Determine whether the tests for symmetry detect symmetry with respect to
a. The polar axis. Replace (r, Θ) by (r, -Θ).
b. The line Θ = π/2 . Replace (r, Θ) by (r, π - Θ).
c. The pole. Replace (r, Θ) by (-r, Θ).
1.) r = 4cos 2Θ
A) a. Inconclusive b. Yes c. Yes
B) a. Yes b. Yes c. Yes
C) a. Yes b. Yes c. Inconclusive
D) a. Inconclusive b. Inconclusive c. Yes
Answers
To determine whether the tests for symmetry detect symmetry with respect to the given conditions, we will apply the respective transformations to the polar equation r = 4cos 2Θ and see if the equation remains unchanged.
1. Test for symmetry with respect to the polar axis (replace (r, Θ) by (r, -Θ)):
r = 4cos 2(-Θ) r = 4cos(-4Θ)
r = 4cos 4Θ (since cosine is an even function) Since the transformed equation is not the same as the original equation, the test is inconclusive.
2. Test for symmetry with respect to the line Θ = π/2 (replace (r, Θ) by (r, π - Θ)):
r = 4cos 2(π - Θ) r = 4cos (2π - 4Θ)
r = 4cos (-4Θ) (since cosine is a periodic function with period 2π) r = 4cos 4Θ (since cosine is an even function)
The transformed equation is the same as the original equation, so the test detects symmetry with respect to the line Θ = π/2.
3. Test for symmetry with respect to the pole (replace (r, Θ) by (-r, Θ)): -r = 4cos 2Θ r = -4cos 2Θ
The transformed equation is not the same as the original equation, so the test is inconclusive.
Your answer: D) a. Inconclusive b. Yes c. Inconclusive
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Related Questions
Which expression is equivalent to 25x â€" 45y?
A. 25(5x â€" 20y)
B. 5(5x - 9y)
C. 70(x â€" y)
D. 10(15x â€" 35y)
Answers
Answer:
D
Step-by-step explanation:
Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica
What is the range of the function g(x) = |x – 12| – 2?
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
Answers
The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.
To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.
The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.
By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.
Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.
Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.
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What is the ratio in the simplest form of a classroom with 9 boys and 27 girls?
Answers
Answer:
1:3
Step-by-step explanation:
One octagon has a side length of about 12. 25 feet and an area of about 724. 56 feet². Find the area of a smaller octagon that has a perimeter of about 82 feet
Answers
The area of the smaller octagon is 505.3 square feet.
An octagon is a geometrical shape that has eight sides and angles. When you are given a problem involving an octagon, the first thing you want to do is figure out its dimensions. In this particular problem, we are given the side length of a larger octagon and its area. We are then asked to find the area of a smaller octagon with a specific perimeter.
Let the length of each side of the smaller octagon be represented by s feet, then its
Perimeter = 8s feet.
Now, the perimeter of the smaller octagon is given as 82 feet.
Therefore,
8s = 82s = 10.25 feet
Area of the larger octagon = 724.56 square feet
Area of the smaller octagon = (s/12.25)² × 724.56 square feet.
Replacing s by 10.25 feet, we have
Area of the smaller octagon = (10.25/12.25)² × 724.56 square feet
= (0.83673)² × 724.56 square feet
= 0.6977 × 724.56 square feet
= 505.3 square feet
Therefore, the area of the smaller octagon is 505.3 square feet.
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Express 13 + 5-14 as a complex number.
Answers
Answer:
the answer is 4
Step-by-step explanation:
Answer:
13+5-14 is equaled to 4 so if i do 18-14 is will still give me 4 because 13+5 is 18 so 18- 14 is 4
The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man
Answers
Answer:
78kg
Step-by-step explanation:
76×5= 380kg
380-72-74-75-81= 78kg
x=(76.5)-302
x=380-302=78
Suppose that A is a rank 2, 4x5, matrix for which X1=[1,2,3,2,1]t, X2=[1,-1,0,1,2]t, and X3=[2,1,4,4,4]t all satisfy AX=0. Do these vectors span the nullspace of A?
