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
nirvana33 [79]
3 years ago
9

Prove algebraically that r = 10/2+2sinTheta is a parabola

Mathematics
1 answer:
Xelga [282]3 years ago
4 0

Answer:

y =  -  \frac{ 1 }{10} {x}^{2}   +  \frac{5}{2}

Step-by-step explanation:

We want to prove algebraically that:

r =  \frac{10}{2 + 2 \sin \theta}

is a parabola.

We use the relations

{r}^{2}  =  {x}^{2}  +  {y}^{2}

and

y = r \sin \theta

Before we substitute, let us rewrite the equation to get:

r(2 + 2 \sin \theta) = 10

Or

r(1+  \sin \theta) = 5

Expand :

r+  r\sin \theta= 5

We now substitute to get:

\sqrt{ {x}^{2}  +  {y}^{2} }  + y = 5

This means that:

\sqrt{ {x}^{2}  +  {y}^{2} }=5 - y

Square:

{x}^{2}  +  {y}^{2} =(5 - y)^{2}

Expand:

{x}^{2}  +  {y}^{2} =25 - 10y +  {y}^{2}

{x}^{2}  =25 - 10y

{x}^{2}  - 25 =  - 10y

y =  -  \frac{ {x}^{2} }{10}  +  \frac{5}{2}

This is a parabola (0,2.5) and turns upside down.

You might be interested in
Andrew Needs 995 tickets to get the prize he wants At the arcade. He Already has 319 tickets and can earn 4w tickets each time h
Anuta_ua [19.1K]
650 tickets
To win the e prize
8 0
3 years ago
Select the correct answer.<br> What is the value of x?
aksik [14]

Answer:

7.5

Step-by-step explanation:

8 0
2 years ago
Solve for w 5w + 9z = 2z + 3w
Mazyrski [523]

5w + 9z = 2z + 3w \\ 5w - 3w = 2z - 9z \\ 2w =  - 7z \\ w =  \frac{ - 7z}{2}
The answer is w = -7z/2
4 0
3 years ago
Read 2 more answers
Use the function f(x) = x2 + 6x + 6 and the graph of g(x) to determine the difference between the maximum value of g(x) and the
Bingel [31]

The answer is 15,

because F(X)'s minimum value is (-3, -3)

and G(X)'s maximum value is (12, 3)

So when you subtract -3 from 12, you get a number that is greater then both. (because of the negative 3)

12 - (-3) = 15

5 0
3 years ago
Help asap ?????? pls help me with question 7
fiasKO [112]

Answer:

the mean is 5

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • twelve and three tenths more than five and thirteen thousandths of a number d is equal to fifteen and three hundred two thousand
    6·1 answer
  • D is reflection over y axis
    13·2 answers
  • <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%20-%20%20%5Cfrac%7B4%7D%7B10%7D%20%20%3D%20" id="TexFormula1" titl
    8·1 answer
  • Solve. 3(x-6)-2(2x+3)=14
    15·2 answers
  • Find the number b such that the line y = b divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions wi
    10·1 answer
  • A line has a slope of 1/7 and passes through the point (14,2). What is its equation in slope-intercept form?​
    13·2 answers
  • Help please I don’t understand any of this
    10·2 answers
  • Triangle abc has the following vertices:
    14·1 answer
  • I need helppppppppppp
    15·1 answer
  • Find x<br> 8x + 14<br> 9x + 2<br> A) 8<br> C) 11<br> B) 7<br> D) 12
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!