Which set of polar coordinates describes the same location as the rectangular coordinates (4,-4)

2 answers:

8 0

R=4
theta=pi/2

x= r cos(theta) = 4 cos(pi/2) = 4(0) = 0
y = r sin(theta) = 4 sin(pi/2) = 4(1) = 4

(0,4) is the answer.

SOVA2 [1]3 years ago

3 0

Answer:

(4 sqrt2, 315 degrees)

Step-by-step explanation:

apex

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Exactly 25%
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Explanations:

By definition, the quartiles split the data into four equal parts. The first quartile (Q1) will have 25% of the data below it.
The second quartile is the exact same value as the median. This is because the median splits the data into two equal halves, i.e. is at the midpoint.
There's not enough info. We can determine that 25% of the company makes more than $60,000, but we don't know how many people total work at the company. This info is missing.
Subtract the third and first quartiles (Q3 and Q1) to get the interquartile range (IQR). So IQR = Q3 - Q1 = 45-21 = 24
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nexus9112 [7]

Answer:

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

Step-by-step explanation:

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

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

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