Answers
Yes, these vectors span the nullspace of A.
The nullspace of a matrix A is the set of all vectors X that satisfy the equation AX=0.
Since X1, X2, and X3 all satisfy this equation, they are all elements of the nullspace of A. Furthermore, since A is a rank 2, 4x5 matrix, the dimension of the nullspace of A is 5-2=3. This means that the nullspace of A is a subspace of R^5 with dimension 3.
Since X1, X2, and X3 are all elements of the nullspace of A and they are linearly independent (i.e., none of them can be written as a linear combination of the others), they form a basis for the nullspace of A. Therefore, these vectors span the nullspace of A.
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Find q
(7q-46)
(3q+6)
Answers
Answer:
\(q = 22\)
Step-by-step explanation:
The angle measure of a straight line is (180) degrees As given in the picture, line (AC) is a straight line, thus its angle measure is (180) degrees. Angles (ABD) and (DBC) make up line (AC). Therefore, one can conclude that the sum of angles (ABD) and (DBC) is (180) degrees. Form an equation, simplify and use inverse operations to solve for the unknown parameter (q).
\((<ABD) + (<DBC) = (AC)\)
Substitute for the angle measures,
\((7q-46)+(3q+6)=180\)
Simplify,
\(10q-40=180\)
Inverse operations,
\(10q-40=180\\\\10q = 220\\\\q = 22\)
Answer:
need pts
Step-by-step explanation:
Persevere the ratio of the volume of cylinder a to the volume of cylinder b is 5:1. Cylinder a is similar to cylinder c with a scale factor of 2:1, and cylinder b is similar to cylinder d with a scale factor of 3:1. What is the ratio of the volume of cylinder c to the volume of cylinder d? explain your reasoning
Answers
The ratio of the volume of cylinder C to the volume of cylinder D is ∛6:1.
To determine the ratio of the volume of cylinder C to the volume of cylinder D, we need to consider the relationship between the scale factors of the cylinders.
Given that the ratio of the volume of cylinder A to the volume of cylinder B is 5:1, we can infer that the scale factor between A and B is the cubic root of the volume ratio, which is ∛(5/1) = ∛5.
Similarly, the scale factor between cylinder B and cylinder D is 3:1, which implies that the cubic root of the volume ratio is ∛(3/1) = ∛3.
Now, we know that cylinder A is similar to cylinder C with a scale factor of 2:1. This means that the scale factor between A and C is 2:1, and the cubic root of the volume ratio is ∛(2/1) = ∛2.
By combining the scale factors, we can find the ratio of the volume of cylinder C to the volume of cylinder D:
Ratio of C to D = (Ratio of A to C) * (Ratio of B to D)
= ∛2 * ∛3
= ∛(2*3)
= ∛6
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the mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. a random sample of 16 students will be selected and the mean number of pets for the sample will be calculated.
Answers
Find the zeros of the function.
Enter the solutions from least to greatest.
h(x) = (-4x- 5)(-x + 5)
lesser x=
greater x =
Answers
someone answer please:)
I think its saying to find out what “b” means
Answers
Answer:
5 kdkdjdnndndjdjdjdjd
II. Computation \& Application - Budget Line (15pts) Tonyo is an employee who earns 30,000 php in 2021. He allots 15% of his salary to his grocery items. His grocery items are normally composed by 2 products, Meat and carbohydrates. In 2021, Pork is 20 php/ unit ; Carbohydrates is 30php/ unit and Fish is 15php/ unit. On year 2022, tonyo has still the same salary, however prices of groceries increased due to inflation by 10%. On year 2023, tonyo got a promoted and had a salary increased by 10%. Still due to inflation, prices of groceries increased by 10%. A) Graph Budget line on year 2021, considering pork and carbohydrates. Please show computations.5PTS B) Graph Budget line on year 2022, considering pork and carbohydrates. Please show computations.5PTS C) In year 2023, Tonyo decided to shift from pork to meat fish to save up for his marriage. Graph the budget line on year 2023 and show computations 5PTS
Answers
A) The coordinates (225, 0) and (0, 150) represent the combinations of pork and carbohydrates that Tonyo can purchase with his grocery budget.
