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
PQ and QR are 2 sides of a regular 10-sided polygon
Can someone please help I've been struggling on this for quite a while.
Answers
Answer:
Step-by-step explanation:
Measure of inner angle of the n-sided polygon is
[tex]\frac{180(n-2)}{n}[/tex]
~~~~~~~~~~~~~~
m∠PQR = [tex]\frac{180(10-2)}{10}[/tex] = 144°
PQ = QR ⇒ m∠QPR = m∠QRP
m∠PRQ = ( 180° - 144° ) ÷ 2 = 18 °
Answer:
∠PRQ = 18°
Step-by-step explanation:
Sum of interior angles of a polygon = (n - 2) × 180°
(where n is the number of sides)
Interior angle of a regular polygon = sum of interior angles ÷ n
(where n is the number of sides)
Given:
n = 10⇒ Sum of interior angles of a polygon = (10 - 2) × 180° = 1440°
⇒ Interior angle of a regular polygon = 1440° ÷ 10 = 144°
Therefore, as PQ and QR are the sides of the polygon, ∠PQR = 144°
Sum of interior angles of a triangle = 180°
⇒ ∠PQR + ∠RPQ + ∠PRQ = 180°
⇒ 144° + ∠RPQ + ∠PRQ = 180°
⇒ ∠RPQ + ∠PRQ = 36°
As the polygon is regular, PQ = QR which means that ΔPQR is isosceles.
Therefore, ∠RPQ = ∠PRQ
⇒ ∠PRQ = 36° ÷ 2 = 18°
can you please help me
Answers
Answer:
42
Step-by-step explanation:
G-14
O-14
O-14
so 14•3=42
If an article is sold for rs 99000 after discount of 10％ on marked price and adding 10％ of Value added tax VAT find marked price
Answers
Answer:
100000 rupees
Step-by-step explanation:
x × 0.90 × 1.10 = 99000x = 100000what is the area of this object?
Answers
Answer: no idea
Step-by-step explanation:
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answers
Answer:
QUESTION:1:TYLERCOMPLETELY FILLED THE BOX SHOWN BELOW WITH UNIT,CUBES WITH NO GAPS OR OVERLAPS.HE THEN VOUNTED THE NUMBER OF CUBES THAT HE USED TO FILL THE BOX WHAT TYPE OF MESUREMENT IS REPRESENTED BY THE NUMBER OF CUBES TYLER COUNTED?(5.MD.3)A.AREA B.HEIGHT C.VOLUME D.PERIMETER The CORRECT OPTION :C.VOLUMEStep-by-step explanation:
pls brainlest me thank youThe diameter of a circle is 8 miles. What is the angle measure of an arc 3 miles long?
Answers
Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
[tex]\sf radius (r)=\dfrac12 \cdot 8=4 \ mi[/tex]arc length = 3 miSubstituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
Magan has a bag that contains pineapple chews, cherry chews, and lime chews. He performs an experiment. Magan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Magan performs the experiment 68 times. The results are shown below:
A pineapple chew was selected 59 times.
A cherry chew was selected 3 times.
A lime chew was selected 6 times.
Based on these results, express the probability that the next chew Magan removes from the bag will be cherry chew as a decimal to the nearest hundredth.
Answers
Answer:
The Answer is 0.04
Step-by-step explanation:
Help picture below problem 15
Answers
Answer:
Supplementary
Step-by-step explanation:
The two angles are completely different from each other and if you combine them together it'll form a straight line making it 180 degrees
Which of the following statements about area is not true?
A. Area is the total space within the outside edges of a two-dimensional object.
B. Area can be found by counting the number of unit squares that fill a space.
C. Area is the total distance around the outside of a shape.
D. Area is used to help describe the dimensions of a shape.
Answers
Answer:
C. Area is the total distance around the outside of a shape.
Step-by-step explanation:
Answer:
Area is the total distance around the outside of a shape, Would be correct.
Step-by-step explanation:
Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(0, −8) and line y = 8.
Answers
Answer:
-1/32 × x
Step-by-step explanation:
let's define and identify the correct markers of the correct parabola.
so, we have the focus point F (0, -8).
we have the directrix y = 8.
that means the the vertex point (the middle between the focus and the directrix) is (0, 0).
a parabola is turning away from the directrix. the vertex here is below the directrix, so the parabola is opening downwards and has therefore a negative factor of x.
so, we can rule out the 2 positive answer options.
to decide between the other 2, let's use a value of x and see, if the point is equidistant to the focus and the directrix.
e.g. x = 1
so,
y = -1/8 × x²
gives us y = -1/8 for x = 1
that means the point is (1, -1/8).
the distance to the focus (0, -8) is
(1 - 0)² + (-1/8 - - 8)² = 1 + (7 7/8)² = 1 + (63/8)² =
= 64/64 + 3969/64 = 4033/64
the distance to the directrix is the distance to the point (1, 8) as the point on the directrix must have the same x value.
