3. Identify the graph described by the function
P(x)= x/10 for x = 1, 2, 3, and 4.

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

The features of the sine function in this problem are given as follows:

The equation is given as follows:

y = 2sin(2πx/3) - 4.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:

2A = 4.

A = 2.

Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:

D = -4.

The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:

2π/B = 3

B = 2π/3.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 2sin(2πx/3) - 4.

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Answer:

6root3

Step-by-step explanation:

Answer:

6 radical 3

Step-by-step explanation:

Answer:

4700 minus 1200 = 3500

Step-by-step explanation:

round 4704 down to 4700 and 1193 up to 1200

Answer:

4704 - 1193 ≈ 3,500

Step-by-step explanation:

We are given the first step to round each number to the nearest hundred.

=====================================

4,704 can be rounded down since the rounding digit (zero) is less than or equal to 4.

4,704 ≈ 4,700

1,193 can be rounded up since the rounding digit (nine) is greater than more equal to 5.

1,193 ≈ 1,200

=====================================

We will now take the difference of these two numbers:

4700 - 1200 = 3500

=====================================

Hope this helps!

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

The side of a square is the square root of the area.

Side = sqrt(155)

Side = 12.45 inches. (Round answer as needed)

Hay cero milésimas en los parámetros dados.

El valor posicional se refiere al valor representado por un dígito en un número sobre la base de su posición en el número.

De los parámetros dados:

Si sumamos los valores juntos, podremos determinar la cantidad de milésimas que tenemos:

= 2200+515+176.5

= 2891.5

Por tanto, podemos concluir que hay cero milésimas en los parámetros.

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The conclusion is that the sample data does not support the claim that the variance in the number of patients seen per day is equal to 10.

To answer this question, we need to perform a hypothesis test to determine whether the sample data supports the claim that the variance in the number of patients seen per day is equal to 10.

The null hypothesis is that the variance is equal to 10:

H0: \(\sigma^2 = 10\)

The alternative hypothesis is that the variance is not equal to 10:

Ha: \(\sigma^2 \neq 10\)

The level of significance is set at 0.10. To calculate the test statistic, we first need to find the sample variance. Using the formula for the sample variance, we get:

\(s^2 = (\sum(x_i - mean)^2)/(n-1) = (104.22)/8 = 13.03\)

The test statistic is calculated as follows:

\(t = (s^2 - 10)/(10/\sqrt{9}) = (13.03 - 10)/(1) = 3.03\)

We can now use Table 3 from Appendix B to determine whether the test statistic is significant at the 0.10 level of significance. Looking at the critical values for a two-tailed test with 8 degrees of freedom and a significance level of 0.10, we find that the critical value is ±2.306. Since our test statistic of 3.03 is greater than 2.306, we reject the null hypothesis.

The conclusion is that the sample data does not support the claim that the variance in the number of patients seen per day is equal to 10.

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Answer:

x = -2

∠A = 35

Step-by-step explanation:

x + 37 + x + 57 = 90

reduce:

2x = -4

x = -2

∠A = 37-2 = 35

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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\(\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(1)}~~~~ ,~~~~ 3-\cfrac{ (6)^2}{4(1)}\right) \implies \left( - \cfrac{ 6 }{ 2 }~~,~~3 - \cfrac{ 36 }{ 4 } \right)\implies (\stackrel{x}{-3}~~,~~-6)\)

Answer:

C

Step-by-step explanation:

\(x = (- b + - \sqrt{ {b}^{2} - 4ac } ) \div 2\)

\(x1 = (- ( - 1) - \sqrt{ {( - 1)}^{2} - 4 \times (1) \times ( - 3) }) \div 2 = \\( 1 - \sqrt{1 + 12}) \div 2 = (1 - \sqrt{13} )\div 2 \)

\(x1 = ( - ( - 1) + \sqrt{ {( - 1)}^{2} - 4 \times (1) \times ( - 3) }) \div 2 = \\( 1 + \sqrt{1 + 12} ) \div 2=( 1 + \sqrt{13} ) \div 2\)

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:

$43.7

Step-by-step explanation:

272-10/6

272-10=262

262/6=43.66666=43.7

The amount of monthly allowance of Brad will be $43.67 per month.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Brad, a teenager, saves up his monthly allowance over a period of six months to buy a pair of high-resolution headphones. He lends his friend, Jorge $10 from his savings. If Brad has $272 now.

Then a monthly allowance of Brad will be given as,

⇒ ($272 - $10) / 6

⇒ $262 / 6

⇒ $43.67

The amount of monthly allowance of Brad will be $43.67 per month.

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The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)

The definition of the function is given as

4/5, 1/5, 1/20. 1/80.....

The above definitions imply that we simply multiply 1/4 to the previous term to get the current term

Using the above as a guide, we have

First term, a = 4/5

Ratio, r = 1/4

So, we have the following equation

an = 4/5(1/4)^(n - 1)

Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)

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Answer:

It's all in the picture. good luck :)

Step-by-step explanation:

Domain : R

Range :   ( - ∞, 0)

(Refer the image attached for complete question)

We have the following function -

k(x) = \(-2^{x}\)

We have to determine its domain and range.

