Numerical solutions of the Lorenz equations [8 marks] Consider using a Runge-Kutta solver to compute numerical solutions in 0

Answer:

0.222222222

Step-by-step explanation:

Answer:

y = 1/2x

Step-by-step explanation:

y - 2 = 1/2 (x-4)

y = 1/2x - 2 + 2

y = 1/2x

(The y - intercept is 0 because -2 and 2 cancels each other out)

Hope this helps :)

Let me know if there are any mistake!!

The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be

⇒ y = 1/2x

What is equation of line?

The equation of line in slope intercept form is defined as;

y = mx + b

Where, 'm' is slope of line and 'b' is y-intercept.

Given that;

The equation of line is;

y - 2 = 1/2 ( x - 4 )

Now,

We can change the equation of line in slope intercept form as,

y - 2 = 1/2 ( x - 4)

Solve as;

y - 2 = 1/2 x - 1/2 × 4

y - 2 = 1/2 x - 2

Add 2 both side,

y - 2 + 2 = 1/2 x - 2 + 2

y = 1/2 x

Thus, The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be;

⇒ y = 1/2x

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The value of c that makes the area of the region between the curves 25x^2 - c^2 and c^2 - 25x^2 equal to 512/15 is approximately c = 23.571.

To find the value of c that corresponds to an area of 512/15 for the region between the curves, we need to set up and solve an integral. The area between two curves can be calculated by integrating the difference between the upper curve and the lower curve with respect to x over the desired interval.

The two curves given are 25x^2 - c^2 and c^2 - 25x^2. To find the limits of integration, we set the two curves equal to each other and solve for x:

25x^2 - c^2 = c^2 - 25x^2

Simplifying the equation, we get:

50x^2 = 2c^2

x^2 = c^2/25

Taking the square root of both sides, we find:

x = ± c/5

Now, we can set up the integral to find the area:

Area = ∫[(25x^2 - c^2) - (c^2 - 25x^2)] dx

Simplifying the integral, we get:

Area = ∫(50x^2 - 2c^2) dx

Evaluating the integral and setting it equal to 512/15, we get:

(2/3) * [50x^3 - 2c^2x] |[c/5, -c/5] = 512/15

Solving this equation for c, we find that c is approximately 23.571.

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Given:

Mean , median and mode are given.

Median: Put all the number in order and find the middle number, or if there are two middle numbers, average them by adding them and dividing by two.

Mode: The number or numbers which appear with the highest frequency in the list.

Mean: Add all the numbers and then divide by how many numbers there are.

Answer:

8.2 CM

Step-by-step explanation:

ACCORDING TO THE MODEL

radius = 9*2 - 8*2

Diameter = 2 times radius

ok I cant too hard to explain because Im typing so its 8.2cm so

Answer:

19 1/16

Step-by-step explanation:

Answer:

305/16

Step-by-step explanation:

Simplify the following:

(5 (30 + 1/2))/8

Hint: | Express (5 (30 + 1/2))/8 as a single fraction.

(5 (30 + 1/2))/8 = (5 (30 + 1/2))/8:

(5 (30 + 1/2))/8

Hint: | Put the fractions in 30 + 1/2 over a common denominator.

Put 30 + 1/2 over the common denominator 2. 30 + 1/2 = (2×30)/2 + 1/2:

(5 (2×30)/2 + 1/2)/8

Hint: | Multiply 2 and 30 together.

2×30 = 60:

(5 (60/2 + 1/2))/8

Hint: | Add the fractions over a common denominator to a single fraction.

60/2 + 1/2 = (60 + 1)/2:

(5 (60 + 1)/2)/8

Hint: | Evaluate 60 + 1.

60 + 1 = 61:

(5×61/2)/8

Hint: | Express 5×61/2 as a single fraction.

5×61/2 = (5×61)/2:

((5×61)/2)/8

Hint: | Express ((5×61)/2)/8 as a single fraction.

((5×61)/2)/8 = (5×61)/(2×8):

(5×61)/(2×8)

Hint: | Multiply 2 and 8 together.

2×8 = 16:

(5×61)/16

Hint: | Multiply 5 and 61 together.

5×61 = 305:

Answer:  305/16

Answer:

So first you have to make all the denominaters (bottom #s) the same so we would get 12/20-8/20+5/20 and you would solve this to equal 9/20 and to divide it by 1/6 would equal 2 7/10.

Hope this helps! (pls read the comment for free gift cards)

Answer:

the axis of symmetry is 0 which is x=0

Step-by-step explanation:

Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

Step-by-step explanation:

Probability Density Function(PDF) is a statistical

expression that defines a probability distribution for a descrent random variable as opposite to a continuous random variable.

Answer:

U ARE A QUEEN

Step-by-step explanation:

HAY BESTIE

Answer:

d=5h because the number of hours run multiplied by 5 would equal the

total distance.

Answer:

Step 4

Step-by-step explanation:

Im pretty sure becuse in step 4 the negative is swtiching sides which also would flip the greaterthan or equal too sign to a lessthan or equal too sign.