so, the distance (1, -1/8) to (1, 8) is
(1 - 1)² + (-1/8 - 8)² = 0 + (-65/8)² = 4225/64
that is not equal to the distance to the focus.
so, let's try
y = -1/32 × x
the point for x = 1 is (1, -1/32)
distance to focus
(1, -1/32) to (0, -8) = (1-0)² + (-1/32 - -8)² = 1 + (255/32)² =
= 1024/1024 + 65025/1024 = 66049/1024
distance to directrix
(1, -1/32) to (1, 8) = (1-1)² + (-257/32)² = 66049/1024
which is the same distance as to the focus.
so, y = -1/32 × x is the right answer.
FYI - for an actual distance I would have to create the square roots of the numbers used here.
but since we only needed to see, if distances are equal or not, it was sufficient to check if the squares of the distances are equal or not.
solve the formula P = 2l + 2w for w.
Answers
We are given the following equation :
[tex]{:\implies \quad \sf P=2L+2w}[/tex]
And we need to solve for w, so let's start :
[tex]{:\implies \quad \sf P=2L+2w}[/tex]
Now, transpose 2L to LHS ;
[tex]{:\implies \quad \sf P-2L=2w}[/tex]
[tex]{:\implies \quad \sf 2w=P-2L}[/tex]
[tex]{:\implies \quad \boxed{\bf{w=\dfrac{(P-2L)}{2}}}}[/tex]
Hence, Option a) is correct
15 POINTS ANSWER FAST!
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answers
Diagonal of the rectangle PQRS:
7^2 + 14^2 = SQ^2
SQ = 7 root 5
Diagonal of the square LMNO:
7^7 + 7^7 = OM^2
OM = 7 root 2
When dividing SQ or multiplying OM by 2, you don’t get the exact answer so she’s wrong
A student was asked to simplify the expression 2(x+3)+(4x−8)−7x.
Identify the line which contains the initial error.
1: 2(x+3)+(4x−8)−7x
2: 2x+6+4x+8−7x
3: (2x+4x−7x)+(6+8)
4: −x+14
Answers
Answer:
Line 2
Step-by-step explanation:
When factoring the second bracket, 1 x -8 is -8.
Answer:
4
Step-by-step explanation:
2{x+3}+{4x_8}_7x is same2x+6+4x+8_7x the first bracket was multiply by 2 {2x+4x_7x}+{6+8} the like term was collected and grouped with bracketshelp please .and thank u :)
Answers
Answer:
5/8
Step-by-step explanation:
because 1 minus 3/8 is 5/8
Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3.
What is the length of line segment LJ?
9 units
12 units
15 units
18 units
Answers
Answer:
I think 9 units is the correct answer
Answer:
its 15 units
Step-by-step explanation:
momma told me it was right
The Greyhound bus going to Michigan leaves the station every 20 minutes. Another bus going to Arkansas leaves the station every 40 minutes. If it is 10:40 a.m., what will be the first time both Greyhound buses leave the station at the same time?
Answers
The Greyhound bus going to Michigan leaves the station every 20 minutes.
it's 10:40
so next departure on 10:60 => 11:00 then 11:20 then 11:40...
Another bus going to Arkansas leaves the station every 40 minutes.
it is 10:40
so next departure on 11:20 then 12:00
=> 11:20
A teacher teaches 8 students how to fold an origami model. Each of these students goes on to teach 8
students of their own how to fold the same model. If this teaching process goes on for 6 generations,
how many people total will know how to fold the origami model
Answers
Answer:
8x8= 64
64x6= 384
384 is the answer
Let me know if i helped!
can someone help me answer this question?
Answers
check picture uploaded to see steps
children = 201
adults = 277
x -5 = 2x -8 solve this equation
Answers
Answer:
x = 3
Step-by-step explanation:
x - 5 = 2x - 8
First subtract x from both sides: -5 = x - 8
Finally, add 8 to both sides: 3 = x
Hope this helps!
99x78
123x56
98x172
38x900
Answers
Answer:
99x78=7722
123x56=6888
98x172=16856
900x38=34200
Step-by-step explanation:
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answers
Answer:
143
Step-by-step explanation:
I'm not sure if this is correct but this is what I came up with:
all angles combined must add to 360
125+55+37= 217
360-217=143
Which of the binomials below is a factor of this trinomial?
x^2 - 9x + 18
A. x + 2
B. x - 2
C. x - 3
D. x + 3
Answers
Answer:
C is the answer
Hope this helps you :) Good Luck!!!
What is the value of X?
Sin 55° = cos X.
Enter your answer in the box.
