question in the picture!


looking for the answer of 1) by the way! :))

The parametric equations for the particle's motion in the xy-plane are:

x = 6 cos(2t)

y = 6 sin(2t)

To find a Cartesian equation for the particle's path, we can eliminate the parameter t by squaring both equations and adding them:

\(x^2 + y^2 = (6 cos(2t))^2 + (6 sin(2t))^2\\x^2 + y^2 = 36 (cos^2(2t) + sin^2(2t))\\x^2 + y^2 = 36\)

This equation represents a circle centered at the origin (0, 0) with a radius of 6. Therefore, the particle's path is a circle.

As for the graph, since I cannot display it, please refer to a graphing tool or software to plot the Cartesian equation \(x^2 + y^2 = 36\), which represents the particle's circular path.

The portion of the graph traced by the particle is the entire circle, and the direction of motion is counterclockwise around the circle as t increases from 0 to π.

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The question is about Particle motion. The Cartesian equation for the particle's path is y = ± √(36 - x^2), which represents a circle with radius 6 centered at the origin. The particle follows the upper or lower half of the circle depending on the positive or negative square root, respectively.

The given parametric equations are:

x = 6 cos (2t)

y = 6 sin (2t)

0 ≤ t ≤ π

To find the Cartesian equation, we can eliminate the parameter t by solving for t in one equation and substituting it into the other equation:

x = 6 cos (2t)

t = cos-1(x/6)

Substituting the value of t into the equation y = 6 sin (2t), we get:

y = 6 sin [2 cos-1(x/6)]

Simplifying the equation further, we get the Cartesian equation for the particle's path:

y = ± √(36 - x2)

The graph of the Cartesian equation y = ± √(36 - x2) represents the path traced by the particle. It is a circle with radius 6 centered at the origin (0,0). The positive square root represents the upper half of the circle, while the negative square root represents the lower half of the circle. The direction of motion can be determined by observing which part of the circle the particle traverses.

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The expanded form of (4x³ + 2y²)⁶ is 4096x¹⁸ + 12288x¹⁵y² + 3840x¹²y⁴ + 5120x⁹y⁶ + 3840x⁶y⁸ + 768x³y¹⁰ + 64y¹².

To expand the binomial (4x³ + 2y²)⁶, we can use the binomial expansion formula, which states that for any binomial (a + b)ⁿ, the expanded form can be determined using the binomial coefficients and the powers of a and b. The formula is as follows:

(a + b)ⁿ = C(n, 0) * aⁿ * b⁰ + C(n, 1) * aⁿ⁻¹ * b¹ + C(n, 2) * aⁿ⁻² * b² + ... + C(n, n-1) * a¹ * bⁿ⁻¹ + C(n, n) * a⁰ * bⁿ

Let's apply this formula to expand (4x³ + 2y²)⁶:

(4x³ + 2y²)⁶ = C(6, 0) * (4x³)⁶ * (2y²)⁰ + C(6, 1) * (4x³)⁵ * (2y²)¹ + C(6, 2) * (4x³)⁴ * (2y²)² + C(6, 3) * (4x³)³ * (2y²)³ + C(6, 4) * (4x³)² * (2y²)⁴ + C(6, 5) * (4x³)¹ * (2y²)⁵ + C(6, 6) * (4x³)⁰ * (2y²)⁶

Now, let's simplify each term by applying the binomial coefficients and simplifying the powers:

= 1 * (4x³)⁶ * 1 + 6 * (4x³)⁵ * (2y²)¹ + 15 * (4x³)⁴ * (2y²)² + 20 * (4x³)³ * (2y²)³ + 15 * (4x³)² * (2y²)⁴ + 6 * (4x³)¹ * (2y²)⁵ + 1 * (4x³)⁰ * (2y²)⁶

Now, let's simplify the powers of (4x³) and (2y²):

= 1 * 4⁶ * (x³)⁶ * 1 + 6 * 4⁵ * (x³)⁵ * 2¹ * (y²)¹ + 15 * 4⁴ * (x³)⁴ * 2² * (y²)² + 20 * 4³ * (x³)³ * 2³ * (y²)³ + 15 * 4² * (x³)² * 2⁴ * (y²)⁴ + 6 * 4¹ * (x³)¹ * 2⁵ * (y²)⁵ + 1 * 4⁰ * (x³)⁰ * 2⁶ * (y²)⁶

Simplifying the coefficients and combining like terms:

= 1 * 4096 * x¹⁸ * 1 + 6 * 1024 * x¹⁵ * 2 * y² + 15 * 256 * x¹² * 4 * y⁴ + 20 * 64 * x⁹ * 8 * y⁶ + 15 * 16 * x⁶ * 16 * y⁸ + 6 * 4 * x³ * 32 * y¹⁰ + 1 * 1 * 64 * y¹²

Finally, combining the simplified terms:

= 4096x¹⁸ + 12288x¹⁵y² + 3840x¹²y⁴ + 5120x⁹y⁶ + 3840x⁶y⁸ + 768x³y¹⁰ + 64y¹²

So, the expanded form of (4x³ + 2y²)⁶ is 4096x¹⁸ + 12288x¹⁵y² + 3840x¹²y⁴ + 5120x⁹y⁶ + 3840x⁶y⁸ + 768x³y¹⁰ + 64y¹².

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False.

Hi! You asked whether aliasing is expected to happen when the waveform s(t) = 5 sin(4πt) + 12 sin(20πt) is sampled at 24 Hz. To answer this, let's follow these steps:

1. Identify the frequencies of the individual sinusoidal components in the signal s(t). The frequencies are given by (ω/2π) where ω is the coefficient of t in the sine function.
  - For 5 sin(4πt), the frequency is (4π/2π) = 2 Hz
  - For 12 sin(20πt), the frequency is (20π/2π) = 10 Hz

2. Calculate the Nyquist frequency, which is half of the sampling rate. In this case, the sampling rate is 24 Hz, so the Nyquist frequency is 12 Hz.

3. Compare the frequencies of the signal components to the Nyquist frequency. If any component has a frequency higher than the Nyquist frequency, aliasing is expected to occur.

In this case, both 2 Hz and 10 Hz are below the Nyquist frequency of 12 Hz. Therefore, we do not expect aliasing to happen in this sampling process. So, the answer is false.

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Answer:

42 minutes.

Step-by-step explanation:

We know that:

y = 0.2*x

is the equation that that defines the distance, in miles, that the boat travels in x minutes.

We know that the dolphins are at 8.4 miles from the boat.

Then when we have y = 8.4, this will mean that the boat reached the dolphins.

Then we need to solve the equation:

y = 8.4 = 0.2*x

for x

To do that, we just need to isolate x in one side of the equation, so we can just divide both sides by 0.2 to get:

8.4/0.2 = (0.2*x)/0.2

42 = x

And x is time in minutes, thus, the boat needs to travel for 42 minutes to reach the dolphins.

For having a discriminant equal to or larger than zero we must have:

k ≤ 2 and k ≥ 10

For a quadratic equation of the form:

y = a*x^2 + b*x + c

The discriminant is:

D = b^2 - 4ac

And the equation has real roots only if the discriminant is equal to or larger than zero.

Here our equation is:

x^2 + (k - 2)*x + (2k - 4) = 0

The discriminant is:

D = (k - 2)^2 -4*1*(2k - 4)

D = k^2 -  4k + 4 - 8k + 16

D = k^2 -12k + 20

The solutions of :

k^2 -12k + 20 = 0

are:

k = (+12 ± √( (-12)^2 - 4*1*20))/(2)

k = (+12 ± 8)/2

The two values of k are:

k = 20/2 = 10

k = 4/2 = 2

The possible values of k are:

k ≤ 2 and k ≥ 10

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The argument that can be used to oppose the dividend plan is that excess reserves can be used in financing positive NPV projects.

It should be noted that the excess reserves can increase the firm's value and the shareholders value.

Also, it should be noted that the shareholders are not required to pay any tax on an increase in their share value while the dividend payment results in tax payment.

In conclusion, the excess reserves can be used in generating further income for the company.

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The standard deviation of returns is 0.0665 when a person is holding stock and there are three possible outcomes.

To calculate the expected return, we multiply the probability of each state by its corresponding return and sum them up:

Expected return = (20% * 18%) + (55% * 9%) + (25% * -5%)

Expected return = 0.20 * 0.18 + 0.55 * 0.09 + 0.25 * (-0.05)

Expected return = 0.036 + 0.0495 - 0.0125

Expected return = 0.073

The expected return is 7.30%.

To calculate the standard deviation of returns, we need to find the variance first. The variance is calculated as the weighted sum of squared deviations from the expected return:

Variance = (20% * (18% - 7.30%)^2) + (55% * (9% - 7.30%)^2) + (25% * (-5% - 7.30%)^2)

Variance = 0.20 * (0.1077)^2 + 0.55 * (0.0177)^2 + 0.25 * (-0.123)^2

Variance = 0.00232 + 0.000173 + 0.001903

Variance = 0.004423

The standard deviation is the square root of the variance:

Standard deviation = √(0.004423)

Standard deviation = 0.0665

Therefore, the value obtained is 0.0665.

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Step-by-step explanation:

0.00047. = 47÷10 000

=4.7×10/10^-5

= 4.7×10^-4

The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:

mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018

So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.

The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:

standard deviation = standard error of the mean * sqrt(sample size)

standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5

So the standard deviation of the average number of moths in 30 traps is approximately 0.5.

Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.

To do this, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257

Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

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Answer:

my answer isn't on the list, but doing the math the median increased from 39 to 40, but the mean decreased from 49.16 to 45.57

Answer: 29

Step-by-step explanation: 3 times 7 = 21 + 8 = 29

Answer:

7=3x+8

x=-1/3

Step-by-step explanation:

we just replace f(X) with 7

7=3x+8

-8.    -8

-1=3x

/3. /3

-1/3=x

Hopes this helps please mark brainliest

Answer:

they are 4 i think

Step-by-step explanation:

5 x 4 = 20

Answer:

100

Step-by-step explanation:

20 divided by 1/5 = 20 x 5/1 = 100

Answer:

The cost of 7 pens is Rs. 60,  so 2.45

Step-by-step explanation:

find the cost of 7 pens. so 3 divided by 1.05 = 0.35 then multiply by 7 =  2.45 hope this helps can i get brainlyesti tried my best;]

The scale factor was used for each dilation are-

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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Answer:

x=92°

Step-by-step explanation:

x+21+66+59+x+30=360

2x+176=360

2x=184

x=92°

Answer:

it's two and three tenths / option a

Step-by-step explanation:

4-2 = 2

8-5 = 3

Answer:

y = 43, z = 16

Step-by-step explanation:

congruent essentially means they're the same. If you mentally map one triangle onto the other, you'll see that 43, the hypotenuse, lines up with y, and 16 lines up with z.

Answer:

8

Step-by-step explanation:

The answer is 8 because 1/2 times 1/2 times 1/2 is 1/8, which means that 8 B cubes can fit into cube A.

Step-by-step explanation:

Step 1:  Match the questions

1.  Dividing the same base → \(\frac{x^7}{x^3}\) is an example of this and to divide exponents (or powers) with the same base, subtract the exponents.  Therefore we match this with option E

2.  Negative exponent with a fraction base → \((3)^{-3}\) is an example of this and in other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.  Therefore we match this with option H

3.  Product to a Power → \((2x)^3\) is an example of this and what we do is basically distribute out the exponent to everything inside of the parenthesis.  Therefore we match this with option B

4.  Power of 0 → \((15)^0\) is an example of this and what we do is basically say that the exponent of a number shows how many times the number is multiplied by itself. The zero property of exponents is applied when the exponent of any base is 0.  Therefore we match this with option C

5.  Negative exponent → \((\frac{3}{10})^{-4}\) is an example of this and a negative exponent is defined as the multiplicative inverse of the base, raised to the power which is opposite to the given power. In simple words, we write the reciprocal of the number and then solve it like positive exponents.  Therefore we match this with option G

6.  Power to a Power → \((x^2)^2\) is an example of this and what we do is multiply the powers by each other by doing \((x^{2*2})\) which would give us \(x^4\).  Therefore we match this with option A

7.  Multiplying the same base → \(x^5*x^3\) is an example of this and according to the exponent rule for multiplication with the same base, we simply add the powers.  Therefore we match this with option D

8.  Quotient to a Power → \((\frac{a}{b})^x\) is an example of this and when you raise a quotient to a power you raise both the numerator and the denominator to the power.  Therefore we match this with option F

Answer:

12 Times

Step-by-step explanation:

According To The Question,

The Probability of Rolling An 8 is 1/8 .

Thus , 1/8=X/96

So, X=96/8⇔X=12

Answer: 624 ft^3

work is in the image i attached

Answer:

13x2−10/2 is your answer

Step-by-step explanation:

d = 17.3 m

Step-by-step explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

\( {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} \)

or

\(d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } \)

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

\(d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } \)

or

\(d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m\)

This becomes

d = 17.3 m

The height of the building is approximately 86.60 meters.

To find the height of the building, we can use trigonometric ratios, specifically the tangent function.

In this scenario, the angle of elevation is 60 degrees, and the distance from the foot of the building to the point where the angle is measured is 50 meters.

Let's denote the height of the building as 'h'. According to trigonometry, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the foot of the building (50 meters).

Using the tangent function, we have:

tan(60 degrees) = h/50

Simplifying this equation, we can solve for h:

h = 50 × tan(60 degrees)

Using a scientific calculator or trigonometric table, we find that tan(60 degrees) is approximately 1.732.

Therefore, h = 50 × 1.732 ≈ 86.60 meters.

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Answer:

maybe 65 degrees

sorry if its wrong

Answer:

45 degrees

Step-by-step explanation:

All three angles equal 180

Its a right triangle, C=90

Two angle, 90 degrees left, and they're equivalent so divide by 2

B=45, A=45