find the distance from the point (-2,6) to the line y=x-8

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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Based on the table, in every two additional tangerines, there is an additional 80 calories added to it as well.

Hence, at 10 tangerines, there will be 320 + 80 = 400 calories.

Based on the choices:

a. 10 x 20 = 200

b. 10 x 40 = 400

c. 80 + 320 = 400

d. 160 + 240 = 400.

Therefore, it is Option A that does not show a way to find the number of calories in 10 tangerines.

The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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Answer: Let's say that Jenna made enough strawberry jam to fill one jar. Then, we can express the amount of raspberry jam she made in terms of the amount of strawberry jam. We know that she made 2/3 as much raspberry jam as strawberry jam, so she made:

(2/3) x (1 jar) = 2/3 jar of raspberry jam.

Since Jenna made enough strawberry jam to fill 3/5 of a jar, the amount of strawberry jam she made can also be expressed as:

(3/5) x (1 jar) = 3/5 jar of strawberry jam.

Now, to find out how many jars the raspberry jam will fill, we can use proportions. Since 2/3 jar of raspberry jam is equivalent to 3/5 jar of strawberry jam, we can set up the proportion:

(2/3) jar of raspberry jam / x jars = 3/5 jar of strawberry jam / 1 jar

where x is the number of jars the raspberry jam will fill.

We can cross-multiply to get:

(2/3) x 1 = (3/5) x

Simplifying, we get:

x = (2/3) / (3/5) = (2/3) x (5/3) = 10/9

Therefore, Jenna's raspberry jam will fill 10/9 jars. However, since we cannot have a fraction of a jar, we need to round up to the nearest whole number. So the answer is that Jenna's raspberry jam will fill 2 jars.

Step-by-step explanation:

Answer:

Volume of figure = 289 m³

Step-by-step explanation:

Given figure is in the half cylindrical shape.

So calculate the volume of the whole cylinder first then half the volume.

Since, formula to calculate the volume of a cylinder is,

V = πr²h

Here, r = radius of the cylinder

h = height of the cylinder

Therefore, volume of a cylinder with 'r' = \(\frac{7}{2}\) m and h = 15 m will be,

V = π(3.5)²(15)

V = 577.268 m³

Half of the volume = \(\frac{577.268}{2}\)

                               = 288.634 m³

                                ≈ 289 m³

Therefore, volume of the figure shown in the picture = 289 m³

Answer:

easy 9/3 it's not about the numbers it's if you look a the fraction.

if you look at a pie that has 9/3 left there is more then 11/4

Step-by-step explanation:

Answer: 11/4

Step-by-step explanation: Correct me If I'm Wrong, thanks for the points!!

The width and height of the model are;

Width of model = 13.5 inches

Height of model = 2.25 inches

A scale model is defined as a physical model that is geometrically similar to an object. Scale models are usually smaller than large prototypes such as vehicles, buildings, or people. However, these scale models may be larger than small prototypes such as anatomical structures or subatomic particles.

Now, we are given that the dimensions of the new medical complex are;

Length = 400 ft

Width = 180 ft

Height = 40 ft

Thus, for a scale model with length of 30 in(2.5 ft) long, the scale factor is; Scale factor = 2.5/400

Thus;

Width of model = 180 * (2.5/400)

= 1.125 ft = 13.5 inches

Height = 30 * (2.5/400)

= 0.1875 ft = 2.25 inches

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The volume of the larger pipe is

50π cubic inches = 157 cubic inches

Assuming the larger pipe has the same length as the smaller one, we can use the formula for the volume of a cylinder

V = πr^2h

where

V is the volume

r is the radius and

h is the height  of the cylinder

For the smaller pipe we have

V = π(1)² x 8 = 8π cubic inches

For the larger pipe

V = π x (2.5)² 8 = 50π cubic inches

the volume of the larger pipe is 50π cubic inches.

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Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

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Answer:

the date is 4 January today what was the date of week before is

Step-by-step explanation:

the the date is 29 December

Substract 8/12 minus 1/8 , we getting a 19/24

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

We have to subtract the digits :

\(\frac{8}{12}-( -\frac{1}{8})\)

=> Taking L.C.M:

L.CM. of (12, 8) is 24

=> \(\frac{16+3}{24}\)

Subtract the numerator, we get

=> \(\frac{19}{24}\)

Hence, Substract 8/12 minus 1/8 , we getting a 19/24

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Answer:

B=30,000

Y=The Plane's altitude

M= -2,000

X= Minutes

Equation: y=-2,000x+30,000

Slope= ?

Y-intercept= the point where you start at

what is the altitude after 10 minutes?=10,000

How Long does it take to get to 0 altitudes?=15 (Minutes)

Step-by-step explanation:

What are the choices for slope

The given equation is

To solve for x, the logarithm to indices relationship will be applied

That is

Hence

This is simplified to get

Therefore, the value of x = 4

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

To find the probability that a tomato grown in the special soil will be a winner, we need to determine the probability that its diameter is greater than 4 inches.

Let's denote the mean diameter as μ and the standard deviation as σ.

Given:

Mean diameter (μ) = 3.2 in.

Standard deviation (σ) = 0.4 in.

To calculate the probability, we need to standardize the value 4 inches using the standard normal distribution.

The standardized value (z-score) can be calculated using the formula:

z = (x - μ) / σ

Substituting the values into the formula:

z = (4 - 3.2) / 0.4

z = 0.8 / 0.4

z = 2

Now, we need to find the probability of a z-score greater than 2. This can be determined using a standard normal distribution table or a calculator.

Looking up the z-score of 2 in a standard normal distribution table, we find that the probability associated with it is approximately 0.9772.

However, since we are interested in the probability of the tomato's diameter being greater than 4 inches, which corresponds to the right tail of the distribution, we subtract this probability from 1 to obtain the desired probability:

P(diameter > 4) = 1 - 0.9772 ≈ 0.0228

Therefore, the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

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2880 ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions.

The list of the digits is: { 1, 2, 2, 3, 4, 5, 6 }

Here we have to determine how many ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions

We have one number in consecutive positions in this question

That is: (2, 2)

Number of ways that (2,2) are in consecutive positions = \($\frac{6!}{2!}\) = 360

The permutation of 1, (2, 2), 3, 4, 5, 6 = 6!

6! = 720

To get the total number of permutations

= \($\frac{7!}{2!}\)

= \($\frac{5040}{2}\)

= 2520

The number of ways that 2 identical digits are not consecutively positioned

= 2520 - 360 + 720

= 2880

There are 2880 ways to list the digits { 1, 2, 2, 3, 4, 5, 6 }.

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The solution will illustrate that the equation has one solution at x=0.

Given that  adds 2 to both sides, the equation 4x = 3x results.

An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.

The equation is 4x=3x.

As given that add 2 on both sides, we get

4x+2=3x+2

Now, we will subtract 3x from both sides, we get

4x+2-3x=3x+2-3x

x+2=2

Further, we will subtract 2 from both sides, we get

x+2-2=2-2

x=0

Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.

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Check the picture below.

so let's simply get the area of each rectangle and the two triangles.

\(\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{two rectangles} }{2(41)(48)}~~ + ~~\stackrel{rectangle }{(18)(48)}~~ + ~~\stackrel{ \textit{two triangles} }{2\left[ \cfrac{1}{2}(\underset{b}{18})(\underset{h}{40}) \right]}} \\\\\\ 3936~~ + ~~864~~ + ~~720\implies \text{\LARGE 5520}~cm^2\)

Answer:

800 ft, you should write ur own sentence tho

Step-by-step explanation:

520 - (-280) = 800

Answer:

Quadrant 1

Step-by-step explanation:

how I understood this is first understanding how a graph works. Once you understand that you can count 13 horizontal on the "X" Axis, then go 18 up on the "Y" axis. you should get a point in the upper left area and that area is called Quadrant 1. Say if 13 was negative instead of going horizontal east you would go horizontal west. And the point should end up in Quadrant 2. Any more questions feel free to ask me below.

