5

The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,0). X = 2ySelect the equation in polar coordinates_0A 2r ...

Question

The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,0). X = 2ySelect the equation in polar coordinates_0A 2r cos 0 - sin 0 = 00 B. 2r cos 0 - / sin 20 =0 0D. 72 cos 20 - 2r sin 0 = 012 cos 0 - 2r sin 0 = 0

The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,0). X = 2y Select the equation in polar coordinates_ 0A 2r cos 0 - sin 0 = 0 0 B. 2r cos 0 - / sin 20 =0 0D. 72 cos 20 - 2r sin 0 = 0 12 cos 0 - 2r sin 0 = 0



Answers

The letters $x$ and $y$ represent rectangular coordinates. Write each equation in polar coordinates $r$ and $\theta .$ $$ x^{2}+y^{2}-2 x+4 y=0 $$

Okay, we are given a polar equation and we are going to be writing it in actually rectangular. So we're going to quickly jot all of our nice relationships between our polar and rectangular here to the side. Now the big goal for um the conversion is to be able to find these things. We prefer our squares, we refer prefer arco sine thetas. So the first thing I'm gonna do is I am going to multiply both sides by our so now I have two things I like and then one thing that I don't really like here, like my R squared and I like my arc assigned data now um there are a lot of books that don't mind you replacing a R. With a square root of X squared plus y squared. Um One of the books I teach out of does not really like that, but others are okay with it. So you know it kind of depends on um what you've communicated with your teacher however, um so at this point you could bring in for our square that X. Squared plus Y. Squared for are the square root of X. Squared plus Y squared. And then that our coastline data. So um because mine um you know doesn't I'm going to try to keep going here and make it so something that my textbook would like. So what I've done here is I squared both sides and I moved all my ours over. So that means I had a four R. Squared on my right. So now I can do my four times my X. Squared plus Y. Squared. So I don't really have any square roots. Now. It is very ugly and my exes and wise are all mixed up for this equation. We wouldn't be able to get it to a pretty form anyway.

So remember that remember that are squared is equal to X squared, so are squared is equal to x squared plus y squared and all our X is equal to our co signer Fada and why is equal to our sign of data? And so if we re manipulate this equation to look like r squared times are is equal to is equal to our co sign a fader. In other words, we multiply both sides of the equation by and are well, we know R squared is just X squared plus y squared and our would be the square root of expertos y squared. So we have times a squared of X squared Plus why squared and then this is equal to our coast on a fado which is equal to X. So this is our new equation in terms of X is and why So this is our rectangular equation.

Okay we're given equation in terms of X's and Wise and we are going to convert that to polar. So with our nice right triangle um that we can draw, we can really drive any equation that we would need to use for this process. Now before we go too far, I just like to note um that we do have an X squared plus y squared in here, you know that looks like a circle and then with the minus four X. That means it's probably been moved to the right um two units. So um we'll talk about what you know, we'll go through the process of actually converting it but it's good to think about what you think that it looks like. Okay so notice that we have that X squared plus Y squared equals R squared. So we can take that out and we can just put in our R squared for those two pieces. Now when we get to our value of X we also have equation for that we can place in our co sign data and then um notice that there are ours in both terms. You can either factor it out or you can just add that for our cosign data over. And then when you do divide both sides by an art, you get that are equals for cosign data. Well what we know about that a co sign data is it does it makes a circle that's a metric on the X. Axis and um it has a radius or diameter four. So that means it's a radius of two bits, definitely that transposed circle that we thought it was.

So since we know that X squared plus y squared is equal to R squared and that X is equal to our co sign of data, then we have we have r squared is equal to So let's there are squared is equal to our co sign of data is equal to our co sign of data. And so we find that if we divide both sides by are we get our is equal to co sign of data and so this is our solution.


