PLS HELP!!!

A circle whose radius is 5 meters is divided by a central
angle. The arc subtended by this central angle has a
length of
\( \frac{5\pi}{2} \)
meters. What is the measure of the central angle?

Select one:

A: 60°
B: 180°
C: 120°
D: 90° ​

Answer:

D) Segment YZ and segment Y"Z" are proportional after the dilation and congruent after the translation.

Step-by-step explanation:

After a dilation, a figure remains proportional because its angles and betweenness of points remain the same. After a translation, the image stays congruent to the pre-image.

The largest composite less than 1000 with a GPF of 3 is 996. To prove that it is the largest, we can note that any larger multiple of 3 would either be a prime or have a larger prime factor than 3.

a) To determine the sequence of GPFs for the composites from 60 to 65, we can list the prime factors of each number and take the largest:

- 60 = 2 x 2 x 3 x 5, so the GPF is 5

- 61 is prime

- 62 = 2 x 31, so the GPF is 31

- 63 = 3 x 3 x 7, so the GPF is 7

- 64 = 2 x 2 x 2 x 2 x 2 x 2, so the GPF is 2

- 65 = 5 x 13, so the GPF is 13

Therefore, the sequence of GPFs for the composites from 60 to 65 is 5, prime, 31, 7, 2, 13.

b) The given sequence of GPFs is 41, 19, 79. All of these numbers are prime, so any successive composites that would give this sequence of GPFs would have to be divisible by each of these primes. The product of 41, 19, and 79 is 62,999, which is a four-digit number. Therefore, any composite that would give the sequence of GPFs 41, 19, 79 would have to have at least four digits.

c) To find the smallest composites that give the sequence of GPFs 17, 73, 2, 19, we can start with 17 x 73 x 2 x 19 = 45634, which is a five-digit number. The next composite with these GPFs would be obtained by adding the product of these primes to 45634. This gives 3215678, which is a seven-digit number. Therefore, the smallest successive composites that give the sequence of GPFs 17, 73, 2, 19 are 45634 and 3215678.

d) To find the largest composite less than 1000 with a GPF of 3, we can list the multiples of 3 less than 1000 and eliminate the primes by inspection:

- 3 x 1 = 3

- 3 x 2 = 6

- 3 x 3 = 9 (prime)

- 3 x 4 = 12

- 3 x 5 = 15

- 3 x 6 = 18

- 3 x 7 = 21 (prime)

- 3 x 332 = 996

- 3 x 333 = 999 (prime)

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The percentage of -0.57 that is greater than 34 is effectively zero.

To find the percentage of -0.57 that is greater than 34, we first need to standardize the values using z-scores. This allows us to compare values that are measured on different scales. The formula for calculating a z-score is:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean of the data set, and σ is the standard deviation of the data set.

For the value of -0.57, we can calculate its z-score as follows:

z = (-0.57 - 27) / 3.5 = -7.734

For the value of 34, we can calculate its z-score as follows:

z = (34 - 27) / 3.5 = 2

Finally, to find the percentage of -0.57 that is greater than 34, we need to multiply the percentage of values that are more than 2 standard deviations away from the mean (4.55%) by the probability that a value with a z-score of -7.734 would occur by chance.

This probability is extremely low, since a value with a z-score of -7.734 is more than 7 standard deviations away from the mean. As a result, we can assume that the probability is effectively zero, and therefore the percentage of -0.57 that is greater than 34 is essentially zero.

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The antiderivative of the function f(x) = e^(-x) - e^(4x) is given by -e^(-x) - (1/4)e^(4x)/4 + C, where C is the constant of integration. This represents the general solution to the indefinite integral of the function.

In simpler terms, the antiderivative of e^(-x) is -e^(-x), and the antiderivative of e^(4x) is (1/4)e^(4x)/4. By subtracting the antiderivative of e^(4x) from the antiderivative of e^(-x), we obtain the antiderivative of the given function.

To evaluate a definite integral of this function over a specific interval, we need to know the limits of integration. The indefinite integral provides a general formula for finding the antiderivative, but it does not give a specific numerical result without the limits of integration.

To compute the antiderivative of the function f(x) = e^(-x) - e^(4x), we can use basic integration formulas.

∫(e^(-x) - e^(4x))dx

Using the power rule of integration, the antiderivative of e^(-x) with respect to x is -e^(-x). For e^(4x), the antiderivative is (1/4)e^(4x) divided by the derivative of 4x, which is 4.

So, we have:

∫(e^(-x) - e^(4x))dx = -e^(-x) - (1/4)e^(4x) / 4 + C

where C is the constant of integration.

This gives us the indefinite integral of the function f(x) = e^(-x) - e^(4x).

If we want to compute the definite integral of f(x) over a specific interval, we need the limits of integration. Without the limits, we can only find the indefinite integral as shown above.

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Answer:

the ratio of black to all is 7:16

Step-by-step explanation:

1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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To calculate the interest owed after 93 days, we use the formula for simple interest: Interest = Principal x Rate x Time. Substituting the given values, the interest amounts to $624.49.

This is the total interest that Melissa will owe to the bank after 93 days.Melissa took out a loan of $15,400 from a bank for home renovations. The bank charges a simple interest rate of 16% per year If Melissa doesn't make any payments towards the loan, the total amount owed after 93 days is obtained by adding the principal and the interest together.

Therefore, the total amount owed would be $16,024.49. This means that if Melissa does not make any payments during the 93-day period, her loan balance will increase to approximately $16,024.49, including both the original principal amount and the accrued interest.

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Answer:

0.00273            Smallest

27.3 × 10^-3

2.73 × 10^3

273 × 10^2        Largest

The minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, given a satellite orbiting at a height of 140 km, is approximately 0.062 meters or 6.2 cm.

To determine the minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, we can use the Rayleigh criterion. The Rayleigh criterion states that two points can be resolved if the central maximum of one point falls on the first minimum of the other point's diffraction pattern. The formula for the minimum resolvable angle is given by:

θ = 1.22 × (λ / D)

where:

θ is the minimum resolvable angle,

λ is the wavelength of light,

D is the diameter of the lens aperture.

In this case, we have the following values:

Separation between points (d) = 7 cm = 0.07 m

Wavelength (λ) = 550 nm = 550 × 10⁻⁹ m

To find the minimum lens aperture (D), we need to rearrange the formula as follows:

D = (1.22 × λ) / θ

Now, we need to find the minimum resolvable angle (θ). The angular resolution can be determined by the formula:

θ = d / r

where d is the separation between points and r is the distance to the satellite, which is the sum of the Earth's radius and the satellite's height.

The Earth's radius is approximately 6,371 km, so the distance to the satellite is:

r = Earth's radius + satellite's height

r = (6,371 km + 140 km) = 6511 km = 6,511,000 m

Now we can calculate the minimum resolvable angle:

θ = d / r

θ = 0.07 m / 6,511,000 m

θ ≈ 1.074 x 10⁻⁸ radians

Now we can substitute this value along with the wavelength into the formula for D

D = (1.22 × λ) / θ

D = (1.22 × 550 × 10⁻⁹ m) / (1.074 x 10⁻⁸ radians)

D ≈ 0.062 m

Therefore, the minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, given a satellite orbiting at a height of 140 km, is approximately 0.062 meters or 6.2 cm.

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By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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The value of ∠ADC is,

⇒ ∠ADC =  108°.

Since, We know that,

An angle is combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

In the circle P,

ABCD is inscribed quadrilateral.

And, ∠DAB = 110°,

⇒ ∠ABC = 72°

Hence, To find the value of ∠ADC.

We know that,

Theorem:

A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary that is, sum of the opposite angles will be 180°.

Hence, According to the theorem,

⇒ ∠ABC + ∠ADC = 180°

⇒ ∠ADC + 72 = 180

⇒ ∠ADC = 108°

Therefore, We get;

The value of ∠ADC is 108°.

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The requried, graph is a line that goes through points (1.4) and (2,8). Option B is correct.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
The given equation is y + 4 = 4(x + 1). To determine which statement is true about its graph, we can simplify the equation into slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y + 4 = 4(x + 1)

y + 4 = 4x + 4

y = 4x + 4 - 4

y = 4x

Now we can see that the slope of the line is 4, and the y-intercept is 0. This means that the graph passes through the origin (0,0), and any point on the line can be found by starting at the origin and moving 4 units up for every 1 unit to the right.

From the given options, the only statement that is true about the graph of this equation is, B. The graph is a line that goes through points (1.4) and (2,8).

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The highest point on the graph of the normal density curve is located at its mean represented by μ.

The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.

It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.

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The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.

To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.

First, let's rewrite the equation in a standard form:

\(4x^2 - 16y^2 + z^2 = 16\)

By rearranging terms, we have:

\((x^2/4) - (y^2/1) + (z^2/16) = 1\)

Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.

The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).

When y = 0, the equation becomes:

\(4x^2 + z^2 = 16\)

This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.

When z = 0, the equation becomes:

\(4x^2 - 16y^2 = 16\)

This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.

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identify the surface from the following equation \(4x^2-16y^2 z^2=16\)

Answer:

What value of x makes this equation true? 2(4x-3) - 8= 4+2x​  HERE YOU GO!!

Step-by-step explanation:

We need to eliminate one of the variables to solve the other.

4x+5y = 8

2x-3y = 18

I will multiply the second equation by -2.

-2*(2x-3y = 18)

-4x + 6y = -36 and then add the two equations

4x + 5y = 8

-4x + 6y = -36

+ adding here

11y = -24

y = -24/11

substitute x in one of the equations to find y.

2x-3y=18

2x - (3*-24/11) = 18

2x = 126/11

x = 126/22

Answer:

EH is 25

Step-by-step explanation:

7+7+11=25

EH is 25

The area of ∆BCD is 1/2 the area of ▢ABCD. b = h = √72. Thus, A = 1/2 (√72)(√72) = 1/2 (72) = 36/2 = 18.

To prove this, we need to find the area of both shapes and show that the area of ∆BCD is half the area of ▢ABCD.

First, we need to find the length of DC, which is a side of ▢ABCD. Using the distance formula, we get DC = √((8-2)² + (2-8)²) = √(36+36) = √72.

Next, we can find the area of ▢ABCD using the formula A = s², where s is the length of one side of the square. Thus, A = 6² = 36.

To find the area of ∆BCD, we can use the formula A = 1/2 bh, where b and h are the base and height of the triangle. Since DC is a side of the square, its length is equal to the base and height of ∆BCD. Therefore, b = h = √72. Thus, A = 1/2 (√72)(√72) = 1/2 (72) = 36/2 = 18.

Since the area of ∆BCD is 18 and the area of ▢ABCD is 36, we can see that the area of ∆BCD is indeed half the area of ▢ABCD. Therefore, the statement is proved.

It is worth noting that this proof relies on the fact that the given square is a perfect square, with sides of equal length and right angles at each vertex. If the shape were not a perfect square, the proof would require additional calculations and geometric reasoning.

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Answer: sqrt(56) 11.2 16.2 In order

Step-by-step explanation:

x = sqrt(9^2-5^2)=sqrt(56)

x^2+y^2+9^2 = (y+5)^2

y^2+137 = y^2+10y+25

112 = 10y

y = 11.2

z = 11.2+5 = 16.2

Answer:

$6.50,$6.75,$7.00,$7.25,$7.50,$7.75+

Step-by-step explanation:

all you need to do is add .25

9514 1404 393

Answer:

  4 + x/11

Step-by-step explanation:

The quotient of a number (x) and 11 is x/11.

When 4 is added to that, the sum is ...

  4 + x/11

Answer:

The formula for relative change is x = 100 * (final - initial) / initial  Using this concept, we can plug in our values. x = (3.95 - 3.45) / 3.45 = 0.5. 0.5 * 100 = 14.49%. Rounded to the nearest tenth would give us the value 14.5%.

Step-by-step explanation:

To solve this problem, we need to use the concepts of orbital mechanics and gravitational potential energy.

Part A

The velocity of the satellite in the inner circular orbit is given by the equation:

v = sqrt(GM/r)

where G is the gravitational constant, M is the mass of the earth, and r is the radius of the orbit. Substituting the given values, we get:

v = sqrt(6.674 x 10^-11 N*m^2/kg^2 * 5.97 x 10^24 kg / (260 x 10^3 m))

v = 7760 m/s

Part B

The velocity of the satellite at the low point of the elliptical orbit can be found using the equation:

v = sqrt(2GM/r1 - 2GM/r2)

where r1 and r2 are the radii of the inner and outer circular orbits, respectively. Substituting the given values, we get:

v = sqrt(2 * 6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (260 x 10^3 m) - 2 * 6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (35,900 x 10^3 m))

v = 1.004 x 10^4 m/s

Part C

The work done by the rocket motor to transfer the satellite from the circular orbit to the elliptical orbit is given by the difference in gravitational potential energy between the two orbits. This can be calculated using the equation:

W = mgh = m * G * M/r

where m is the mass of the satellite, g is the acceleration due to gravity, h is the height of the orbit above the earth's surface, and r is the radius of the orbit. Substituting the given values, we get:

W = 1000 kg * 6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (260 x 10^3 m) - 1000 kg * 6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (35,900 x 10^3 m)

W = 3.80 x 10^9 J

Part D

The velocity of the satellite at the high point of the elliptical orbit can be found using the equation:

v = sqrt(GM/r1 + GM/r2)

Substituting the given values, we get:

v = sqrt(6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (260 x 10^3 m) + 6.674 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / (35,900 x 10^3 m))

v = 2.24 x 10^4 m/s

Part E

The velocity of the satellite in the outer circular orbit can be found using the equation in Part A, with the radius of the orbit set to 35,900 km. This gives:

v = sqrt(6.674 x 10^-11 N*m^2/kg^2 * 5.97 x 10^24 kg / (35,900 x 10^3 m)) v = 2.74 x 10^3 m/s

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Answer:

\( \large \boxed{y = - 0.5x + 5}\)

Step-by-step explanation:

Goal

Given

Step 1

\( \large{m = \frac{y_2-y_1}{x_2-x_1} }\)

Substitute the coordinate points in

\(m = \frac{3 - 2}{4 - 6} \\ m = \frac{1}{ - 2} \\ m = - \frac{1}{2} \longrightarrow - 0.5 \\ m = - 0.5\)

Step 2

\( \large{y = mx + b}\)

Substitute m = -0.5

\(y = - 0.5x + b\)

Step 3

Substituting both coordinate points still give the same answer.

Step 3.1

\(y = - 0.5x + b \\ 3 = - 0.5(4) + b \\ 3 = - 2.0 + b \\ 3 = - 2 + b \\ 3 + 2 = b \\ 5 = b\)

Step 3.2

\(y = - 0.5 x+ b \\ 2 = - 0.5(6) + b \\ 2 = - 3.0 + b \\ 2 = - 3 + b \\ 2 + 3 = b \\ 5 = b\)

Step 4

\(y = - 0.5x + b\)

Substitute b = 5 in the equation.

\(y = - 0.5x + 5\)

Hence, the equation is y = -0.5x + 5

The required sample size as calculated from the data given is 605.

Because we are determining the interval for a proportion in this example, using the z distribution is necessary in order to determine the critical value.

Our significance level would be determined by and as our interval has a 90% level of confidence. The crucial value would then be determined by:

This formula provides the proportion interval's margin of error,

ME = z√pq/n     - (a)

According to estimates, the faulty percentage is 0.1 .

In this instance, the error margin is and we are interested in determining the value of n; hence, when we solve n from equation (a), we obtain,

n = pq/ ( ME / 2)²   - (b)

And by substituting the values from part a's equation (b), we obtained:

n = 0.1( 1 - 0.1) / ( 0.02 / 1.64 )²   = 605.16

On rounding off,

n = 605

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Answer:

C and D (maybe)

Step-by-step explanation:

75 hundeds are equal to 75%

The position function becomes s(t) = 2t³ + 2t² + 9t + 8. Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. The particle's position at time t = 15 is 3378 units.

Given, the acceleration of the particle is a(t) = 12t + 4 and the particle's position and velocity at t = 0 are s(0) = 8 and v(0) = 9 respectively. To find the particle's position at time t = 15, we need to integrate the acceleration function and use the initial conditions to determine the constants of integration as follows: Integrating the acceleration function yields the velocity function:v(t) = ∫a(t) dt = ∫(12t + 4) dt = 6t² + 4t + C where C is the constant of integration. Using the initial condition that v(0) = 9, we have:9 = 6(0)² + 4(0) + C => C = 9.

Therefore, the velocity function becomes: v(t) = 6t² + 4t + 9 Now, we integrate the velocity function to obtain the position function as follows: s(t) = ∫v(t) dt = ∫(6t² + 4t + 9) dt = 2t³ + 2t² + 9t + D where D is the constant of integration. Using the initial condition that s(0) = 8, we have:8 = 2(0)³ + 2(0)² + 9(0) + D => D = 8Therefore, the position function becomes: s(t) = 2t³ + 2t² + 9t + 8Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. Therefore, the particle's position at time t = 15 is 3378 units.

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