calories you should consume in one week to meet your goal
Answers
Answer:
13,377 in one week
Step-by-step explanation:
2100*0.09=189
2100-189=1911
1911*7=13,377
hope that helps
Solve the equation for all real solutions 4z^2-8z+5=2
Answers
Answer:
z=1/2 and z=3/2
Step-by-step explanation:
5. In the equation for exponential functions, y = a.b*, how does the a term relate to a key feature of the graph?
Answers
Step-by-step explanation:
A shows the initial value or y intercept.
Why.
A exponential function is shown as
\(a(b {}^{x} )\)
If we are trying to find the y intercept, we first set this equal to y
\(a( {b}^{x} ) = y\)
Set x=0
\(a {b}^{0} = y\)
And solve for y.
Remeber that anything raised to the zero power is 1. So
\(b {}^{0} = 1\)
So we have
\(a(1) = y\)
Anything times 1 is itself so we have
\(a = y\)
This means that the y intercept of a exponential function is (0,a). A gives us the y intercept.
Solve 6 - 5x = 7 + 3x
Answers
Answer:
hol up
x=-1/8 negative one over eight
Step-by-step explanation:
Name the constant in the expression:
3x + 5
please explain how I can solve problems like this
Answers
Equivalence Class and Partition Prove that: (1) Let R be an equivalence relation on set A, then the set of equivalent classes of R is a partition on A. (2) Conversely, given a partition of A, there exists an equivalence relation on A such that this partition is the set of its equivalence classes. 5 Partial Order Is R={(x,y)∈R+×R+∣x≤y} a partial order on R+? Why or why not?
Answers
(1) The set of equivalent classes of an equivalence relation R on set A is a partition on A.
(2) Conversely, given a partition of set A, there exists an equivalence relation on A such that this partition is the set of its equivalence classes.
(5) The relation R={(x, y)∈R+×R+|x≤y} is not a partial order on R+ because it does not satisfy the antisymmetry property.
(1) Let R be an equivalence relation on set A. We want to prove that the set of equivalent classes of R is a partition on A.
To show this, we need to demonstrate three properties of a partition:
(i) Every element in A belongs to at least one equivalent class:
Since R is an equivalence relation on A, for every element a in A, there exists an equivalent class [a] such that a is an element of [a]. Therefore, every element in A belongs to at least one equivalent class.
(ii) No two distinct equivalent classes have any elements in common:
Suppose there exist two distinct equivalent classes [a] and [b] such that there is an element c that belongs to both [a] and [b]. Since c belongs to [a], it implies that c is equivalent to a. Similarly, c belongs to [b], which implies c is equivalent to b. Since equivalence relations are transitive, if a is equivalent to c and c is equivalent to b, then a must be equivalent to b. This contradicts the assumption that [a] and [b] are distinct equivalent classes. Therefore, no two distinct equivalent classes can have any elements in common.
(iii) The union of all equivalent classes is equal to A:
Let's assume there exists an element a in A that does not belong to any equivalent class. Since R is an equivalence relation, a is equivalent to itself, which means a belongs to the equivalent class [a]. This contradicts the assumption that a does not belong to any equivalent class. Therefore, every element in A belongs to at least one equivalent class. Additionally, since every element in A belongs to exactly one equivalent class, the union of all equivalent classes is equal to A.
Based on the three properties demonstrated above, we can conclude that the set of equivalent classes of R is a partition on A.
(2) Let's verify the three properties of the equivalence relation:
(i) Reflexivity: For every element a in A, (a, a) belongs to the equivalence relation.
Since a belongs to the same subset as itself, (a, a) satisfies the reflexivity property.
(ii) Symmetry: If (a, b) belongs to the equivalence relation, then (b, a) also belongs to the equivalence relation.
If a and b belong to the same subset, it implies that (b, a) also belongs to the same subset, satisfying the symmetry property.
(iii) Transitivity: If (a, b) and (b, c) belong to the equivalence relation, then (a, c) also belongs to the equivalence relation.
If a and b belong to the same subset, and b and c belong to the same subset, it implies that a and c also belong to the same subset, satisfying the transitivity property.
Therefore, we have shown that the given partition of A defines an equivalence relation on A, where each subset of the partition corresponds to an equivalence class.
Hence, we have proved both statements (1) and (2).
(5) To determine if R={(x, y)∈R+×R+|x≤y} is a partial order on R+ (the set of positive real numbers), we need to verify three properties:
(i) Reflexivity:
For every x in R+, (x, x) belongs to R, since x is always less than or equal to itself.
(ii) Antisymmetry:
The relation R={(x, y)∈R+×R+|x≤y} does not satisfy the antisymmetry property. Consider the example where x = 2 and y = 3. Both (2, 3) and (3, 2) belong to R since 2 ≤ 3 and 3 ≤ 2. However, x ≠ y, violating the antisymmetry property.
(iii) Transitivity:
The relation R={(x, y)∈R+×R+|x≤y} satisfies the transitivity property. If (x, y) and (y, z) belong to R, it means that x ≤ y and y ≤ z. By the transitive property of real numbers, it follows that x ≤ z. Therefore, (x, z) belongs to R.
Since R does not satisfy the antisymmetry property, it cannot be considered a partial order on R+.
To know more about equivalence relation, refer here:
https://brainly.com/question/14307463
#SPJ4
Find a polar equation for the curve represented by the given Cartesian equation. x2+y2=25. x2+y2=−8y. y=√3x
Answers
The polar equation for this curve is: theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))
To find the polar equation for the curve represented by the given Cartesian equations, we can use the conversion formulas between Cartesian and polar coordinates.
\(x^2 + y^2 = 25:\)
In polar coordinates, the conversion formulas are:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation \(x^2 + y^2 = 25:\)
\((r cos(theta))^2 + (r sin(theta))^2 = 25\)
\(r^2 (cos^2(theta) + sin^2(theta)) = 25\)
\(r^2 = 25\)
The polar equation for this curve is simply:
r = 5
\(x^2 + y^2 = -8y:\)
In polar coordinates:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation \(x^2 + y^2 = -8y:\)
\((r cos(theta))^2 + (r sin(theta))^2 = -8(r sin(theta))\)
\(r^2 (cos^2(theta) + sin^2(theta)) = -8r sin(theta)\)
\(r^2 = -8r sin(theta)\)
The polar equation for this curve is:
r = -8 sin(theta)
y = sqrt(3) x:
In polar coordinates:
x = r cos(theta)
y = r sin(theta)
Substituting these values into the equation y = sqrt(3) x:
r sin(theta) = sqrt(3) (r cos(theta))
r sin(theta) = sqrt(3) r cos(theta)
tan(theta) = sqrt(3)
The polar equation for this curve is:
theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))
Learn more about polar equation here:
https://brainly.com/question/28847870
#SPJ11