Consider the following IVP, x²y" - 2xy' + 2y + λ²y = 0, y' (1) = 0, y(2) = 0, and a. What is the general solution to this differential equation? b. Find the eigenvalue of the system. c. Find the eigenfunction of this system. d. Compute the first four positive eigenvalues and eigenfunctions

The average number of sim cards that are at the repair machine at any given time, based on the Poisson distribution and the given parameters.

Based on the information provided, we can use the Poisson distribution to calculate the average number of sim cards at the repair machine.
First, we need to find the rate parameter, which is the average number of defects per unit time. We know that the time in between defects follows an exponential distribution with an average of 2.5 minutes. The rate parameter (λ) is the inverse of the average time between defects, so λ = 1/2.5 = 0.4 defects per minute.
Next, we can use the Poisson distribution formula:
P(k defects in t minutes) = (λt)^k * e^(-λt) / k!
We want to find the expected number of sim cards at the repair machine, which is the average number of defects that occur in the 2 minutes it takes to repair each sim card. So we can set t = 2 and solve for k:
P(k defects in 2 minutes) = (0.4 * 2)^k * e^(-0.4 * 2) / k!
We can use a table or calculator to find the probabilities for different values of k. For example, P(0 defects) = 0.329, P(1 defect) = 0.391, P(2 defects) = 0.195, etc.
To find the expected number of sim cards at the repair machine, we can multiply each probability by the corresponding number of sim cards (k) and add them up:
E(number of sim cards) = 0 * 0.329 + 1 * 0.391 + 2 * 0.195 + ...
This sum can be approximated using a calculator or spreadsheet. The answer will be the average number of sim cards that are at the repair machine at any given time, based on the Poisson distribution and the given parameters.

Learn more about parameters here

https://brainly.com/question/29344078

#SPJ11

The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y

Let's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,

Let S represent the total cost of purchasing a pool membership from the Swimming Hole.

Then we can write the following system of inequalities:

A = 75 + 20x (total cost of Aquatics Club membership)

S = 15 + 65x (total cost of Swimming Hole membership)

Alfonso has no more than y dollars to spend

So, we have

75 + 20x ≤ y

15 + 65x ≤ y

Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y

Read more about system of inequalities at

https://brainly.com/question/23093488

#SPJ1

Step-by-step explanation:

Interior angles of a 5-gon    sum to   ( 5-2)(180 = 540 degrees

smallest angle =x

largest angle = x + 4d    

          where d is the arithmetic sequence common difference

x + 4d     -x     =  44    shows d = 11

then    x    + x+d    + x+2d   + x+3d   + x + 4d = 540

      5x + 10d = 540      we know d = 11

       5x + 10(11) = 540

         5x = 430

           x = smallest angle = 86 degrees

The smallest interior angle of the pentagon is 86 degrees. This was found by setting up an equation involving the common difference "d" in the arithmetic sequence of angles and solving for "x."

Let's denote the five interior angles of the pentagon as follows:

Let the smallest angle be "x" degrees.

The other four angles form an arithmetic sequence, so we can represent them as x + d, x + 2d, x + 3d, and x + 4d, where "d" is the common difference between the angles.

Now, we know that the difference between the largest angle and the smallest angle is $44^\circ$. Therefore, we can write the equation:

(x + 4d) - x = $44^\circ$

Simplify and solve for "d":

4d = $44^\circ$

Now, divide both sides by 4 to find the value of "d":

d = $44^\circ / 4 = $11^\circ

Now that we know the common difference "d" is $11^\circ", we can find the smallest angle "x" by using the equation for the sum of angles in a pentagon, which is 540 degrees:

x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 540

Simplify and solve for "x":

5x + 10d = 540

5x + 10($11^\circ) = 540

5x + $110 = 540

Now, subtract $110 from both sides:

5x = 540 - $110

5x = $430

Finally, divide by 5 to find the smallest angle "x":

x = $430 / 5 = $86

So, the smallest angle of the pentagon is $86 degrees.

For more such questions on pentagon :

https://brainly.com/question/29673128

#SPJ2

The equation of a straight line is given in the form:

where m is the slope and b is the intercept on the y axis.

The question already provides the value of the slope to be:

Therefore, the value of b can be gotten by substituting any pair of x and y values into the equation:

The unknown value is 0.

The equation will be:

Answer:

Option (C) : y = 6 / 11

Step-by-step explanation:

To find Horizontal Asymptote of the function, you need to see degree of of numerator and denominator.

Since, the degrees of the numerator and denominator are the same,

Horizontal Asymptote = leading coefficient of the numerator divided byleading coefficient of the denominator

Therefore,

Horizontal Asymptote = 6 / 11

The future value of the deposits at the end of 5 years is approximately $6,138.74.

To calculate the future value of the deposits, we can use the formula for compound interest:

FV = P(1 + r/n)^(nt)

Where: FV is the future value

P is the principal amount (initial deposit)

r is the annual interest rate (3% in this case)

n is the number of times interest is compounded per year (quarterly in this case)

t is the number of years

In this case, the principal amount is $1,000, the annual interest rate is 3% (or 0.03), the number of times interest is compounded per year is 4 (quarterly), and the number of years is 5.

Plugging in these values into the formula, we get: FV = $1,000(1 + 0.03/4)^(4*5)

Calculating this, the future value of the deposits at the end of 5 years is approximately $6,138.74.