Similar Solved Questions

5 answers
Evala te fy 4x+2 cAwhtre p i rein exloseX 69 5 =x2 Y=2*
Evala te fy 4x+2 cA whtre p i rein exloseX 69 5 =x2 Y=2*...
5 answers
Solve the following limiting reactants problems using the reaction given and dimensional analysis.Ca(OH)z KzsCas2 KOHWhat is the theoretical vield of KOH if there are 11.2 g Ca(OHJz and 13.7 g KzS initially?What is the limiting reactant?C, If the actual yield of potassium hydroxide is 10.9 &, what is the percent vield?
Solve the following limiting reactants problems using the reaction given and dimensional analysis. Ca(OH)z Kzs Cas 2 KOH What is the theoretical vield of KOH if there are 11.2 g Ca(OHJz and 13.7 g KzS initially? What is the limiting reactant? C, If the actual yield of potassium hydroxide is 10.9 &am...
2 answers
You mey Want jararenco (Pages 76 85) Section 2 2 uhile complaling thls probien Calculale Ia wavclcngb each outne following lrequencios 0d clcctromaglelic rudialionMHx (ypkol hoxnency FM rdic broudc !slirig) Erolety VOuIAneun (nelens Weinnour cenilicau[ ligurosA2dnaninReauestanttpan E1065 KHz (typical Irequenc; ar AMtatng taadcastng Expies$ Your aneter metets using four siondlicant fgurespuna
You mey Want jararenco (Pages 76 85) Section 2 2 uhile complaling thls probien Calculale Ia wavclcngb each outne following lrequencios 0d clcctromaglelic rudialion MHx (ypkol hoxnency FM rdic broudc !slirig) Erolety VOuIAneun (nelens Weinnour cenilicau[ liguros A2d nanin Reauestantt pan E 1065 KHz ...
2 answers
At the interactive prompt;, define list named that contains four strings or numbers 9., L-[0; 2,3])- What happens when you try to index out of bounds (e.g., L[4])? What - bout slicing out of bounds g-, L(-1OOO:100])? Finally, how does Python handle you try to extract sequence in reverse with the lower bound greater than the higher bound (e.g . L[3:1J)? Hint: try assigning to this slice(L[3:1]-['? ]) and see where the value is put:
At the interactive prompt;, define list named that contains four strings or numbers 9., L-[0; 2,3])- What happens when you try to index out of bounds (e.g., L[4])? What - bout slicing out of bounds g-, L(-1OOO:100])? Finally, how does Python handle you try to extract sequence in reverse with the low...
5 answers
Balance the the reaction (find the values of A B, C, and D for the questions below): CoCl,(aq) Na,PO (aq) Co(PO ) (s) NaCLlaq)
Balance the the reaction (find the values of A B, C, and D for the questions below): CoCl,(aq) Na,PO (aq) Co(PO ) (s) NaCLlaq)...
5 answers
Problem 6.3. Compute the limits of the following sequences (show your work):(2n+3)(3n+2) n2_6 b) (n+3) _ (n+1)? (where a? = aVa) 3"+1, 7n +3 4".5"-2n (-2)"+3" (2)n+1+3n+I(n3+1)3 sin?(n3_1)H(n3_1)3 cos?(n3+1) 3 2 (E) (2.3,2.33,2.333,2.3333,where a is a real number(h)
Problem 6.3. Compute the limits of the following sequences (show your work): (2n+3)(3n+2) n2_6 b) (n+3) _ (n+1)? (where a? = aVa) 3"+1, 7n +3 4".5"-2n (-2)"+3" (2)n+1+3n+I (n3+1)3 sin?(n3_1)H(n3_1)3 cos?(n3+1) 3 2 (E) (2.3,2.33,2.333,2.3333, where a is a real number (h)...
5 answers
Sketch the graph of = Tunctior that satisies the stated conditions Vimit at * = butitis not continuous at* = continuous d* = Dul Valut ]* = charged Irorr f()=Ito f (3) = continuuus 4 * TEGIQuable discontinuityak=carwhich f (c) wndelined; has 3 removable discontinultv atr cfor vhich f (c) is definedbecomies
sketch the graph of = Tunctior that satisies the stated conditions Vimit at * = butitis not continuous at* = continuous d* = Dul Valut ]* = charged Irorr f()=Ito f (3) = continuuus 4 * TEGIQuable discontinuityak=carwhich f (c) wndelined; has 3 removable discontinultv atr cfor vhich f (c) is defined...
5 answers
(7 pts: Let T € L(C?) be defined byTz (-921.422). Vz = (21,22) € C?Additionally let R € C(C?) be defined byRz (3iz1. 222) . Vz € C2.Does R = VT? YES or NO. Please box vour answer
(7 pts: Let T € L(C?) be defined by Tz (-921.422). Vz = (21,22) € C? Additionally let R € C(C?) be defined by Rz (3iz1. 222) . Vz € C2. Does R = VT? YES or NO. Please box vour answer...
2 answers
Suppose {ak} is a sequence of numbers with the property that ak > 0 for all k Suppose that there exists an M € R so that for all n € N we have M Under these hypotheses, prove that ak converges
Suppose {ak} is a sequence of numbers with the property that ak > 0 for all k Suppose that there exists an M € R so that for all n € N we have M Under these hypotheses, prove that ak converges...