B) Quantity of carbohydrates (Qc) = 136.36 units
A) Graph Budget line on year 2021, considering pork and carbohydrates:
To graph the budget line for year 2021, we need to calculate the quantity combinations of pork and carbohydrates that Tonyo can purchase with his allotted budget. Given that Tonyo allocates 15% of his salary to groceries and his salary is 30,000 PHP, his grocery budget for 2021 would be:
Grocery budget for 2021 = 0.15 * 30,000 PHP = 4,500 PHP
Let's assume that Tonyo spends all of his grocery budget on either pork or carbohydrates.
Assuming he spends all on pork:
Quantity of pork (Qp) = Grocery budget for 2021 / Price of pork = 4,500 PHP / 20 PHP = 225 units
Assuming he spends all on carbohydrates:
Quantity of carbohydrates (Qc) = Grocery budget for 2021 / Price of carbohydrates = 4,500 PHP / 30 PHP = 150 units
We can now graph the budget line with pork on the x-axis and carbohydrates on the y-axis. The coordinates (225, 0) and (0, 150) represent the combinations of pork and carbohydrates that Tonyo can purchase with his grocery budget.
B) Graph Budget line on year 2022, considering pork and carbohydrates:
In year 2022, prices of groceries increased by 10%. To calculate the new prices for pork and carbohydrates, we multiply the original prices by 1.10.
New price of pork = 20 PHP * 1.10 = 22 PHP
New price of carbohydrates = 30 PHP * 1.10 = 33 PHP
Using the same budget of 4,500 PHP, we can now calculate the new quantity combinations:
Quantity of pork (Qp) = Grocery budget for 2021 / New price of pork = 4,500 PHP / 22 PHP ≈ 204.55 units
Quantity of carbohydrates (Qc) = Grocery budget for 2021 / New price of carbohydrates = 4,500 PHP / 33 PHP ≈ 136.36 units
We can now graph the budget line for 2022, using the new quantity combinations.
C) Graph the budget line on year 2023, considering fish and carbohydrates:
In year 2023, Tonyo decided to shift from pork to fish. Let's assume that the price of fish remains the same as in 2022, while the price of carbohydrates increases by 10%.
Price of fish = 15 PHP
New price of carbohydrates = 33 PHP * 1.10 = 36.30 PHP
With a 10% increase in salary, Tonyo's new salary in 2023 would be:
New salary = 30,000 PHP * 1.10 = 33,000 PHP
Using the same grocery budget of 15% of his salary:
Grocery budget for 2023 = 0.15 * 33,000 PHP = 4,950 PHP
Let's calculate the new quantity combinations:
Quantity of fish (Qf) = Grocery budget for 2023 / Price of fish = 4,950 PHP / 15 PHP ≈ 330 units
Quantity of carbohydrates (Qc) = Grocery budget for 2023 / New price of carbohydrates = 4,950 PHP / 36.30 PHP ≈ 136.27 units
We can now graph the budget line for 2023, using the new quantity combinations.
Please note that the actual graphing of the budget lines would require plotting the points based on the calculated quantity combinations and connecting them to form the budget line. The computed quantities provided here are approximate and should be adjusted according to the specific graphing scale and precision desired.
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in a multiple regression model, which of the following is correct regarding the value of the adjusted r^2?
A. It can be negative
B. It has to be positive
C. It can be larger than 1
D. It has to be larger than the coefficient of multiple determination
Answers
The correct option is option (B) .
In a Multiple regression Model , the value of adjusted r-Squared is positive.
Adjusted r-Squared :
Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.
The formula for r-squared,
Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]
where
N --> number of points in the data sample.
K --> number of independent regressors, i. number of variables in the model excluding or constant.
r²--> Indicates how well a term (data point) fits a curve or line.
r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.
100% r-squared means that all movements in the security are completely explained by movements in the index.
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Find the quotient. Simplify your answer.
s + 1/
s²1
÷
s^2/
6s²
Enter the correct answer.