Learn more about interest rate at

https://brainly.com/question/32122915

#SPJ11

Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.

The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:

5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups

Now, we can find three-fourths (3/4) of 17/3:

(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups

Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

Learn more about three-fourths here

https://brainly.com/question/16953584

#SPJ11

Answer:

so uh yall probably never heard of her but shiiiiiiiiiii

Step-by-step explanation:

her name is chicken nuggies ;)

Answer:

2.5%

2.2kg=2200g

\( \frac{x}{100} \times 2200 = 55 \\ 22x = 55 \\ x = 2.5\%\)

The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

Learn more about the values and function rule here:

https://brainly.com/question/20527725

#SPJ1

Given that the √123 in this case is 11.09, it is sufficient to check the number's divisibility by 2, 3, 5, 7 or 11.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.

Given Data,

123 is prime, we merely need to test divide it by 2,3, 5 and 7 the fact that 123 is not divisible by those.

We can use the finding that any number, let's say N, is prime if it cannot be divided by any prime number less than  √N to test for such numbers.

Given that the √123 in this case is 11.09, it is sufficient to check the number's divisibility by 2, 3, 5, 7 or 11.

To learn more about prime number, visit:

https://brainly.com/question/9315685

#SPJ4

The series of transformations that would map Figure Q onto Figure R is given as follows:

The five more known rotation rules are given as follows:

Two equivalent vertices are given as follows:

(3,3) and (0,-3).

The figure was rotated from the first quadrant to the fourth quadrant, hence a possible rule is:

(x,y) -> (y, -x).

Which is a 90º clockwise rotation.

Then the equivalent vertex of (3,3) would be of:

(3, -3).

The equivalent vertex is (0, -3), meaning that the figure was also translated 3 units left.

More can be learned about rotation rules at brainly.com/question/17042921

#SPJ1

If triangle ABC is reflected over the y-axis, reflected over the x-axis, and rotated 180 degrees, point A' will lie on (2,-1).

Triangle ABC has three vertices namely A, B and C. If the triangle ABC is reflected over the y-axis, the x-coordinate changes its sign while the y-coordinate remains the same. Therefore, point A(x,y) becomes A'(-x,y) after reflection over y-axis.If the triangle ABC is reflected over the x-axis, the y-coordinate changes its sign while the x-coordinate remains the same. Therefore, point A'(-x,y) becomes A''(-x,-y) after reflection over x-axis.If the triangle ABC is rotated 180 degrees, the point A''(-x,-y) becomes A'''(x,y).Therefore, point A(x,y) becomes A'''(x,y) after reflection over y-axis, reflection over x-axis, and rotation of 180 degrees.

Therefore, A will lie on (2, -1).

To know more about reflection, click here

https://brainly.com/question/15487308

#SPJ11

Answer:

true

to find missing side u need to use Pythagoras theorem

hope it helps

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

Learn more about intergal here:

https://brainly.com/question/31109342

#SPJ1

Answer:

81.25%

Step-by-step explanation:

58-32=26

26/32=0.8125

0.8125x100=81.25

Sorry I'm not that good at explaining but here is something that helped me.

Answer:

C is -14, 7, 14, 28

not sure what D is

Step-by-step explanation:

Answer: -3/4

Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.

Nice helping out!

Answer:

There are no solutions.

Step-by-step explanation:

Hello!

Isolate the absolute value equation first:

Now stop and think.

An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.

So the solution is No Solutions.

Answer: Outsourcing

Step-by-step explanation: I just took a test.

The use of workers that use networked computers to work at lower rates of pay than American workers is called outsourcing.

The term outsourcing has to do with a situation in which workers from outside the company are contrated to do the work of the company. This could be done remotely most times by the use of a computer.

In this case, the American companies that contracted European and Asian companies, where well educated workers could do jobs on networked computers at lower rates of pay than American workers is called outsourcing.

Learn more about outsourcing: https://brainly.com/question/14356798

I AM HERE TO HELP--- nope I'm sorry

Answer:

-9

Step-by-step explanation:

C + D

-----------

C - D

= 8/11 + 10/11

- - - - - - - - - -

8/11 - 10/11

=18/11

- - - - -

- 2/11

=18/11 x 11/-2

= - 9

Answer:

The answer is -9

Step-by-step explanation:

8/11 + 10/11

8/11 - 10/11

18/11

-2/11

= -9

Answer:

5 × 5

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length ) , then

A = 5² = 5 × 5 = 25 in²

Answer:

it's either 3√36 or 2.002

Answer:

x-3

Step-by-step explanation:

Laura's age goes first. You don't know what it is, so you have to leave it as x. You know Jeri is 3 years younger, so you subtract from x.

Answer:

The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

From the given figure

∵ The line passes through points (0, 2) and (2, 3)

∴ x1 = 0 and y1 = 2

∴ x2 = 2 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = \(\frac{3-2}{2-0}\) = \(\frac{1}{2}\)

∴ m =  \(\frac{1}{2}\)

→ b is the value of y at x = 0

∵ At x = 0, y =2

∴ b = 2

→ Substitute the value of m and b in the form of the equation above

∵ y =  \(\frac{1}{2}\) x + 2

∴ The equation of the line is y =  \(\frac{1}{2}\) x + 2

∵ The line is dashed

∵ The shaded area is over the line

∴ The sign of inequality is >

→ Replace = in the equation by >

∴ y >  \(\frac{1}{2}\) x + 2

∴ The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2