Find the area of a circle having a circumference of 231 pi units. Round to the nearest tenth.

A. 355 units squared
B. 415.5 units squared
C. 831 units squared
D. 462.3 units squared

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Answer:

x= 55

Step-by-step explanation:

Answer:

x is 55 degrees

Step-by-step explanation:

since it is a right angle set up the equation

20+x+15=90

then solve to get 55

Answer:

C.  12    is the correct answer

Step-by-step explanation:

1.2 x 10¹²

Answer:

C

Explanation:

:) hope this helps

Answer:

they are neither

Step-by-step explanation:

because if you connect the dots they are neither parallel or perpendicular

The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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You end up at the point (5, 5).

Answer:

25 dollars is the ANSWER

Step-by-step explanation:

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

12x+4x-7y+45b+78a-44b+1a+1z+0d+1.1a+1.1a+2+2+2

Answer: 3 dollars for a book.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: 3,348 cubic inches

Step-by-step explanation:

1. Since we know that volume= length x width x height, then we can plug our values into this equation.

2. So, we would do volume= 9 x 12 x 21.

3. 9 x 12 = 108, and 108 x 21 =2,268.

4. Now that we have both of the volumes, we have to add them together.

5. 1,080 + 2,268 = 3,348

6. The combined volume is 3,348 cubic inches.

Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

Clark will have $5820.80 in his account when he turns 22.

With an example, what is compound interest?

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

Clark reportedly placed $5000 at a constant 3.8% interest rate when he was 18 years old.

Using the compound interest calculation, we can calculate how much Clark will make when he turns 22.

\(A=P . e^{rT}\)

A= Amount after T years.

P= Principal amount.

e= Mathematical constant e.

r= Interest rate (in decimal form).

T=  Time in years.

Let's decimalize the interest rate we've been given.

3.8 percent = 3.8/100 = 0.038

When we enter our provided values into the formula above, we will obtain,

\(A=5000 * e^{0.038(22-18)} \\A=5000*e^{0.038(4)}\\A=5000*e^{0.152}\\A=5000*1.1641\\A=5820.80\)

Clark will therefore have $5820.80 in his account when he turns 22.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53\)

Answer:

your answer is B

Step-by-step explanation:

Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire

Let's draw the circle and the lines to see more clear:

The AB and CD are diameters of the circle, so the intersection point K is the center of the circle.

We know the angle BKD=100°, but the angle AKC=BKD because they are opposite angles.

So the measure of arc AC is:

You should note the angle AKC in the above equation must be in radians. To convert degrees to radians use the following equation:

So,

\(\text{Given that,}~f(j) = -5j-4\\\\f(p-5) = -5(p-5) -4\\\\~~~~~~~~~~~~=-5p+25-4\\\\~~~~~~~~~~~~=-5p+21\)

Answer: 0.4 >-8 /9(8+7)

Sorry if it isn't correct!!

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer:

Try D if it's wrong i'm sorry

Step-by-step explanation:

Answer:

D. 4

Step-by-step explanation:

The 55 degree angle can be either a base angle or the apex angle.

The 6 inch length can be either the length of the base or the length of each leg.

There are therefore 4 possible triangles:

1. 55 degree base angle and 6 inch leg length

2. 55 degree base angle and 6 inch base length

3. 55 degree apex angle and 6 inch leg length

4. 55 degree base angle and 6 inch base length

(2 with only 1 angle of 55 degrees (1 with the equal sides of 6 inches each, 1 with the unequal side of 6 inches)

2 with 2 angles of 55 degrees (1 with the equal sides of 6 inches each, 1 with the unequal side of 6 inches).)

Answer:

A

Step-by-step explanation:

1. Get 15% of 870:

   First, get 10 percent of 870, which is 87, then half that, which is 43.5

   Get the 87 and add the 43.5 on it, to get the full 15%, you end up with $130.5, which is the monthly payment.

(Only problem is that im pretty sure you put an extra 0, because if you just wrote 87 dollar's then you would've got 13.05, the actual answer, but if you add an extra 0 then you end up with 130$, just to let you know.)

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

The number of different combinations that are possible for Nick, given his baseball hats are A. 4 combinations.

Nick has two options for hats, and two options for sweatshirts/sweaters. To find the number of combinations, we can multiply the number of options for each item.

There are two baseball hats and two clothes - sweatshirt and sweater.

The number of combinations is:

= 2 (hats) x 2 (sweatshirts/sweaters)

= 4 combinations

In conclusion, as regards the number of combinations that Nick can make, there are four.

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Answer: The answer is -3/16

Step-by-step explanation: brainlest please

Reason:

The horizontal width spans from 8 to 20. This is a distance of 20-8 = 12 units.

The height is some unknown, which I'll call x. We multiply the width and height to get the area. This area must be 1 to represent 100%. You can think of it like a pie chart. This applies to any probability distribution.

area = base*height

1 = 12*x

x = 1/12

Therefore, the height of this rectangle must be 1/12 so that the area of this rectangle is 1.

Answer:

1,3,4,6,8} { 1 , 3 , 4 , 6 , 8 }. Range:{2,4,5,7,9}

Step-by-step explanation:

The domain is the set of all the values of x x . The range is the set of all the values of y y .