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.

According to question, we have -

k(x) = \(-2^{x}\)

for x = 0, the function k(0) = 1

The function k(x) has the exponential function (\(e^{x}\)) as its parent function.

If we plot the graph of the function k(x), it will look like as shown in the figure attached.

The graph of the function k(x) =  \(-2^{x}\) is the reflection of the graph \(2^{x}\) along x - axis.

The Domain of the function k(x) : R

The Range of the function k(x) : ( - ∞, 0)

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer: 3.718 miles

Just simply take 26x0.143

With a calculator you'll find thats it is 3.718

Answer:

h = 0.4 inches

Step-by-step explanation:

Given that,

The volume of the pyramid is 8 in³.

The sides of the pyramid are 5 in and 4 in.

We need to find the height of the pyramid.

The formula for the volume of pyramid is given by :

V = lbh

Where h is the height of the pyramid

So,

\(h=\dfrac{V}{lb}\\\\h=\dfrac{8}{5\times 4}\\\\h=0.4\ in\)

So, the height of the pyramid is 0.4 inches.

The number of students that bike to school is 18

The median is described as the middle number of a set of data when the values are arranged in an ascending order from the least to the greatest.

We should also know that the median is one of the measures of central tendency.

From the information given, we have that the data set representing the number of students is;

10, 11, 12 , 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Then, we have that the median number is;

Median = 17 + 18/2

add the values

Median = 35/2

Divide the values

Median = 18 students

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The image's distance from the mirror is -1.87, by using the mirror equation.

Note:-  Although the question is missing, I believe the issue is asking where the image is located.

To find the solution to the problem, the mirror equation can be used:

Mirror equation =  \(\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }\)

Where,

f = mirror's focal length

\(d_{o}\) = object's distance from the mirror

\(d_{i}\) =  image's distance from the mirror

The focal length is assumed to be negative for a convex mirror in our problem.

f = -2.8 m

The object's distance (do) = 5.6m

By using the mirror equation, the image's distance from the mirror can be determined

\(\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }\)

i.e, \(\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }\)

= \(-\frac{1}{2.8} -\frac{1}{5.6}\) =  \(-\frac{3}{5.6}\)

= - 0.5357

\(d_{i} =\) \(-\frac{5.6}{3}\)

= -1.87 m

The virtual nature of the image is indicated by the negative sign (located behind the mirror)

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Hello !

Answer:

\(\boxed{\sf V_{hemisphere}=144\pi\ mm^3}\)

Step-by-step explanation:

The volume of a sphere is given by the following formula : \(\sf V_{sphere}=\frac{4}{3}\pi r^3\) where r is the radius.

Moreover, we know that the volume of a hemisphere is half the volume of a sphere : \(\sf V_{hemisphere}=\frac{1}{2} V_{sphere}\)

We obtain : \(\sf V_{hemisphere}=\frac{2}{3}\pi r^3\)

Given :

\(\sf r=\frac{1}{2} d=\frac{12}{2} \\\underline{\sf r=6mm}\)

Let's substitue r with it value in the previous formula :

\(\sf V_{hemisphere}=\frac{2}{3} \pi\times 6^3\\\boxed{\sf V_{hemisphere}=144\pi\ mm^3}\)

Have a nice day ;)

Answer: 0.625 possibly

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

\(r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}\)

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

\(sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\\)

Since sin θ, is negative in the fourth quadrant, \(sin \theta = -5/\sqrt{61} \\\)

\(cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\\)

\(sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}\)

For tanθ:

\(tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\\)

Since tan θ, is negative in the fourth quadrant, \(tan \theta = -5/6\)

 \(SIN\Theta=\frac{-5}{\sqrt{61} }\),

\(SEC\Theta=\frac{\sqrt{61} }{6}\)  

\(TAN\Theta=\frac{-5}{6}\).

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

\(H=\sqrt{6^{2} +(-5)^{2} }\)

\(H=\sqrt{61}\)

We know from trigonometric ratios,

\(SIN\Theta=\frac{Perpendicular}{hypotenuse} \\\)

\(SIN\Theta=\frac{5}{\sqrt{61} }\)

Since \(SIN\Theta\) is negative in 4th quadrant,

so,

\(SIN\Theta=\frac{-5}{\sqrt{61} }\)

Similarly,

\(SEC\Theta=\frac{hypotenuse}{base}\)

\(SEC\Theta=\frac{\sqrt{61} }{6}\)

And,

\(TAN\Theta=\frac{perpendicular}{base}\)

\(TAN\Theta=\frac{-5}{6}\)

Hence,  \(SIN\Theta=\frac{-5}{\sqrt{61} }\), \(SEC\Theta=\frac{\sqrt{61} }{6}\)  and \(TAN\Theta=\frac{-5}{6}\).

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Answer:

19.6 in²

Step-by-step explanation:

area of circle = π r²

= π (3 1/2)²

= π (5/2)²

= π 25/4

= 22/7 x 25/4

= 275/14

=19.6 in²