Answers
Let's see
\(\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}\)
\(\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}\)
\(\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}\)
\(\\ \rm\Rrightarrow \dfrac{5s^2}{s}\)
\(\\ \rm\Rrightarrow 5s\)
5) An alpha particle moves through a magnetic field along the parabolic path y = x2 – 4. Determine the closest that the particle comes to the origin.
Answers
The closest distance that the alpha particle comes to the origin is √6 units, which occurs at x = ±√2 on the parabolic path y = \(x^{2}\) - 4.
To find the minimum distance, we can use the concept of calculus. The distance between two points (x, y) and (0, 0) is given by the formula √(x^2 + y^2). Substituting the equation of the parabolic path, we have the distance function d(x) = √(x^2 + (x^2 - 4)^2).
To find the minimum, we take the derivative of the distance function, set it equal to zero, and solve for x. Then we substitute the obtained value of x back into the distance function to find the minimum distance.
By solving the equation, we find that the closest distance occurs at x = ±√2. Substituting this value into the distance function, we obtain the minimum distance of √6.
Therefore, the closest distance that the alpha particle comes to the origin is √6 units.
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May someone please help me??!! I would appreciate it a lot!!! :)
The table below shows the relationship between the cost and the number of pounds of apples for three different businesses.
- The business called Annies apples has 5 pounds of apples and costs $17.50
- The business called Frankie’s farm has 3 1/4 pounds of apples and costs $13.65
- The business called Gabby’s Groceries has 4.5 pounds of apples and costs $17.55
Write the ratio of the cost of the apples to the number of pounds of apples for each pair of numbers in the table.
Answers
Answer:
A: (3, 10.50)
B: (1, 3.5)
Step-by-step explanation: A is (3,10.50) becuae the x-value is always based off of how many pounds of apples there are while the y-value is always the price.
B is (1, 3.5) because unit rates are when x = 1. When x = 1 y equals to 3.5.
there were 75 more nurses than doctors. in fact, 8 times the number of nurses exceeded 10 times the number of doctors by 140. how many nurses were there?
Answers
As there were 75 more nurses than doctors and the no. of nurses exceeded 10 times the no. of doctors by 140, there were 305 nurses in total.
Let 'x' be the no. of doctors and 'n' be the no. of nurses.
The first equation would be,
x + 75 = n, as the no. of nurses are 75 more than the no. of doctors
The second equation would be,
8n = 10x + 140, as 8 times the no. of nurses exceeded 10 times the no. of doctors by 140
Substituting equation 1 in 2 we get,
8( x + 75) = x + 140
8x + 600 = 10x + 140
600 - 140 = 10x - 8x
460 = 2x
x = 460/2
x = 230
Hence, the no. of doctors is 230 and the no. of nurses is 230+75 as 'n = x + 75'
Therefore, the no. of nurses is 305
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on blue?
The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fourth, and the experimental probability is 50%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 50%.
Answers
Answer:
Step-by-step explanation:
The statement that best compares the theoretical and experimental probability of landing on blue is:
The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
Theoretical probability is the probability of an event occurring based on the assumption that the spinner is fair, and the experimental probability is the probability of an event occurring based on the data collected from the spins.
Since the spinner has four equal sections, the theoretical probability of landing on any section is 1/4 or 25%. Therefore, the theoretical probability of landing on blue is 1/4 or 25%.
On the other hand, the experimental probability is the number of times an event occurs, divided by the total number of trials.
In this case, the experimental probability of landing on blue is 7/20 or 35%.
So the theoretical probability of landing on blue is one fourth or 25% and the experimental probability is 35%.
“Find 24% of $240.”
I keep trying and getting a different answer each time, please help
Answers
Answer:
$57.60
Step-by-step explanation:
The first thing you want to do is convert 24% to a decimal. To do this you just need to take the current decimal place and move it 2 places to the left. Since this percentage is a whole number the decimal is just after the 4.
(0.24)
Multiply that decimal by the number you want to find the percentage of
$240 * .24 = $57.60
X Is the 24%
So (24x240)/100
5760/100 = $57.60
Or you can just do 240x0.24=$57.60
24% is the same as 0.24
And 100% is the same as 1
pls help, 'll mark the brainliest. SOS
Answers
Answer:
Which one do you need the answer for
Step-by-step explanation:
Find the values of x and y by writing two equations and solving the system of equations.