Answers
Answer:
x = 35°
Step-by-step explanation:
sin x = cos (90° - x)
sin 55° = cos (90° - 55°)
sin 55° = cos 35°
x = 35°
A bag contains 9 green marbles, 6 purple marbles, 4 red marbles, 10 blue marbles, and 7 orange marbles. One marble is randomly selected from the bag.
What is the probability that the marble selected is blue or purple?
Answers
The probability that the marble selected is blue or purple is the likelihhood of selecting a blue or purple marble
The probability that the marble selected is blue or purple is 0.444
How to determine the probability?From the question, we have:
Green = 9
Purple = 6
Red = 4
Blue = 10
Orange = 7
So, the total number of marbles is:
Total = 9 + 6 + 4 + 10 + 7
Total = 36
The number of blue or purple marbles is;
Blue or purple = 10 + 6
Blue or purple = 16
So, the probability that the marble selected is blue or purple
p = 16/36
Evaluate
p = 0.444
Hence, the probability that the marble selected is blue or purple is 0.444
Read more about probability at:
https://brainly.com/question/251701
Abby is shooting a rocket off the top of a 128 foot tall building at a velocity of 96 feet per second. The equation to represent this is h(t) = -16t? +960 + 128 where h(t) represents the height of the rocket and t is the time after takeoff.
What is the maximum height of the rocket?
How many seconds does ot take to get to the maximum height?
Find the time it takes (in seconds) for the rocket to crash to the ground.
Answers
Answer:
a) 272 feet
b) 3 seconds
c) 7.123 seconds
Step-by-step explanation:
A graphing calculator provides an easy way to answer questions about the parameters of a quadratic function. Here the graph shows ...
a) the maximum height is 272 feet
b) it takes 3 seconds to get there
c) the rocket crashes after about 7.123 seconds
__
You can solve this algebraically by rewriting the equation in vertex form.
h(t) = -16t² +96t +128 . . . . . . given
h(t) = -16(t² -6t) +128 . . . . . . . factor out leading coefficient
h(t) = -16(t² -6t +9) +128 -(-16)(9) . . . . complete the square
h(t) = -16(t -3)² +272 . . . . . . write in vertex form
The vertex of the height function is (3, 272) meaning the rocket reaches a maximum height of 272 feet after 3 seconds.
__
The zero of the function can be found to be ...
0 = -16(t -3)² +272
0 = (t -3)² -17 . . . . . . divide by -16
t -3 = ±√17 . . . . . . add 17, take the square root
t = 3 +√17 ≈ 7.123106 . . . . . positive time value for h(t) = 0
It takes about 7.12 seconds for the rocket to crash.
What is the mean , median
Answers
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
. There is 40% decresed in price on a sale. It is futher decresed by 5% find the total decreased percentage
Answers
Let x be the original price of the object.
After the 40% discount, the price of the object now becomes;
x-0.4x=0.6x
0.6x is our new price after the first discount.
Now if we want to find the price after the second discount, (5%)
That would come off to be;
0.6x-0.6(0.05)x=0.6x-0.03x=0.57x
Our last price is 0.57x
If you notice, there was a 43% discount in total, as it goes to 57% of its original price.
This is very non intuitive for some people, as they may think there will be a 45% discount.
How to solve x + y[tex]\frac{dy}{dx}[/tex] = 0
Given that solution goes to (2,0) Neither x nor y can exceed 2
Answers
Answer:
The answer is {D}
Step-by-step explanation:
in november 1958 the cover scientific american showed this diagram on its cover. Each of the interior rectangles is a square. if square D is 81 spuare units and square c is 64 square units what is the area of the other seven squares? what is the area of the of the entire figure? what is the perimeter of the figure
Answers
From the 32 by 33 rectangular figure, having interior squares, we have
The area of the squares in square units are;
A = 324 B = 225E = 100F = 196G = 16H = 49I = 1Area of the entire figure = 1056The perimeter of the figure = 130 unitsHow can the area and perimeter be found?The areas in square units are;
Area of square A = 18 × 18 = 324
Area of square B = 15 × 15 = 225
Area of square E = 10 × 10 = 100
Area of square F = 14 × 14 = 196
Area of square G = 4 × 4 = 16
Area of square H = 7 × 7 = 49
Area of square I = 1 × 1 = 1
Area of a rectangle = Length × Breadth
Therefore;
Area of the entire figure = 32 × 33 = 1056
Area of the entire figure = 1056 square unitsThe perimeter, P, of the rectangular figure is therefore;
P = 2 × 32 + 2 × 33 = 130
The perimeter of the figure = 130 unitsLearn more about finding the area of plane figures here;
https://brainly.com/question/2669479
Question
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−1/3+4
Answers
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = -1/3 x +4
So : product for two slopes = -1 means : m×-1/3=-1
m = 3
now : y = 3 x+b
but this line :
through the point (4,3) : 3 =3(4)+b....... b=-9
conclusion :
the equation is : y =3x -9