5 answers
Use the tangent feature of a calculator to display the curve and the tangent line for the given values of $x$$$y= rac{2}{x+1} ; x=-0.5, x=0, x=1$$
Use the tangent feature of a calculator to display the curve and the tangent line for the given values of $x$ $$y=\frac{2}{x+1} ; x=-0.5, x=0, x=1$$...
5 answers
Suppose that 700 W of radiation in = microwave oven is absorbed by 250 g of water in very lightwelght cup.PanAHow long will it take for the water t0 warm Up from 10 C to 90C? Express your answer in seconds_AZdE )AtSubmitRequest Answer
Suppose that 700 W of radiation in = microwave oven is absorbed by 250 g of water in very lightwelght cup. PanA How long will it take for the water t0 warm Up from 10 C to 90C? Express your answer in seconds_ AZd E ) At Submit Request Answer...
1 answers
Find the centroids of the geometric structures. Be alert for symmetries and opportunities to use Pappus's Theorem. The solid obtained by rotating the region in Figure $7.41(\mathrm{a})$ about the $y$ -axis. (FIGURE CAN'T COPY)
Find the centroids of the geometric structures. Be alert for symmetries and opportunities to use Pappus's Theorem. The solid obtained by rotating the region in Figure $7.41(\mathrm{a})$ about the $y$ -axis. (FIGURE CAN'T COPY)...
5 answers
24 Z6eIa ( (65
24 Z6e Ia ( (65...
5 answers
Preuouilk Arthur contuncted Gonndsno Intnenlltttc smple mean 0f 63 populbtionutandald daadan 04 6 9574uuareanai undaneumnla ala 200]Hix colloanucs corvince hlm Inaaian JabUrnr pooubbonmnratadrd drtattum @aa Whlen euna ier Eer OUrEnrrnr Aetam HrntatJricretanTha cujutoe intawn larcre uLt0 Tho munin Frror Lmncmzersuduru error of the mejn will drcrzto
Preuouilk Arthur contuncted Gonndsno Intnenlltttc smple mean 0f 63 populbtionutandald daadan 04 6 9574uuareanai undaneumnla ala 200]Hix colloanucs corvince hlm Inaaian JabUrnr pooubbonmnratadrd drtattum @aa Whlen euna ier Eer OUr Enrrnr Aetam Hrntat Jricretan Tha cujutoe intawn larcre uLt 0 Tho mu...
5 answers
If the frequency factor is 1.2×1013s−1, what is the activationbarrier? The rate constant of a reaction at 31 ∘C was measured tobe 5.9×10−2 s−1 .
If the frequency factor is 1.2×1013s−1, what is the activation barrier? The rate constant of a reaction at 31 ∘C was measured to be 5.9×10−2 s−1 ....
5 answers
D+4+4+4-[Ipl] Thc tNss supportcd by tollcrs #t and by pin-iint Find thc forcc mcmbcrs CD, LD , and KL 3EsuMC 1,78 m, - If the member COIDIEsSOf ejller negative force .3960 N,F 5070 N,F; 7530 N,Fa S010N,Entcr Fc"Aster:ubri;AnBCEC5. [Ipt] Entet _Asrer:Submi: AII Ansmem;[1pt] Enter _Answer:Suhmi; 4/ Answars
d+4+4+4- [Ipl] Thc tNss supportcd by tollcrs #t and by pin-iint Find thc forcc mcmbcrs CD, LD , and KL 3EsuMC 1,78 m, - If the member COIDIEsSOf ejller negative force . 3960 N,F 5070 N,F; 7530 N,Fa S010N, Entcr Fc" Aster: ubri; AnBCEC 5. [Ipt] Entet _ Asrer: Submi: AII Ansmem; [1pt] Enter _ Ans...
5 answers
Consider the following equilibrium reaction which has anequilibrium constant K = 10.48:A(s) ⇌ A(g)86.7 moles of A(s) are inserted in a 5.00 L container. When thesystem reaches equilibrium, how many moles of A(s) remain in thecontainer?
Consider the following equilibrium reaction which has an equilibrium constant K = 10.48: A(s) ⇌ A(g) 86.7 moles of A(s) are inserted in a 5.00 L container. When the system reaches equilibrium, how many moles of A(s) remain in the container?...
4 answers
Moving to another question will save this response:estion 16Is? + 35 + 8 Find the inverse Laplace transfor of FG) = 45 +s8.2 + cos(2t) + 2 sin(2t) ~p- 2 " 9cox2t) + sin(2t) c.2+9c052t) + 3sin(2t) 9cos2t) + sin(2t)26() + cos2t) + 3sin(2t)Moving to another question will save this response
Moving to another question will save this response: estion 16 Is? + 35 + 8 Find the inverse Laplace transfor of FG) = 45 +s 8.2 + cos(2t) + 2 sin(2t) ~p- 2 " 9cox2t) + sin(2t) c.2+9c052t) + 3sin(2t) 9cos2t) + sin(2t) 26() + cos2t) + 3sin(2t) Moving to another question will save this response...
5 answers
Evaluat bc dfinik Iakzgral dx 7.: Ss XtL -4+ Bx+ C xlt+h) x+l X+l = Al" +i) +Bx+€ )x X-o Azl A .1 X < % 2 = ZA+ B+c Ba -1 How i s Ba-1 X--1 0 = Za+B-C c=1 Kow is C = 1
Evaluat bc dfinik Iakzgral dx 7.: Ss XtL -4+ Bx+ C xlt+h) x+l X+l = Al" +i) +Bx+€ )x X-o Azl A .1 X < % 2 = ZA+ B+c Ba -1 How i s Ba-1 X--1 0 = Za+B-C c=1 Kow is C = 1...

-- 0.023815--