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Shalnov [3]
3 years ago
14

The letters r and Θ represent polar coordinates. perform the following.

Mathematics
1 answer:
nexus9112 [7]3 years ago
5 0

Answer:

\boxed{(x - \frac{1 }{ 2})^{2} + y^{2} = \frac{21 }{ 4}}\\

Step-by-step explanation:

r = \frac{5}{r - cos\theta}\\r^{2} - rcos\theta = 5\\\\

\text{Use the relationships}\\r^{2} = x^{2} + y^{2}; cos\theta = \frac{ x}{r }\\

\begin{array}{ll}x^{2} + y^{2} - r(\frac{x }{r }) = 5 & \text{Made the substitutions } \\x^{2} + y^{2} - x = 5 & \text{Simplified } \\x^{2} -x + y^{2} = 5 & \text{Rearranged } \\x^{2} -x + \frac{1 }{ 4} + y^{2}= 5 + \frac{1 }{ 4} & \text{Completed the square } \\(x - \frac{1 }{ 2})^{2} + y^{2}= \frac{21 }{ 4} & \text{Wrote as sum of squares} \\\end{array}\\\\

\text{This is the equation of a circle with centre at (0.5, 0 ) and radius equal to}\\\frac{\sqrt{21} }{ 2} \approx 2.291\\

\boxed{(x - \frac{1 }{ 2})^{2} + y^{2}= \frac{21 }{ 4}}\\

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4 years ago
A recipe calls for 2/3 of a cup of milk. Zeinab wants to make 1/4 of the original recipe. How many cups of milk does Zeinab need
hjlf

Answer:

1/6 of a cup of milk. Or at least that's my answer.

Step-by-step explanation:

Okay, we need to find out 25% of 2/3.

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6 0
3 years ago
Rachel is making a planter box. If her box measures 345 inches long and 543 inches wide, how many inches of board will she needs
dimaraw [331]

Rachel needs 1776 inches of board

<em><u>Solution:</u></em>

Given that, Rachel is making a planter box

Her box measures 345 inches long and 543 inches wide

Length = 345 inches

Width = 543 inches

<em><u>To find: Inches of board she needs</u></em>

So we need to find the perimeter of the board

The board is usually of rectangular shape

<em><u>Perimeter of rectangle is given as:</u></em>

Perimeter = 2(length + width)

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6 0
4 years ago
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nlexa [21]

Answer:

2 1/2

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3 0
3 years ago
Read 2 more answers
The school principal determined that 1/4 of the original students schools desks would need to be replaced this year. 50 teachers
Aleksandr-060686 [28]

Answer:

The  number of original students desk were there before the purchase is 980 .  

Step-by-step explanation:

Given as :

The total number of students and teachers new desks to be purchased = 295

The number of teacher's new desk to be purchased = 50

So , The number of student's new desk to be purchased = 295 - 50 = 245

The number of student's new desk to be replaced this year = \frac{1}{4} of the original students desk

Let The number of original students desk were there before the purchase = x

Or, According to question

\frac{1}{4} of x = 245

Or, x = 245 × 4

∴   x = 980

Hence The  number of original students desk were there before the purchase is 980 .  Answer

7 0
3 years ago
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