what's the distance between theses two. (-5, 1) (2, 4)

The solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

To find a solution of the second-order initial value problem (IVP) consisting of the differential equation y" - y = 0 and the given initial conditions y(1) = 0, y'(1) = e -x-1, we can follow these steps:

Determine the general solution of the differential equation y" - y = 0:

The characteristic equation is r^2 - 1 = 0. Solving this equation, we find two distinct roots: r = 1 and r = -1.

Therefore, the general solution is y(x) = c₁e^x + c₂e^(-x), where c₁ and c₂ are constants.

Apply the initial condition y(1) = 0:

Substituting x = 1 and y = 0 into the general solution:

0 = c₁e^1 + c₂e^(-1)

Dividing through by e:

0 = c₁ + c₂e^(-2)

Apply the initial condition y'(1) = e -x-1:

Differentiating the general solution:

y'(x) = c₁e^x - c₂e^(-x)

Substituting x = 1 and y' = e^(-1) into the differentiated solution:

e^(-1) = c₁e^1 - c₂e^(-1)

Dividing through by e:

e^(-2) = c₁ - c₂e^(-2)

We now have a system of two equations:

Equation 1: 0 = c₁ + c₂e^(-2)

Equation 2: e^(-2) = c₁ - c₂e^(-2)

Solving this system of equations, we can find the values of c₁ and c₂:

Adding Equation 1 and Equation 2:

0 + e^(-2) = c₁ + c₁ - c₂e^(-2)

e^(-2) = 2c₁ - c₂e^(-2)

Rearranging this equation:

2c₁ = e^(-2)(1 + c₂)

Substituting this value back into Equation 1:

0 = e^(-2)(1 + c₂) + c₂e^(-2)

0 = e^(-2) + c₂e^(-2) + c₂e^(-2)

0 = e^(-2) + 2c₂e^(-2)

-1 = 2c₂e^(-2)

Simplifying:

c₂e^(-2) = -1/2

Substituting this value back into Equation 1:

0 = c₁ - 1/2

c₁ = 1/2

Therefore, the values of c₁ and c₂ are c₁ = 1/2 and c₂ = -1/(2e^2).

Now we can write the particular solution to the IVP:

y(x) = (1/2)e^x - (1/(2e^2))e^(-x)

This is the solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

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Answer:

35°

Step-by-step explanation:

Due to the parallelism, angle2=angle4

Answer:

i think it is A CiNiyah

Step-by-step explanation:

Answer:

From the given information, we can see that when x = -3, f(x) = 1 and g(x) = -3. Since g(x) = kf(x), we can substitute the values of f(x) and g(x) to solve for k: g(x) = kf(x) -3 = k(1) k = -3 So the value of k is -3, which corresponds to answer choice D.

Answer: 24/25

Step-by-step explanation:

Sin = opposite/hypotenuse

Sin = 24/25

Answer:

$9015.20

Step-by-step explanation:

A = 4000[1 + (.063/4)]^13·4

Answer:

3276

Step-by-step explanation:

4000(6.3*13)÷100

Answer:

The volume of the cone is 3140cm³

Step-by-step explanation:

Volume of come = 1/3 × πr²h

r = diameter/2 = 20/2 = 10cm

h = 30cm

π = 22/7

Volume = 1/3 × 22/7 × 10² × 30

Volume = 1/3 × 22/7 × 100 × 30

Volume = 3142.86cm³

Volume = 3140cm³

Answer:

y= -3

Step-by-step explanation:

Substitute x as 0

6(0)-3y=9

-3y=9

y= -3

The power series representation of f(x) = (x - 4)² is f(x) = 9 - 6x + x² + ..., and the radius of convergence, R, is infinity (∞).

To find a power series representation for the function f(x) = (x - 4)², we can expand it using the binomial theorem.

