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dolphi86 [110]
3 years ago
14

Two points in the xy plane have cartesian coordinates (2.00, 24.00) m and (23.00, 3.00) m. determine (a) the distance between th

ese points and (b) their polar coordinates
Mathematics
1 answer:
Natasha2012 [34]3 years ago
6 0
Part A:

The distance between two points can be calculated through the equation,
         d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Each of the point may take the 1st or the 2nd coordinates. Substituting the known values,
        d = sqrt ((23 - 2)² + (3 - 24)²)
        d = 21√2
        d = 29.7

Part B:
We get the angle between the lines generated from points and the origin. 

Angle 1: θ = tan⁻(3/23) = 7.43°
Angle 2: θ = tan⁻(24/2) = 85.24°

Subtracting the values,
Angle = 77.8°

Thus, the polar coordinate is (29.7, 77.8°). 

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A research company desires to know the mean consumption of meat per week among people over age 40. A sample of 610 people over a
Papessa [141]

Answer: (3.0,\ 3.2)

Step-by-step explanation:

Confidence interval for population mean is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}  (1)

, where \overline{x} = Sample mean

z_{\alpha/2}= Critical z-value

\sigma = Population standard deviation.

n= Sample size.

As per given , we have

n= 610

\sigma=1.1

\overline{x}=3.1

Significance level for 85% confidence : \alpha=1-0.85=0.15

By z-table critical two tailed z-value : z_{\alpha/2}=z_{0.075}=1.44

Put all values in (1) , we get

3.1\pm 1.44\dfrac{1.1}{\sqrt{610}}

3.1\pm 1.44\dfrac{1.1}{24.698}

3.1\pm 0.064

=(3.1-0.064,\ 3.1+0.064)=(3.036,\ 3.164)\approx(3.0,\ 3.2)

Hence, the 85% confidence interval for the mean consumption of meat among people over age 40.  = (3.0,\ 3.2)

5 0
3 years ago
The steps for solving the equation 2x-3=7
saw5 [17]

Step 1: Add 3 to both sides.

2x-3+3=7+3

2x=10

Step 2: Divide both sides by 2.

2x/2=10/2

x=5


3 0
3 years ago
Read 2 more answers
A bicycle shop advertised all mountain bikes priced at a 1/3 discount. If the original cost of the bikes is $327, what is the ne
nataly862011 [7]
Answer- B


Explanation- 327 divided by 3 would be 109 and a 109 + 109 would equal 218 and 218 would be 2/3 of 327
3 0
2 years ago
Ahhhh i need help again.
qwelly [4]

Answer:

B

Step-by-step explanation:

A. these simply to 21 + 7x and 21 + 3x

  • this one is incorrect because the 7x and 3x are different

B. these simplify to 10 + x and 10 + x

  • this is the correct one since they are exactly the same

C. these simplify to 21x and 7x + 21

  • these two are not the same because one expression has only a number with a variable but the other one has a number with a variable <em>and </em>another number

D. these simplify to  \frac{7}{3-x}  and  \frac{7}{x-3}

  • in subtraction, the order of the 3 and the x matters, so the equations are not the same
  • example: 6 - 4 = 2 but 4 - 6 = -2
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3 years ago
Find the pattern rule for <br> 1 - 210<br> 2 - 200<br> 3 - 190<br> 4 - 180<br> 5 - 170
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It’s deducting 10 each
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