1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yanalaym [24]
3 years ago
11

Rewrite in Polar Form.... x^(2)+y^(2)-6y-8=0

Mathematics
1 answer:
skad [1K]3 years ago
3 0
\bf x^2+y^2-6y-8=0\qquad 
\begin{cases}
x^2+y^2=r^2\\\\
y=rsin(\theta)
\end{cases}\implies r^2-6rsin(\theta)=8
\\\\\\
\textit{now, we do some grouping}\implies [r^2-6rsin(\theta)]=8
\\\\\\\
[r^2-6rsin(\theta)+\boxed{?}^2]=8\impliedby 
\begin{array}{llll}
\textit{so we need a value there to make}\\
\textit{a perfect square trinomial}
\end{array}

\bf 6rsin(\theta)\iff 2\cdot r\cdot  \boxed{3\cdot sin(\theta)}\impliedby \textit{so there}
\\\\\\
\textit{now, bear in mind we're just borrowing from zero, 0}
\\\\
\textit{so if we add, \underline{whatever}, we also have to subtract \underline{whatever}}

\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\
\left. \qquad  \right.\uparrow \\
\textit{so-called "completing the square"}
\\\\\\\
[r-3sin(\theta)]^2=8+[3sin(\theta)]^2\implies [r-3sin(\theta)]^2=8+9sin^2(\theta)
\\\\\\
r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}\implies r=\sqrt{8+9sin^2(\theta)}+3sin(\theta)
You might be interested in
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your
love history [14]

If we substitute x=r\cos\theta and y=r\sin\theta, we get r^2=x^2+y^2, so that

z=\cos(x^2+y^2)=\cos(r^2)

which is independent of \theta, which in turn means the surface can be treated like a surface of revolution.

Consider the function f(t)=\cos(t^2) defined over 0\le t\le1. Revolve the curve C described by f(t) about the line t=0. The area of the surface obtained in this way is then

\displaystyle2\pi\int_C\mathrm dS=2\pi\int_0^1\sqrt{1+f'(t)^2}\,\mathrm dt

=\displaystyle2\pi\int_0^1\sqrt{1+(-2t\sin(t^2))^2}\,\mathrm dt

=\displaystyle2\pi\int_0^1\sqrt{1+4t^2\sin^2(t^2)}\,\mathrm dt\approx7.4144

4 0
3 years ago
PLZ HELP ASAP I'LL GIVE BRAINLY sketch the solution set to the system of inequalities shown below
earnstyle [38]

Answer:

hi! you can use desmos graphing calculator to help you graph these- just look it up and plug the equation in. its nice for future use as well.

Step-by-step explanation:

and no , (5,10) isn't a solution to the equation because it falls under x≥2 but not under y<x+3. Hope this helps !

6 0
3 years ago
Wats the volume of a cube 8ft by8ft
WITCHER [35]
Assuming that the cube has equal dimensions, it would be:

8 x 8 x 8 = 512 ft^3
8 0
3 years ago
Read 2 more answers
The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
marusya05 [52]

Answer:

19 liters 800 milliliters

Step-by-step explanation:

0.33 * 12 * 5 = 19.8 liters

6 0
1 year ago
X<img src="https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2Bx%2B2%29%28x%5E%7B2%7D%20%2B4x%2B2%29%2B2x%5E%7B2%7D" id="TexFormula1" ti
Natasha_Volkova [10]

Answer:

x

(

2

x

5

+

11

x

4

+

21

x

3

+

28

x

2

+

20

x

+

4

)

5 0
2 years ago
Other questions:
  • How does a digit in the ten thousands place compare with a digits in the thousands place?
    5·1 answer
  • A bicyclist travels 60.0 kilometers in 3.5 hours. what is the cyclist's speed?
    5·2 answers
  • A researcher is studying end-times beliefs of Christians by surveying members of his Methodist church.
    14·1 answer
  • A jewler buys a ring for $85 he sells it for 135% increase what is theretail of the ring
    11·1 answer
  • The US Department of Energy reported that 48% of homes were heated by natural gas. A random sample of 333 homes in Oregon found
    10·1 answer
  • If f(x)= x-3/x and g(x)= 5x-3, what is the domain of (f•g)(x)
    14·1 answer
  • Hey guys, please help with my last question, you will be rewarded handsomely with ten points ​
    8·1 answer
  • Help me please please please please the question is in the picture
    7·1 answer
  • Find the length of CD shown in red below. Show all work.<br><br> PLEASE HELP
    14·1 answer
  • What is an angle that is supplementary to
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!