The binomial theorem states that for any real number r and a real number x such that |x| < 1, we have:

[tex](1 + x)^r[/tex] = 1 + rx + (r(r-1))/2! * x² + (r(r-1)(r-2))/3! * x³ + ...

In our case, we have f(x) = (x - 4)², which can be rewritten as (1 + (x - 4))². Using the binomial theorem with r = 2, we get:

f(x) = (1 + (x - 4))² = 1 + 2(x - 4) + (2(2-1))/2! * (x - 4)² + ...

Simplifying this expression, we have:

f(x) = 1 + 2x - 8 + (2/2) * (x² - 8x + 16) + ...

Expanding further, we get:

f(x) = 1 + 2x - 8 + x² - 8x + 16 + ...

Now we can write the power series representation of f(x) as:

f(x) = 9 - 6x + x² + ...

To determine the radius of convergence, R, we need to find the interval of x for which the series converges. In this case, the series converges for all real numbers x since there are no terms involving powers of x that could cause divergence.

Therefore, the radius of convergence, R, is infinity (∞).

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8,99,999 in international system:-

899,999= Eight hundred ninety-nine thousand nine hundred ninety-nine

Answer:

-2[tex]x^{2}[/tex]+3xy+8[tex]y^{2}[/tex]

Step-by-step explanation:

A) Logical vector diagram of the flight is drawn below. B) The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°. C) The vacation island is approximately 1301 kilometers from the airport of departure.

A.  a logical vector diagram of the flight is given in image.

B. To determine the aircraft's ground velocity, we need to find the resultant vector of the aircraft's velocity and the wind vector. We can use vector addition to calculate this:

Aircraft's velocity = 250 km/hr at a heading of 170°

Wind velocity = 50 km/hr at a heading of 270° (since it's blowing from the south/west)

To add these vectors, we need to resolve them into their horizontal (x) and vertical (y) components:

Aircraft's velocity:

[tex]V_x[/tex] = 250 km/hr * cos(170°)

[tex]V_{y}[/tex] = 250 km/hr * sin(170°)

Wind velocity:

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°)

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°)

Now, we can add the horizontal and vertical components separately:

[tex]V_{x} total = V_x + V_{x}wind\\V_{y} total = V_y + V_{y}wind[/tex]

To find the magnitude and direction of the resultant vector, we can use the Pythagorean theorem and trigonometry:

Magnitude of the resultant vector (ground velocity):

[tex]V_{total} = \sqrt{V_x total^2 + V_y total^2}[/tex]

Direction of the resultant vector:

[tex]\theta = tan^{-1} 2(V_y total, V_xtotal)[/tex]

Let's calculate the values:

[tex]V_x[/tex] = 250 km/hr * cos(170°) ≈ -235.83 km/hr

[tex]V_y[/tex] = 250 km/hr * sin(170°) ≈ -62.85 km/hr

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°) = 0 km/hr

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°) ≈ -50 km/hr

[tex]V_x[/tex]_total = -235.83 km/hr + 0 km/hr = -235.83 km/hr

[tex]V_y[/tex]_total = -62.85 km/hr + (-50 km/hr) = -112.85 km/hr

[tex]V_{total}[/tex] =  [tex]\sqrt{((-235.83 km/hr)^2 + (-112.85 km/hr)^2) }[/tex] ≈ 260.2 km/hr

θ = [tex]tan^{-1} 2(-112.85 km/hr, -235.83 km/hr)[/tex] ≈ -153.7°

The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°.

C. If the entire flight took about 5 hours, we can calculate the distance traveled by multiplying the ground velocity by the time:

Distance = Velocity * Time

Distance = 260.2 km/hr * 5 hours = 1301 km

The vacation island is approximately 1301 kilometers from the airport of departure.

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Answer:

l=8k

Step-by-step explanation:

Answer:

y=8k

Step-by-step explanation:

Answer:

8

x

3

+

2

x

2

−

3

x

+

18

Step-by-step explanation:

simply the answer thought bc i didn't simplify

The simplification based on Laurent series of the function (22-9)(2+3) centered at z = −3

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

The given problem involves finding the Laurent series of a function centered at z = -3 and evaluating the integral of another function over a specific interval. The Laurent series simplifies to a constant term of 65.

