The speed of sound in dry air at 68 degrees F is 343.2 meters per second. Which of the expressions below could be used to compute the number of kilometers that a sound wave travels in 10 minutes (in dry air at 68 degrees F)?

Surface Area = 358ft²

First find the area for each shape on the box.

Base x Height

Bottom rectangle = 9ft x 4ft = 36ft

There are two of the same rectangle (top and bottom)

So 36ft + 36ft = 72ft

Side rectangles = 4ft x 11ft = 44ft

There are two side rectangles so,

44ft + 44ft = 88ft

Front and back facing rectangles,

9 x 11 = 99ft

99 + 99 = 198ft

Add them all together:

198 + 88 + 72 = 358ft²

Surface Area = 358ft²

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

Learn more about differential equations click;

https://brainly.com/question/32645495

#SPJ4

Answer:

i think its the 3 one

Step-by-step explanation:

sorry if im wrong

True, Every normal unitary operator u: x! x exists.
False, An if only if it is invertible, a matrix qualifies as unitary.

What is the matrix?

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix, are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

Here, we have

a. Every unitary operator U:X→X is normal as an operator A is unitary if A*A = AA* = I and an operator is normal if A*A = AA*.

Hence, every unitary operator u: x → x is normal.

b. A unitary matrix is always invertible but an invertible matrix need not be unitary. An invertible matrix A is unitary if A⁻¹ = A*

Hence, it is not true.

To learn more about the matrix from the given link

https://brainly.com/question/12567347

#SPJ4

The inputs that are solutions for the inequality are:

x = 2

x= 1

Here we have the following inequality:

-5x < 2

We want to see which of the given inputs is a solution for this.

First we can isolate the variable in our inequality, so we get:

-5x < 2

-2 < 5x

-2/5 < x

-0.4 < x

So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:

x = 1

x = 2.

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1

Answer:x=-3

Step-by-step explanation:

if you were to plug in -3 for f(x) you would get, f(-3)=1/3(-3) +2, which then equals f(-3)=-1+2, so f(-3)=1

Now you do the same thing for g(x), so you would get g(-3)=2^(-3+3), meaning you first add -3 and 3 leaving you with g(-3)=2^0, which is equal to 1.

f(-3)=1=g(-3)

Answer:

400 markers.

Step-by-step explanation:

4,000 × ¹/10 = 400.

.Answer:

To calculate a/b of some number c, where a, b, and c are any number, we do the following: a/b x c

Step-by-step explanation:

1/10 x 4,000 = 4,000/10

400 x 10

    10

= 400

= 4 x 100

= 4 x 10 2

400 = 4 x 10 2 markers

When parallel parked along a curb, the front and rear bumpers of your vehicle must be no more than 12 inches or one foot away from other vehicles. This distance is to ensure that there is enough space for other vehicles to maneuver around your car and to prevent any accidental collisions or damage.

It is important to note that this distance may vary depending on local laws and regulations, so it is always best to check with your local authorities for specific guidelines. In addition, it is crucial to use your mirrors and signals when parallel parking to ensure that you are not blocking traffic or causing any hazards on the road. By following these guidelines and being mindful of others on the road, you can safely and effectively parallel park your vehicle.

Know more about parallel here:

https://brainly.com/question/22746827

#SPJ11

Let the age of students in a certain public high school be x;

So, we create a table of values as follows;

First, we fine the mean of the distribution, we have;

Thus, the standard deviation of the distribution is;

Then, we will insert the deviation in the table above,

Then, we have;

The standard deviation of the ages is 1.2751

Also, the variance is;

The variance is the square of standard deviation, we have;

Thus, the variance of the ages is 1.6259

Answer:

41.61

Step-by-step explanation:

Just divide.

\(\begin{matrix}4\overline{|\smallspace166.44}\:\:\:\:\:\:\:\end{matrix}\)

Answer: We have the equation:

166.44 ÷ 4 = 41.610

Calculated to 3 decimal places.

 0 4 1. 6 1 0

4 1 6 6. 4 4 0

− 0          

 1 6        

− 1 6        

   0 6      

 −   4      

     2 4    

   − 2 4    

       0 4  

     −   4  

         0 0

       −   0

           0

Step-by-step explanation: hope this helps

The monthly payment for the four wheeler from Bank A would be = $261 and from Bank B would be =$268.9

The reason why someone should chose bank A over bank B is that the monthly interest payment is lower than bank B.

Simple interest is defined as the amount of money that an individual receives due to an investment my in account for a period of time.

For bank A;

The principal amount = $5400

The rate of the investment= 8%

The time for the investment = 2 years.

Simple interest = 5400× 8×2/100

= 86400/100

= $864

The total amount = 5400 + 864 = $6264

The monthly payment for the 2years (that is, 24 months) =

6264/24 = $261.

For bank B;

The principal amount = $5400

The rate of the investment= 6.5%

The time for the investment = 3 years.

Simple interest = 5400× 6.5×3/100

= 105300/100

= $1,053

The total amount = 5400 + 1,053 = $6,453

The monthly payment for the 3years (that is, 36 months) =

6,453/24 = $268.9.

Since, the monthly interest payment for bank A is less than bank B, it will be wiser for an individual to choose bank A.

Learn more about simple interest here:

https://brainly.com/question/25793394

#SPJ1

Step-by-step explanation:

For crossing chords in a circle, the products of the segments are equal

6 * 4  =   x   *   14 -x

24 = -x^2 + 14x

-x^2 + 14x - 24 = 0      Use quadratic Formula ( or factoring ) to find:

x = 2   or  12      ( drawing is not to scale)

To compute the determinant of matrix A, we perform row operations to transform A into an upper triangular matrix.

