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ExtremeBDS [4]
3 years ago
13

Divide. Enter the answer in simplest form. 2 1 3 ÷ 2 3

Mathematics
2 answers:
Ronch [10]3 years ago
3 0

Answer:

9 and 6/23

Step-by-step explanation:

213/23= 9 6/23

borishaifa [10]3 years ago
3 0

Answer:

9 remander 6

Step-by-step explanation:

            9 R6

 ____________

23  | 213

    - 207

     --------

           6

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Given cos alpha = 8/17, alpha in quadrant IV, and sin beta = -24/25, beta in quadrant III, find sin(alpha-beta)
polet [3.4K]
Given \cos\alpha=\frac{8}{17}, \alpha is in Quadrant IV,  \sin\beta=-\frac{24}{25}, and \beta is in Quadrant III, find \sin(\alpha-\beta)

We can use the angle subtraction formula of sine to answer this question.

\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta

We already know that \cos\alpha=\frac{8}{17}.

We can use the Pythagorean identity \sin^2\theta+\cos^2\theta=1 to find \sin\alpha.

\sin^2\alpha+(\frac{8}{17})^2=1 \\ \sin^2\alpha+\frac{64}{289}=1 \\ \sin^2\alpha=\frac{225}{289} \\ \\\sin\alpha=\pm\frac{15}{17}

Since \alpha is in Quadrant IV, and sine is represented as y value on the unit circle, we must assume the negative value \sin\alpha=-\frac{15}{17}.

As similar process is then done with  \sin\beta=-\frac{24}{25}.

(-\frac{24}{25})^2+\cos^2\beta=1 \\ \frac{576}{625}+\cos^2\beta=1 \\ \cos^2\beta=\frac{49}{625} \\ \\\cos\beta=\pm\frac{7}{25}

And since \beta is in Quadrant III, and cosine in represented as x value on the unit cercle, we must assume the negative value \cos\beta=-\frac{7}{25}.

Now we can fill in our angle subtraction formula!

\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta \\\\ \sin(\alpha-\beta)=(-\frac{15}{17}\times-\frac{7}{25})-(\frac{8}{17}\times-\frac{24}{25}) \\\\\sin(\alpha-\beta)=\frac{105}{425}-(-\frac{192}{425}) \\\\ \boxed{\sin(\alpha-\beta)=\frac{297}{425}}
7 0
3 years ago
Instructions: Select the correct answer.
NNADVOKAT [17]
The formula for the area of a circle (in this case, the disc) is
\pi {r}^{2}
So, we apply the given radius to the formula to give us our answer:
\pi \times  {7.6}^{2}  = 181.4583917
So, your approximate answer is C.
6 0
4 years ago
Read 2 more answers
Which statement is true about the parentheses in this expression? 10 ÷ (8 − 6) − 2 A) The parentheses indicate that 6 − 2 should
Hoochie [10]

Answer:B

Step-by-step explanation: When solving expressions with parentheses it’s important to always solve what’s in parentheses first. And when there’s parentheses in parentheses, solve the parentheses that are in the parenthesis. Whew...I hope this helps :)

8 0
3 years ago
Which function has the same domain as y= 2√x?<br> Oy= √2x<br> O y=2³√x<br> 0₁y = √x-2<br> O y=³√x-2
dybincka [34]

The option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y= 2√x

From the above function the domain should be:

x ≥ 0 (because square root of negative values does not exist)

The function:

y = √(2x)

2x ≥ 0

x ≥ 0

Thus, the option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

3 0
2 years ago
What is the slope of a line that is parallel to the line with the following equation?
Natali [406]

Answer:

D)

Step-by-step explanation:

we know that,

Parallel lines have the same slope

given equation is in the form given by

\displaystyle y = mx + b

where m is know

as m_{parallel}=m, the answer is -⅔

3 0
3 years ago
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