(a) To find the Laurent series of the function (22-9)(2+3) centered at z = −3, we can expand the function in powers of (z + 3):

(22-9)(2+3) = (13)(5) = 65

Since there are no negative powers of (z + 3), the Laurent series of the function is simply the constant term:

f(z) = 65

(b) To evaluate the integral ſc[−3,3] (z²−9)(z+3) dz, we can first simplify the integrand:

(z² - 9)(z + 3) = (z - 3)(z + 3)(z + 3) = (z - 3)(z + 3)²

Now, let's integrate the simplified expression:

∫[(z - 3)(z + 3)²] dz

Expanding the expression:

∫[z³ + 6z² + 9z - 27] dz

Integrating each term:

(1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z

Now, we can evaluate the integral over the given interval [−3, 3]:

∫[−3,3] (z²−9)(z+3) dz = [((1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z)] evaluated from z = -3 to z = 3

Substituting the upper and lower limits into the expression and simplifying, we get:

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

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Answer: I think it’s the first choice. Foreign Language, Math/CS, and social studies

Step-by-step explanation:

Counterexample: The statement is not true. For n = 41, the expression n^3 + n^2 + 41 equals 41^3 + 41^2 + 41, which is divisible by 41 and therefore not prime.

To prove or disprove the statement, we need to find a counterexample, i.e., a natural number n for which n^3 + n^2 + 41 is not prime. By substituting n = 41 into the expression, we obtain 41^3 + 41^2 + 41. This expression is divisible by 41 since it can be factored as 41(41^2 + 41 + 1). Since a prime number is only divisible by 1 and itself, this means that the expression is not prime and thus disproves the statement. Therefore, the claim that n^3 + n^2 + 41 is prime for every natural number n is false.

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Answer:

B.

Step-by-step explanation:

hope this helps!!

The interval [μ - z (σ/sqrt(n)), μ + z (σ/sqrt(n))] within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

a. The interval is [166.01, 179.99].

b. The interval is [849.07, 898.93].

c. The interval is [74.47, 77.53].

a. μ = 173, σ = 20, n = 42.

Here, we have, μ = 173, σ = 20, n = 42.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 173 - 1.96(20/sqrt(42)) , 173 + 1.96(20/sqrt(42)) ]

i.e [ 166.01, 179.99 ]

Therefore, the interval is [166.01, 179.99].

b. μ = 874, σ = 12, n = 7.

Here, we have, μ = 874, σ = 12, n = 7.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 874 - 1.96(12/sqrt(7)) , 874 + 1.96(12/sqrt(7)) ]

i.e [ 849.07, 898.93 ]

Therefore, the interval is [849.07, 898.93].

c. μ = 76, σ = 2, n = 26.

Here, we have, μ = 76, σ = 2, n = 26.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 76 - 1.96(2/sqrt(26)) , 76 + 1.96(2/sqrt(26)) ].

i.e [ 74.47, 77.53 ]

Therefore, the interval is [74.47, 77.53].

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The expected number of days with non-sunny weather is given as:

E(x) = P(1) + 2P(2)

= 0.26 + 2 × 0.204

= 0.668.

Hence, this is the required answer.

1 Register should be kept open.

(10)a. The expected daily revenue for the MiniGolf $1,920.

(10)b. The average number of days the weather will not be sunny is 0.668.

9. Calculation of the number of registers:

Given that

λ = 18 customers/hour

µ = 1 / 4 min

= 15 customers/hour

So,

λ / µ = 18 / 15

= 1.2

It is given that s is the number of servers we are looking for.

Let's start solving the queuing system:

For calculating the optimal number of cash registers we have the formula;

rho = λ / (s × µ)

Where,ρ = Traffic Intensity

λ = Arrival Rate

µ = Service Rate

The number of Servers (s) is calculated as:

s = ρλ / µ(If s is fractional, round it up to the nearest integer)

Calculation of ρ;

ρ = λ / (s × µ)

= 18 / (s × 15)

For the above equation let's put some values of s to find the value of ρ;s ρ=λ/(s×µ)

18/(15s)=1.2/1.8

= 0.67, rounded up to 1.1.

The register should be kept open.

10.  Calculation of expected daily revenue:

(a) Given that revenue on a sunny day is $2,000.

If it's cloudy, the revenue decreases by 20%, and if it's rainy, the revenue decreases by 80%.

Therefore, Revenue on a cloudy day

= $2,000 - 20% of $2,000

= $2,000 - $400

= $1,600

Revenue on a rainy day = $2,000 - 80% of $2,000= $2,000 - $1,600 = $400

Now, We have to find the expected revenue for the day if it's sunny today.

There is an 80% chance of sunshine tomorrow, which means that there is (a) 20% chance of rain or cloudy weather.

Based on this, Expected Revenue for the day

= 80% of $2,000 + 20% of ($1,600 + $400)

= $1,920

(b) Calculation of the average number of days with non-sunny weather:

Let x be the number of days the weather is not sunny.

Using the probabilities given in the question, the Probability that tomorrow will be sunny if it is sunny today = 80%

The probability that tomorrow will be rainy if it is cloudy today = 20%

The probability that tomorrow will be sunny if it is cloudy today = 30%

The probability that tomorrow will be rainy if it is cloudy today = 20%

The probability that the weather will not be sunny tomorrow if it's rainy today = 80%

Therefore, the Probability of non-sunny weather in a day,

P(x) is given as follows:

P(0) = 0.8 (When it's sunny today, there's an 80% chance it'll be sunny tomorrow)

P(1) = 0.2 × 0.3 + 0.8 × 0.2

= 0.26 (When it's cloudy today, there's a 30% chance it'll be sunny tomorrow and a 20% chance it'll be rainy)

P(2) = 0.2 × 0.7 × 0.1 + 0.8 × 0.2 × 0.2 + 0.2 × 0.3 × 0.2 + 0.8 × 0.8 × 0.1

= 0.204 (When it's rainy today, there's a 10% chance it'll be sunny tomorrow and an 80% chance it'll be rainy tomorrow).

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Answer:

Step-by-step explanation: The purpose of scientific notation is to make the numbers and quantities used easier to comprehend, to read and to write.

Express both numbers with the same power of ten.

Add the base numbers.

Bring the power of ten down to represent the new power of ten for the sum.

Simplify so that the base number is between 1 and 10.

Answer:

What is the purpose of scientific notation?

"to make the numbers and quantities used easier to comprehend, to read and to write. " <----- Credits to: Yahoo

How is scientific notation represented?

"To start with, scientific notation is a form of expressing very small or large numbers in a simpler form." <--------- Credits to: Yahoo

The probability density function (PDF) of the random variable Z, defined as the maximum of X and Y, can be determined as follows:

For z < 0 or z > 2: fz(z) = 0

For 0 < z < 1: fz(z) = z

For 1 < z < 2: fz(z) = 2 - z

To find the PDF of Z, we need to consider the different regions of the interval [0, 2] and determine the probability density function for each region.

For z < 0 or z > 2:

Since Z cannot be less than 0 or greater than 2, the probability density in these regions is 0. Therefore, fz(z) = 0 for z < 0 or z > 2.

For 0 < z < 1:

In this range, the maximum of X and Y is always Y because Y ranges from 0 to 2. Therefore, we can write fz(z) = P(Z < z) = P(Y < z). Since Y is uniformly distributed on (0, 2), its PDF is constant within this range. The probability of Y being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 2), which is z/2. Therefore, fz(z) = z/2 for 0 < z < 1.

For 1 < z < 2:

In this range, the maximum of X and Y can either be X or Y. To determine the PDF, we need to consider the probability of X being the maximum and the probability of Y being the maximum.

Probability of X being the maximum:

Since X is uniformly distributed on [0, 1], the probability of X being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 1), which is z/1 = z. Therefore, the probability of X being the maximum is z.

Probability of Y being the maximum:

Since Y is uniformly distributed on (0, 2), the probability of Y being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 2), which is z/2. Therefore, the probability of Y being the maximum is z/2.

Since X and Y are independent, we can add their probabilities to find the overall probability of Z being less than z. Therefore, fz(z) = P(Z < z) = P(X < z) + P(Y < z) = z + z/2 = 2z/2 + z/2 = (3z)/2.

To find the PDF fz(z) in this range, we need to calculate the derivative of the cumulative distribution function (CDF). The CDF of Z can be obtained by integrating the PDF fz(z):

Fz(z) = ∫[0,z] fz(u) du

Taking the derivative of Fz(z) with respect to z, we get:

fz(z) = d/dz (Fz(z)) = d/dz ∫[0,z] fz(u) du = d/dz (3z^2/4) = 3z/2.

Therefore, fz(z) = 3z/2 for 1 < z < 2.

For z < 0 or z > 2: fz(z) = 0

For 0 < z < 1: fz(z

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Answer:

The average temp was 4

Step-by-step explanation:

The 95% confidence interval of the mean number of jobs is (6.7, 7.5).

Given that, a sociologist found that in a sample of 55 retired men, the average number of jobs they had during their lifetimes was 7.1 and the population standard deviation is 2.1.

The best point estimate of the mean is the sample mean.

Hence the best point estimate of the mean is 7.1.

Therefore, the 95% confidence interval of the mean number of jobs is (6.7, 7.5).

Hence the required solution.

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Answer:

10.7

Step-by-step explanation:

Hello There!

The image shown below shows the relationship between two chords formed inside of a circle

So the product of the lengths of the lines in the same chord is equal to the product of the other length of the chords lines if that makes sense

So basically 6 * 16 = 9 * x

we can now use this equation that was just made to solve for x

6 * 16 = 96

96 = 9x

*divide each side by 9*

96/9=10.66666667 *round to the nearest tenth* 10.7

9x/x

we're left with x = 10.7

Answer:

It is option one

Step-by-step explanation:

I don’t know why but I’m doing a quizzizz with the same question and i picked option 2 but option one was the correct answer

Answer:

x<-8

Step-by-step explanation:

x/8<-1

x<-1×8

x<-8

For a graph with seven vertices, a minimum degree of 3 (8 = 3), and a maximum degree of 5 (Δ = 5), it can be shown that the graph must contain at least 12 edges. The largest number of edges possible in this graph is determined by the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

(a) To show that the graph must contain at least 12 edges, we can use the Handshaking Lemma. The sum of the degrees of all vertices in the graph is equal to twice the number of edges. In this case, with seven vertices and a minimum degree of 3, the sum of the degrees is at least 7 * 3 = 21. Therefore, the minimum number of edges is 21/2 = 10.5, which rounds up to 11. So the graph must contain at least 11 edges, but since the number of edges must be an integer, it must be at least 12.

(b) The largest number of edges possible in this graph can be determined by considering the maximum degree. In this case, the maximum degree is 5. Since the sum of the degrees of all vertices is equal to twice the number of edges, the sum of the degrees is at most 7 * 5 = 35. Therefore, the largest possible number of edges is 35/2 = 17.5, which rounds down to 17. So the largest number of edges possible in this graph is 17.

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Answer:

The total distance the students ran in the race would be 5 1/2 km.

Step-by-step explanation:

2/4 + 3/4 + 2 2/4 + 1 3/4 = 3 10/4 = 5 2/4 = 5 1/2 (Simplified)