The given linear time-invariant (LTI) system is described by a third-order linear constant coefficient differential equation. To determine the frequency response of the system, we can take the Laplace transform of the differential equation and solve in the Laplace domain

(a) To find the frequency response, we start by taking the Laplace transform of the given differential equation. Let \(Y(s)\) and \(X(s)\) represent the Laplace transforms of \(y(t)\) and \(x(t)\) respectively. By applying the Laplace transform, we obtain:

\[2s^3Y(s) + 4s^2Y(s) + 10sY(s) = 5X(s) + 2sX(s)\]

Simplifying the equation, we get:

\[Y(s) = \frac{5X(s) + 2sX(s)}{2s^3 + 4s^2 + 10s}\]

This equation represents the transfer function of the system in the Laplace domain. To obtain the frequency response, we substitute \(s = j\omega\) into the transfer function, where \(\omega\) represents the angular frequency.

(b) To approximate the Bode plot, we analyze the frequency response at low and high frequencies. At low frequencies (\(\omega \to 0\)), the terms involving \(s\) dominate, and the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{2j\omega X(j\omega)}{2j\omega}\]

Simplifying, we find that the low-frequency gain is 1, indicating that the system passes low-frequency signals without significant attenuation.

At high frequencies (\(\omega \to \infty\)), the terms involving \(s\) become negligible compared to the constant term. Thus, the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{5X(j\omega)}{10j\omega}\]

In this approximation, the gain decreases by -20 dB/decade, indicating that the system attenuates high-frequency signals.

The cutoff frequencies of the system can be determined from the Bode plot where the gain decreases by -3 dB. These frequencies represent the boundary between the passband and stopband of the system.

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Answer:

\( A(\triangle ABC) =17.5 \: {units}^{2} \)

Step-by-step explanation:

AB = 4 - (-3) = 4 + 3 = 7 units

BC = 3 - (-2) = 3 + 2 = 5 units

\(A(\triangle ABC) = \frac{1}{2} \times AB\times BC \\ \\ A(\triangle ABC) = \frac{1}{2} \times 7\times 5 \\ \\ A(\triangle ABC) = \frac{1}{2} \times 35 \\ \\ A(\triangle ABC) =17.5 \: {units}^{2} \)

Answer:

thanks for the point

GGGGGGGGGGGGGGDFHNFJYGJTG

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:

I think the answer is

Step-by-step explanation:

8.20 a.m

I don't know it's a guess

Answer:

A. 8:00

Step-by-step explanation:

25 + 15 + 35 = 75 minutes

so that’s a hour so he needs to wake up at 8:00 to be there at 9:15

Answer:

Step 2 is the mistake

Step-by-step explanation:

taking away the 20 on the other side would have made that -5 -25

hope I helped!!

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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The triangles with right angles triangle measurement is

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Given:

First, 5, √50, 5

So, applying Pythagoras theorem

H² = 5² + 5²

H² =25+25

H= √50

So, 5, √50, 5 are sides of Right angle triangle.

second, 6.5, 3.2, 7.8

So, applying Pythagoras theorem

H² = 6.5² + 3.2²

H² = 42.25 + 10.24

H= √52.49

and, 7.8² = 60.84

So, 6.5, 3.2, 7.8  are not the sides of Right angle triangle.

Third, √2, √3, 4

H= √2² + √3²

H= 2+3

H=5

So, √2, √3, 4 are not the sides of Right angle triangle.

Fourth, 12, 13, 20

H= 12² + 13²

H= 144+ 169

H= 313 < 20² = 400

So, 12, 13, 20 are not the sides of Right angle triangle.

Fifth, 0.75, 1.25, 1

H= 0.75² + 1²

H= 0.5625 + 1

H= 1.5625 = 1.25²

So, 0.75, 1.25, 1 are sides of Right angle triangle.

sixth, 18, 80, 82

H= 18² + 80²

H= 324 + 6400

H= 6724 = 82²

So, 18, 80, 82 are sides of Right angle triangle.

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answer:

look

step-by-step explanation:

over? you would have 2 ÷ (5 x 2) ÷ 28. in fraction form.