The expression that represents the perimeter of the rectangle is 8x - 14

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

Length of rectangle(L) = x - 4

Width of rectangle(W) = 3x - 3

Perimeter of rectangle = 2(L + W)

L =  x - 4, W = 3x - 3

Perimeter of rectangle = 2( x - 4 + 3x - 3)

Perimeter of rectangle = 2( 4x - 7) which is 8x - 14

In conclusion 8x - 14 is the expression for the perimeter of the rectangle

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Answer:

F type connector

Step-by-step explanation:

Use an F-type connector for broadband cable connections that use coaxial cable.

The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

T

F

T

T

F

F

F

F

Step-by-step explanation:

....................

Answer:

Step-by-step explanation:

\(\longrightarrow{\green{ x\:=\:12}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\((x - 9) \frac{2}{3} = 2\)

\(➺ \: (x - 9) = 2 \times \frac{3}{2} \)

\(➺ \: x = 3 + 9\)

\(➺ \: x = 12\)

Therefore, the value of \(x\) is 12.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

\((x - 9) \frac{2}{ 3} = 2\)

\(➺ \: (12 - 9) \frac{2}{3} = 2\)

\(➺ \: 3 \times \frac{2}{3} = 2\)

\(➺ \: 2 = 2\)

\(➺ \: L.H.S.=R. H. S\)

Hence verified.

\(\huge\bf\purple{*Mystique 35♡༉}\)

Answer:

8 slices per pizza.

Step-by-step explanation:

To find the number of slices in one pizza, we can use division.

If you order 12 pizzas, you will get 96 slices of pizza. To find the number of slices in one pizza, we can divide the total number of slices by the number of pizzas:

96 ÷ 12 = 8

Therefore, there are 8 slices in one pizza.

Answer:

8

Step-by-step explanation:

12 pizzas have 96 slices
So one pizza must have 96/12 = 8 slices of pizza

Answer:

not exactly sure what is being asked butttt i think it's 90

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Thus, the probability are Zero represents the impossibility.

1/2 equals probable and unlikely

1 = event happens.

Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.

Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.

The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).

Given that probability can only be a number between 0 and 1,

The zeroth value is the impossible.

so there is a 50% chance for both likely and unlikely.

If 1, the event must take place.

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Yes, all the numbers are multiples of prime numbers is a true statement as it get proved by prime factorization theorem.

As given in the question,

Given statement is written as:

All the numbers are representing multiples of prime numbers.

In the field of mathematics,

Using prime factorization theorem also known as fundamental theorem of arithmetic states that:

All the integers which are greater than one are represented as a multiple of prime numbers:

Example of the above stated theorem:

2 = 2×1

3 = 3 × 1

6 = 2 × 3

14 = 2 × 7 ( 2 and 7 both are prime numbers )

98 = 7 × 7 ×2 ..... and so on.

Therefore, all the numbers represents as a multiple of prime numbers is a true statement.

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The experimental probability that the next person Evelyn sees will be wearing loafers is: 1/4.

First step is to calculate the number of shoes

Number of shoes=4+5+6+6+3

Number of shoes=24

Second step is to calculate the  experimental probability

Using this formula

Experimental probability=Number of loafers/Number of shoes

Let plug in the formula

Experimental probability=6/24

Experimental probability=1/4

Therefore the experimental probability that the next person Evelyn sees will be wearing loafers is: 1/4.

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Answer:

1/4

Step-by-step explanation:

The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

So, let 7x, 3x, and 2x be the three numbers.

7x+2x = 9x is the product of the lowest and greatest number.

In accordance with:

9x-30=2(3x)

To make the equation easier:

9x-30=6x

30 extra on both sides:

9x=6x+30 or,9x-6x=30

3x=30, x=10,

So, the numbers will be:

7x=7(10) = 70

3x=3(10) = 30

2x=2(10) = 20

Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

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Answer: Center: (-7,6)

Radius: 4

Answer:

$5.71 a day

Step-by-step explanation:

240/6 = 40

40/7 = 5.71428571429

Round 5.71428571429 = 5.71

Answer:

Step-by-step explanation:

The distance between two points or a line segment can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

\( |AB| = \sqrt{ ({ - 4 - 2})^{2} + ({1 - 9})^{2} } \\ = \sqrt{( { - 6})^{2} + ({ - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Answer:

The length of segment AB is 10

Step-by-step explanation:

The distance formula is d=\(\sqrt{ (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}\)

With the points (-4,1) and (2,9) you know that \(-4=x_{1}, 2=x_{2}, 1=y_{1} ,9=y_{2}\)

Now you put the numbers into the distance formula

d=\(\sqrt{(2-(-4))^{2}+(9-1)^2\)

(2-(-4) turns into (2+4) because two negatives equal a positive.

After adding and subtracting you get d=\(\sqrt{6^2+8^2\)

You then square \(6^2\) and \(8^2\) to get \(\sqrt{36+64\)

After adding 34+64 you get \(\sqrt{100\), which is 10

So the length of segment AB is 10