The determinant of an upper triangular matrix is equal to the product of its diagonal entries. In this case, after applying row operations, we obtain an upper triangular matrix with diagonal entries 2, -3, and 5. Therefore, det(A) = 2 * (-3) * 5 = -30.

To compute the determinant of matrix A, we perform row operations to transform A into an upper triangular matrix. The given row operations R = R - 2R₂² and R = R - 2R₂ result in the following upper triangular matrix:

2 3 10

0 -3 1

0 0 5

The determinant of an upper triangular matrix is equal to the product of its diagonal entries. Therefore, det(A) = 2 * (-3) * 5 = -30. Thus, the determinant of matrix A is -30.

To learn more about matrix click here:

brainly.com/question/29132693

#SPJ11

The end behavior of the graph of f(x) is,

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.

A data set is a collection of organized data. Data is a collection of information that has been obtained by observations, measurements, study, or analysis, as we are all aware. It could contain names, numbers, facts, and even straightforward descriptions of items. For our study, data can be arranged in the form of graphs, charts, or tables.

Given the data,

x           -5     -4     -3     -2      -1       0      1         2         3

f(x)         -6     -2     0       4      4       0     -2      -6      -10

the graph moves towards the negative side for negative values of x,

so from the data, we observed that,

if x tends to -∞ then f(x) will be -∞,

and the value of f(x) again moves towards the negative side for all positive values of x.

so  x tends to ∞ then f(x)  will again -∞.

Hence option D is correct.

Learn more about datasets;

https://brainly.com/question/24058780

#SPJ1

Answer:

They can finish the race in 15 x 14 x 13 x 12 x 11 = 360360 order.

Step-by-step explanation:

There are 15 bicyclists in the race. The first position would come from the first bicyclist to the 15th. Meaning the first position can be occupied by 15 individuals. The second position can only be occupied by 14 individuals since one person is already first. Same way the third, fourth and fifth positions can be occupied by 13, 12 and 11 individuals respectively.

Therefore, they can finish the race in

15 x 14 x 13 x 12 x 11 = 360360 order.

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

For more such questions on triangles, click on:

https://brainly.com/question/17335144

#SPJ8

Answer:

45

Step-by-step explanation:

2 minus 47 equals 45 if that's what your talking about

Answer:

D. 369,600 feet

Step-by-step explanation:

If 1 mile = 5,280 feet, just multiply 70 by 5,280 to get the answer!

Hope this helps! :)

Answer:

D

Step-by-step explanation:

Find the number of feet in 70 miles. 5280 * 70 = 369,600.

Answer:

Step-by-step explanation:

4x + 4 - 3

= 4x + 1

Yes they both are equivalent because the algebraic expression is same

P = 8 + 10 + 8 + 10

P = 36

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

The given statement "In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth" is True.

What is 8 1/2?8 1/2 is an Italian drama movie which was released in the year 1963. It was directed by Federico Fellini. The movie is widely recognized as a highly influential classic of world cinema. The story is about a renowned filmmaker named Guido Anselmi. He is in the middle of making a film but is struggling to come up with a plot for it. In one scene of the movie, Guido steps onto an elevator that takes on the characteristics of a confession booth.MAIN ANS:True, In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth.The elevator in 8 1/2 takes on the characteristics of a confession booth as a result of its setting and characters. The elevator setting in the film emphasizes that Guido is in a confessional box and is confessing his sins. It was a unique way of depicting Guido's guilt. The way the elevator shook and rattled, making him feel like he was in a confessional box, was symbolic of how he felt. It was as if he was being taken to a higher power who was listening to him.

The scene emphasizes the religious imagery in the movie. It allows us to gain insight into Guido's psyche and the struggles he was having. The religious imagery in the movie suggests that Guido is trying to connect with a higher power to overcome his guilt. The scene also shows the extent to which he is willing to go to gain clarity.

Learn more about confessional box here:

brainly.com/question/14768835

#SPJ11

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

To learn more about perpendicular here:

https://brainly.com/question/29268451

#SPJ4

see the figure below to better understand the problem

we have that

If XY is parallel to BC

then

Triangle ABC is similar to triangle DBE

Remember that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.

I will assume that triangle ABC is a right triangle

so

AB^2+AC^2+BC^2

BC^2=9^2-8^2

BC^2=17

BC=√17

Applying proportion

DE/AC=BE/BC

substitute given values

DE/9=2/√17

DE=(2/√17)*9

DE=4.37

therefore

Answer:

11 shots

Step-by-step explanation:

Why we did this:

So therefore, Owen made 11 of 18 shots he attempted.

Owen attempted 11 shots during the hockey practice.

Number of shots attempted by Owen = 18

Percentage of shots made = 60%

Then, the number of shots made will be calculated as:

= Percentage of shots made × Number of shots attempted

= 60% × 18

= 60/100 × 18

= 0.6 × 18

= 10.8 shots

= 11 shots approximately

In conclusion, Owen made 11 shots

Read related link on:

https://brainly.com/question/18298965

Answer:

225

Step-by-step explanation:

6*2.5=15

6*2.5=15

15*15=225

The perimeter and area of square is \(60cm\) and \(225cm^{2}\) respectively.

Option 4 is correct.

It is given that, side of square is enlarged using a scale factor of 2.5.

So that, new side of square is,

                                 \(=6*2.5=15cm\)

Perimeter of square is,

                            \(=4*15=60cm\)

Area of square is,

                             \(=15815=225cm^{2}\)

Thus, the perimeter and area of square is \(60cm\) and \(225cm^{2}\) respectively.

Learn more about the perimeter here:

https://brainly.com/question/19819849

Answer:

y=8

x=3

Step-by-step explanation: