Write the decimal as a fraction or mixed number in simplest form.

On the unit circle, which of the following angles has the terminal point coordinates (√2/2,-√2/2)

aleksandr82 [10.1K]

Answer:

Option B

Step-by-step explanation:

A unit circle means radius of the circle = 1 unit

Let a terminal point on the circle is (x, y) and angle between the point P and x-axis is θ.

Center of the circle is origin (0, 0).

Therefore, ordered pair representing the terminal point will be (OP×Cosθ, OP×Sinθ) = $(\frac{\sqrt{2} }{2},-\frac{\sqrt{2} }{2})$

OP.Cosθ = 1×Cosθ = $\frac{1}{\sqrt{2}}$

Cosθ = $\frac{1}{\sqrt{2}}$

θ = $\frac{\pi }{4}+2\pi n$ , $\frac{7\pi }{4}+2\pi n$ where n = integers

Similarly, OP×Sinθ = 1×Sinθ = - $\frac{1}{\sqrt{2}}$

Sinθ = - $\frac{1}{\sqrt{2} }$

θ = $\frac{5\pi }{4}+2\pi n$ , $\frac{7\pi }{4}+2\pi n$ where n = integer

Common value of θ will be, θ = $\frac{7\pi }{4}$

Option B will be the answer.

5 0

3 years ago

Conditional statement:If the dog barks,thensomeone is at the door.

vesna_86 [32]

1st one is true and second one false.

8 0

3 years ago

In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes

ale4655 [162]

Answer:

The sample mean is $\bar{x}=14.371$ min.

The sample standard deviation is $\sigma = 18.889$ min.

Step-by-step explanation:

We have the following data set:

$\begin{array}{cccccccc}0.15&0.82&0.81&1.44&2.70&3.28&4.00&4.70\\4.96&6.49&7.25&8.03&8.40&12.15&31.89&32.47\\33.79&36.80&72.92&&&&&\end{array}$

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.

The formula for the mean of a sample is

$\bar{x} = \frac{{\sum}x}{n}$

where, $n$ is the number of values in the data set.

$\bar{x}=\frac{0.15+0.82+0.81+1.44+2.7+3.28+4+4.7+4.96+6.49+7.25+8.03+8.4+12.15+31.89+32.47+33.79+36.80+72.92}{19}\\\\\bar{x}=14.371$

The standard deviation measures how close the set of data is to the mean value of the data set. If data set have high standard deviation than the values are spread out very much. If data set have small standard deviation the data points are very close to the mean.

To find standard deviation we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }$

The mean of a sample is $\bar{x}=14.371$ .

Create the below table.

Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 6422.0982$

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 6422.0982 }{ 19 - 1} } \approx 18.889$

7 0

3 years ago

Jo borrowed 3,800 for 4 months from a bank. the bank discounted the loan at 5.5%.

garri49 [273]

A.
I=prt
I=(3800)(.055)(4/12)
I=$69.67

b.
Principal-interest=money received from Bank
3800-69.67=$3730.34

c.
I=prt
69.67=3730.34(r)(4/12)
69.67=1243.45r
69.67/1243.45=1243.45/1243.45r
.056≈r
Rate is 5.60%

8 0

3 years ago

Please solve this equation. Thank you!<br><br>38x-12y = (6+2n)x + (4-n)y

Elis [28]

Step-by-step explanation:

the answer is in the above image

3 0

3 years ago

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