Answers
Answer:
y=2 x=5
Step-by-step explanation:
3x-2y=11
2x-3y=4
you multiply both equations to cancel one variable out. in this case you multiply the first equation by 2 and the second by -3
6x-4y=22
+ -6x-9y=12
--------------------------
0x+5y=10
y=2
you plug that in either equation
3x-2(2)=11
3x-4=11
3x=15
x=5
what is 6 divided by 10.00 (show work)
Answers
Answer:
3/5
Step-by-step explanation:
6/10 => 3/5
in decimal form its 0.6
Answer:
6÷1000=0,6
Step-by-step explanation:
6÷1000=0,006
0,6/100=
0,6%
the Correct answer is 0,6
HELP IM BEING TIMESD KHAN ACADEMY
Answers
Answer:
a
Step-by-step explanation:
Aamena buys a business costing $23000 She pays part of this cost with $12000 of her own money Calculate what percentage of the $23000 this is Show your calculations
Answers
Answer: 52.173913%
Step-by-step explanation:
The answer is 52.173913%, you can round it <3
I hope this helped! <333
Answer: I got 52.17391304%
Step-by-step explanation:
If you are looking for a rate, you should use R=P/B where R is the % B is the base (23000) and P is the portion (12000) So, it would be set up like this R = 12000/23000
After I got my answer I double checked it by using the formula B = 52.17% x 12000 to see if I got 23000, but instead I got 11,999.10 because I rounded down the long percentage number from 52.17391304% to 52.17%, which would usually be ok and work just fine, but using 52.17% I got 11,999.10. Which is still extremely close to 12000, but not exact. So even though rounding down is usually a requirement in homework situations, this one seems to be an exact percentage with all the digits. Let me know if I can help further. I'm in accounting and I'm curious about this one and would like to know how it goes.
what is the value of the expression (1/2)^3
Answers
Step-by-step explanation:
(1/2)³ = 1³/2³ = 1/8
that is all there is to it.
Which of the following is equivalent to the expression below?
log 3-log 15
Answers
Answer:
C log(1/5)
Step-by-step explanation:
log 3-log 15 = -log _10^(5)
log 5 = log _10^(5)
log (-12) = log _10^(-12)
log (1/5) = -log _10^(5)
log 12 = log _10^(12)
Answer:
\(C. =log\frac{1}{5}\)
Step-by-step explanation:
Formula =======================
consider a and b two real numbers
where a > 0 and b > 0.
\(log\frac{a}{b} =loga-logb\)
……………………………………………………………
log 3 − log 15
\(=log\frac{3}{15}\)
\(=log\frac{3}{3\times 5}\)
\(=log\frac{1}{5}\)
Convert 33.6 inches to meters. (2.54 cm=1 inch)\
Answers
Answer:
33.6 inches(2.54 cm/1 inch)(1 m/100 cm)
= .85344 meters
what is the range of the possible values of r2? 0 to 1 any positive numerical value -1 to 1 0 to 100
Answers
The range of the possible values of r^2 is 0 to 1. It represents the proportion of the dependent variable’s variance that can be explained by the independent variable(s).
The coefficient of determination, often denoted as r^2, measures the proportion of the dependent variable’s variance that can be explained by the independent variable(s) in a statistical model. The value of r^2 ranges from 0 to 1.
A value of 0 for r^2 indicates that the independent variable(s) does not explain any of the variance in the dependent variable. On the other hand, a value of 1 implies that the independent variable(s) fully explain the observed variance in the dependent variable.
Therefore, the range of the possible values of r^2 is 0 to 1. Any positive numerical value within this range indicates a degree of explanatory power, while values outside this range are not meaningful in the context of r^2. It serves as a useful tool for assessing the strength of a statistical relationship and the predictive ability of a model.
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PLEASE HELP ASAP WILL GIVE BEST RATE
Answers
Answer:
2nd one i think
Step-by-step explanation: