Determine the type of symmetry of r=-7+ 2cos3ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) none of these
C)line /2
D) polar axis
Answers
well, hmmm to check for polar symmetry, hmmm say we simply replace the value for either "r" or "θ" or both in the original equation, if the equation rendered is the same as the original, there you have it, symmetry, so let's do that.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=-7+2cos(3\theta )\implies (-r)=-7+2cos[3(-\theta )]\implies -r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\implies r=7-2cos(3\theta )\impliedby \textit{woopsie, no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=-7+2cos(3\theta )\implies r=-7+2cos[3(-\theta )]\implies r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\impliedby \textit{low and behold\qquad \Large \checkmark}[/tex]
now, we could run a test for "the pole" or namely the origin by simply changin r = -r, however we already know where the symmetry is, so no need.
Check the picture below.
Related Questions
(3) Need help. Brainliest if correct only, don’t answer if you don’t know HAVE A NICE DAY
Answers
Answer:
5/2
Step-by-step explanation:
In triangle XYZ, the known side is XZ, which is equal to 5. The corresponding side to this side would be MN, which is equal to 2. Divide XZ/MN in order to get 5/2.
Express 9 2/3 out of 100 as a percent .
Answers
Answer:
9 2/3% (or 9.66666666666%)
Step-by-step explanation:
A percent is a ratio out of 100, as this answer is out of 100, the percent is just 9 2/3%.
If you spend 1.5 hours a week studying for English and 5 hours studying for math what is the ratio of time spent studying in math to studying for English?
Answers
Answer:
1.5/5
Step-by-step explanation:
For every 1.5 hours your spend studying English, you spend 5 hours studying Math.
Brainliest please?
what is the mean of 13,5,11,8,14,15
Answers
Answer:
11
Step-by-step explanation:
The mean is the average. To find the average, add up all the numbers, then divide by the amount of numbers there are. 13 + 5 + 11 + 8 + 14 + 15 = 66. There are 6 numbers. 66 divided by 6 = 11.
Answer:
11 is your mean
so urgent pls
Answers
Answer:
B
because if you were looking for time that is less than and equal to you would have to choose (c) as you answerSomeone help me ASAP !!!!
Answers
Answer:
ok sure wait
Step-by-step explanation:
At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate).
Students with Early Classes
Students without Early Classes
Coffee 73 63
Banana 53 103
The marginal cost of coffee is 5 and the marginal cost of a banana is 20.
The café owner is considering three pricing strategies:
1. Mixed bundling: Price bundle of coffee and a banana for 166, or just a coffee for 73.
2. Price separately: Offer coffee at 63, price a banana at 103.
3. Bundle only: Coffee and a banana for 126. Do not offer goods separately.
Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.
For simplicity, assume there is just one student with an early class, and one student without an early class.
Price Strategy
Revenue from Pricing Strategy
Cost from Pricing Strategy
Profit from Pricing Strategy
1. Mixed Bundling
$
$
$
2. Price Separately
$
$
$
3. Bundle Only
$
$
$
Pricing strategy yields the highest profit for the café owner.
Answers
Based on the prices, the willingness to pay of the students and the costs, the profits will be:
Mixed bundling = 209.Price separately = 199.Bundle Only = 202.The pricing strategy that yields the highest profit is the Mixed bundling strategy.
What is the profit from Mixed bundling?First find the willingness to pay for both the students with early classes and those without.
Student with early classes: Students without early classes:
= 73 + 53 = 63 + 103
= 126 = 166
At a mixed bundling price of 166, only students without early classes will be able to afford the bundle as their willingness to pay is 166.
Student with early classes will only take the coffee at 73 because their willingness to pay of 126 is lower than the 166 bundle price.
Profit is:
= (Bundle price + Coffee price) - (Marginal cost of two coffees + Marginal cost of banana)
= (166 + 73) - (2 x 5 + 20)
= 209
What is the profit from pricing separately?At separate only pricing students without early classes will be able to afford the both things at 166.
Student with early classes will only take the coffee at 63 because their willingness to pay of 126 won't allow them to take both items.
Profit:
= (63 + 63 + 103) - (2 x 5+ 20)
= 199
What is the profit from price separately?At a bundle only price of 126, both the students with early classes and those without early classes will be able to afford the bundle as their willingness to pay, match the price.
Profit will be:
= (126 + 126) - (2 x 5 ) for coffee - (2 x 20) for bananas
= 202
In conclusion, the woman should go with the Mixed bundling as it gives the highest profit of 209.
Find out more on pricing strategies at https://brainly.com/question/7303679.
PLS HELP OMG I CANT FIND IT
Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value.
Fix)
X
0-9
10
k= -3
k = 3
k = 5
k = 8
graph below pls help
Answers
Answer:
(d) k = 8
Step-by-step explanation:
The value k in the equation ...
g(x) = f(x) +k
represents a vertical translation by k units.
__
The vertex coordinates for f(x) and g(x) are ...
f(x): vertex = (-3, -3)
g(x): vertex = (-3, 5)
This means ...
f(-3) = -3
g(-3) = 5 = f(-3) +k = -3 +8 ⇒ k = 8
_____
Additional comment
Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.
Jackie has three pieces of ribbon Two of the pieces are q.75 inches in length and the other piece is 6.8 inches long. What is the combined length of Jackie's ribbons?
Answers
Answer:
7.55 inches
Step-by-step explanation:
Add the two values together:
0.75 + 6.8 = 7.55
The combined length of Jackie's ribbons is 7.55 inches!
You open a money market account with $7500 at 5% compound quarterly. After two years, $1500 is withdrawn from the account to buy a new computer. A year later, $2000 is put in the account. What will be the ending balance if the money is kept in the account for another three years?
Answers
Answer:
$10,596.81
Step-by-step explanation:
The balance on an account earning 5% interest compounded quarterly can be found using the formula ...
A = P(1 +0.05/4)^(4t)
where P is the principal invested and t is the number of years.
__
Here, we are investing $7500.00. After 2 years, the account balance will be ...
A = $7500(1 +0.05/4)^(4·2) = $8283.65
After the $1500 withdrawal, the new balance will be ...
$8583.65 -1500.00 = $6783.65
__
This is the amount earning interest for the next year, after which time the balance will be ...
A = $6783.65·(1.0125)^(4·1) = $7129.24
When $2000 is added to the account, the principal earning interest for the last 3 years is ...
$7129.24 +2000.00 = $9129.24
__
The final balance after 3 more years is then ...
A = $9129.24·(1.0125)^(4·3) = $10,596.81
_____
These calculations are conveniently carried out by a spreadsheet, as in the attached. Since the account changes are all done at the end of the year, we don't have to keep track of the quarterly balances. The formula used to calculate the ending balance each year is shown.
Arcs and angles relay puzzle
Answers
Applying the angles of intersecting chords theorem, the value of x in the first figure is: x = 7.
What is the Angles of Intersecting Chords Theorem?If two chords of a circle intersect, the angles of intersecting chords theorem states that, the measure of the angle formed equals 1/2(sum of the measure of the arcs which are intercepted.
Thus, we can use the angles of intersecting chords theorem to find missing angles or value of x in the questions given.
For example, let's find the value of x in the first figure given:
12x + 5 = 1/2(83 + 95)
12x + 5 = 89
12x = 89 - 5
12x = 84
x = 7
Using same strategy, you can solve the rest of the problem given.
Learn more about the angles of intersecting chords theorem on:
https://brainly.com/question/1626547
what is 1.5 +1.5 in a fraction
Answers
Therefore, 1.5 as a fraction is written 3/2.
Answer:
3/1
Step-by-step explanation:
1.5+1.5
calcular los dos primeros términos
3
escribe el número entero como una fracción
3/1
PLEASE HELP BEFORE MIDNIGHT
Answers
Answer:
Step-by-step explanation:
Variance=0.0016
Standard deviation is the square root of variance.
sigma=sqrt(0.0016)=0.04
mean=0.9 inch
Calculating z for 0.936 inch
z = (0.936 - 0.9)/0.04
= 0.036/0.04
= 0.9
Using normal distribution table
P(x<=0.936 inch)
= P(0.9)
= 0.81594
P(x>0.936) + P(x<=0.936) = 1
P(x>0.936)
= 1 - P(x<=0.936)
= 1 - 0.81594
= 0.18406
= 0.1841
In 1992, South Dakota's population was 10 million. Since then, the population has grown by 1.4% each year. Based on this, when will the population reach 20 million?
Answers
Answer:
49.9 years or 50 years later. At year : 2042Explanation:
use compound interest formula: [tex]\sf \boxed{ \sf P ( \sf 1 + \dfrac{r}{100} )^n}[/tex]
[tex]\rightarrow \s \sf 10( 1 + \dfrac{1.4}{100} )^n = 20[/tex]
[tex]\rightarrow \sf ( 1.014) ^n = 2[/tex]
[tex]\rightarrow \sf n( ln( 1.014) ) = ln(2)[/tex]
[tex]\rightarrow\sf n = \dfrac{ln(2)}{ln( 1.014)}[/tex]
[tex]\rightarrow\sf n = 49.8563 \ years[/tex]
Answer:
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is initial valueb is the base (or growth factor in decimal form)x is the independent variabley is the dependent variableIf b > 1 then it is an increasing functionIf 0 < b < 1 then it is a decreasing functionAlso b ≠ 0Given information:
initial population = 10 milliongrowth rate = 1.4% each year⇒ growth factor = 100% + 1.4% = 101.4% = 1.014
Inputting these values into the equation:
[tex]\implies y=10(1.014)^x[/tex]
where y is the population (in millions) and x is the number of years since 1992
Now all we need to do is set y = 20 and solve for x:
[tex]\implies 10(1.014)^x=20[/tex]
[tex]\implies 1.014^x=2[/tex]
[tex]\implies \ln 1.014^x=\ln 2[/tex]
[tex]\implies x\ln 1.014=\ln 2[/tex]
[tex]\implies x=\dfrac{\ln 2}{\ln 1.014}[/tex]
[tex]\implies x=49.85628343...[/tex]
1992 + x = 2041.8562....
Therefore, the population will reach 20 million during 2041, so the population will reach 20 million by 2042.
The mathematics faculty at a college consists of 12 professors, 6 associate professors, 9 assistant professors, and 8 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.
Answers
Answer: [tex]\frac{4}{7}[/tex]
Step-by-step explanation:
P(a) or P(b) = P(a) + P(b)
This means that the probability of a or b is the same of the probability of a plus b
So let's see the probability of a, selecting a professor
[tex]\frac{12}{12+6+9+8} \\\\\frac{12}{35}[/tex]
We won't simplify just yet so that addition will be easier later
Now let's see the probability of selecting b, an instructor
[tex]\frac{8}{12+6+9+8} \\\\\frac{8}{35}[/tex]
Now add the 2 probabilities together
[tex]\frac{12}{35} +\frac{8}{35} =\frac{20}{35}[/tex]
Simplify.
[tex]\frac{20}{35} =\frac{4}{7}[/tex]
HELP WILL GIVE BRAINLIEST!!!!
2. Which of the following equations is FALSE?
BC=20
AC=20
BD= 10
AD= 10
Answers
Answer:
letter c the BD= 10
Step-by-step explanation:
Answer:
BD=10
Step-by-step explanation:
1. BAD=BCD=60
Therefore
BA = BC (sides opposite to equal angles are equal)
BA=20
Therefore BC=20
2.BAC+BCA+ABC=180(sum of the interior angles of a triangle is 180)
60+60+ABC=180
ABC=180-120
ABC=60
ABC=BAC=BCA
Therefore ABC is an equilateral triangle
AC=20
4. AC=AD+DC
AD=DC (BD is a perpendicular bisector)
Therefore
AC=2×AD
AC=20
20=2×AD
AD=20÷2
AD=10
Hope this helps!
A bird is nested on a tree top that is 14 feet above the ground. The bird looks down at a worm at a 30 angle of depression. How far is the worm from the base of the tree?
Answers
Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
What is the Tangent Ratio?Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.
The information given would form a right triangle, where:
Reference angle = ∅ = 30°Opposite side = 14 ftAdjacent side = distance of the worm from the base of the tree = xApplying the tangent ratio, we would have:
tan 30 = 14/x
x = 14/tan 30
x = 24.2 ft.
Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
Learn more about tangent ratio on:
https://brainly.com/question/14169279
Convert 68% As a fraction
Answers
Answer:
68/100
Step-by-step explanation:
It would be this because, with percentages, 100 is full. Therefore, we can just make 68 be out of 100. Hope this helps :)
Which of these describes an angle?
Extends in both directions with no end
The amount of turn between two straight lines that have a common endpoint, or vertex
A part of a line that connects two endpoints
Has a start point but no endpoint
Answers
A test requires two hours to attend five questions if a candidate spent 80 minutes on the first two question what fraction of the time did he spend on the remaining three question
Answers
Answer:
He spent ⅓ of the time on the remaining three questions.
Step-by-step explanation:
Let's first figure out what the question gives us, and what we need to find.
Given:
Test - 2 hours, 5 questions
Candidate - 80 minutes, 2 questions
Find:
Fraction of time he spent on remaining three questions
Start by finding the fraction of time that he spent on the first two questions.
Set up an unit converter to convert two hours to minutes.
[tex]2$ hours($\frac{60\text{ minutes}}{1 \text{ hour}})=2\cdot 60\text{ minutes}=120$ minutes[/tex]
Let "x" represent the fraction of time the candidate spent on the first two questions...
[tex]x=\frac{\text{Amount of Time spent on First Two Questions}}{\text{Total Time}}\\x=\frac{80\text{ minutes}}{120\text{ minutes}}[/tex]
[tex]x=\frac{80}{120}[/tex]
[tex]x=\frac{8}{12}[/tex]
[tex]x=\frac{2}{3}[/tex]
Let "y" represent the fraction of time the candidate spent on the remaining three questions...
[tex]y=1-\text{Fraction of Time spent on First Two Questions}\\y=1-\frac{2}{3}\\[/tex]
[tex]y=\frac{3}{3}-\frac{2}{3}\\[/tex]
[tex]y=\frac{1}{3}[/tex]
He spent ⅓ of the time on the remaining three questions.
Help me pls answer 1&2&3 pls brainless
Answers
Answer:
3,1,5
Step-by-step explanation:
Find the missing side lengths. Leave your answers as radicals in simplest form.
1)
2)
1459
712
b
b
र
45°
a
X
3)
D)
X
у
45 6/3
459
912
X
x
Answers
Answer:
1) y = 7 x = 7
2) y = 4.243 x = 4.243
3) y = 7.348 x = 7.348
4) y = 9 x = 9
Step-by-step explanation:
just use a calculator and put in the given information
search Right Triangle Side and Angle Calculator
Answer:
Below in bold.
Step-by-step explanation:
1. This is an isosceles right angled triangle.
x = y.
The ratio of the sides in this triangle are 1:1:√2
So 1/√2 = x / 7√2
√2 x = 7√2
x = 7.
y = 7.
The other 3 are solved in a similar way as they are all isosceles right angled triangles:
2. b = 6 and a = 6√2.
3. 1 / √2 = x / 6√3
√2 x = 6√3
x = 6√3 / √2
x = 6√3 * √2 / 2
= 3√6
y = 3√6.
4. x = y = 9.
I am not sure how to do for this question! Pls help
Answers
Answer:
wheres the question
Step-by-step explanation:
??????
Evaluate the expression for x = 6 and y = 4.
xy-3y =
Answer:
Answers
Answer:
12
Step-by-step explanation:
Since given that:
x = 6 and y = 4
we can substitute:
xy - 3y
(6)(4)-3(4) {6*4 = 24}
24 - 3(4) {3*4=12}
24 - 12 = 12
Hence, the answer = 12
~lenvy~
Answer: 12
Step-by-step explanation:
Given:
xy - 3y
Plug-in the values we know:
(6)(4) - 3(4)
Multiply 6 by 4 and 3 by 4:
24 - 12
Subtract:
12
xy - 3y = 12
How many possible outcomes exist? 2 3 5 6
Answers
Answer:
1.) C2.) C3.) D4.) D5.) C
Step-by-step explanation:
What is 8x25 to ding out the answer please
Please I need help please help
Answers
Answer: 8x25= 200
Step-by-step explanation: 200
Answer:
8×25
=200 is the answer ok
Blake went shopping for a new pair of pants because of a sale. The store was offering a 10% discount. If the price on the tag was $40, what would be the price after the discount but before tax, to the nearest dollar and cent?
Please don't send a link!
Answers
If you subtract 10% from 40 you get 36… and that’s with no tax
$36 is the price after the discount but before tax.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the store was offering a 10% discount.
The price on the tag was $40
We have to find the price after the discount but before tax,
The discount is 10% of $40, which is:
0.1 x $40 = $4
So the discounted price is:
$40 - $4 = $36
Hence, $36 is the price after the discount but before tax.
To learn more on Percentage click:
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#SPJ2
18.
Given that sin x =
8
and sin y = , where x and y are acute, find the value of cos (x + y).
17
A.
B.
130
221
140
221
140
204
220
22
C.
D.
Answers
Answer:
B
Step-by-step explanation:
[tex]\sin{x}=\frac{5}{13}, \cos{x}=\sqrt{1-(\frac{5}{13})^2}=\frac{12}{13}[/tex]
[tex]\sin{y}=\frac{8}{17}, \cos{y}=\sqrt{1-(\frac{8}{17})^2}=\frac{15}{17}[/tex]
[tex]\cos(x+y)=\cos{x}\cos{y}-\sin{x}\sin{y}\\=\frac{12}{13}\times\frac{15}{17}-\frac{5}{13}\times\frac{8}{17}\\=\frac{140}{221}[/tex]
If P = (-6, 9), Find:
r90°(P)
([?], [ ]
Answers
Answer:
(-9, -6)
Step-by-step explanation:
Rotation 90° = (x, y) --> (-y, x)
(-6, 9) --> (-9, -6)
hope this helps and is right!! p.s. i really need brainliest :)
What is the area?
This is 6th grade math
Answers
Answer:
Find the base, and then the height of this rhombus;
Base: 7 square units
Height: 7 square units
Multiply your base by the height to get the area;
Because the formula for the area of a rhombus is, A = BH
So,
A = 7(7)
A(area) = 49 square units.