4. Reduce the following second order ODE into first order and Solve [4] x?Y" - xy' +y = 0, y(1) = 4.3, y(1) = 0.5. 5. Solve the following Euler-Cauchy equation [4] 224" - 4.ry' + 6y = 0, y(1) = 0.4, y'(1) = 0. 6. Solve the following second order ODE [2] y" + 4y + (72 + 4)y = 0, y(1/2) = 1, y' (1/2) = -2.

Answer:

hi how are you doing today Jasmine

The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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Answer:

Domain: [1, 6]

Range: [1, 7]

General Formulas and Concepts:

Alg I

Step-by-step explanation:

We can find our domain and range from looking from the graph.

Domain

Domain encompasses x-values. According to the graph, the x-values span from 1 to 6. Since both are closed dots, they are included in the domain:

[1, 6] or 1 ≤ x ≤ 6

Range

Range encompasses y-values. According to the graph, the y-values span from 1 to 7. Since both are closed dots, they are included in the range:

[1, 7] or 1 ≤ x ≤ 7

Easy way to remember this: for Domain, look only at the x-axis and for Range, look only for the y-axis.

Answer:

70feet

Step-by-step explanation:

during the

1st sec it travels 28 ft

2nd sec =28-7=21ft

3rd sec= 21-7=14ft

4th sec= 14-7= 7ft

last sec=7-7=0ft, at this point the car stops.

so altogether it travels 28+21+14+7+0= 70 feet

Since it is difficult to evaluate this integral exactly, use technology to approximate it. After calculation, the length is approximately 3.9205 (rounded to four decimal places).

To find the length of the function y =\(2x^(3/2)/3 - x^(1/2)/2\) over the interval [1, 4], you need to evaluate the integral of the square root of [1 + (y')^2] with respect to x, where y' is the derivative of y with respect to x.

First, find the derivative y':
y'(x) = d(2x^(3/2)/3 - x^(1/2)/2)/dx = x^(1/2) - 1/(4x^(1/2))

Now, find (y')^2:
\((y')^2 = (x^(1/2) - 1/(4x^(1/2)))^2\)
Next, find the square root of [1 + (y')^2]:
\(√[1 + (y')^2] = √[1 + (x^(1/2) - 1/(4x^(1/2)))^2]\)

Finally, evaluate the integral:
Length = \(∫(√[1 + (y')^2]) dx\) from x = 1 to x = 4

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Answer:

10

Step-by-step explanation:

Let's break it down:

Answer:

10

Step-by-step explanation:

Step 1: 1/3 of 30 cupcakes for vanilla icing

=10 cupcakes for vanilla icing

Step 2: 30 - 10 cupcakes = 20 remaining cupcakes

1/2 of 20 cupcakes for chocolate icing

=10 cupcakes for chocolate icing

Step 3: 20 - 10 cupcakes= 10 remaining

•

• • 10 cupcakes will get strawberry icing

Answer:

V = 1207

Step-by-step explanation:

Alonzo's graph which shows the proportional relationship between the circumference and the radius, has a starting point of (0, 0), and the value of the circumference (the range), increases proportionately with the values of the radius (the domain).

(a) range: 0 ≤ r < ∞

(b) Domain: 0 ≤ r < ∞

A function can be described as an outline or expression of the relationship between two variables, an input and an output variable, in which input variable has exactly one value in the output.

The given graph in the question is the graph of the circumference of a circle to the radius of the circle.

The relation between the circumference of a circle, C, and the radius is presented as follows;

C = 2·π·r

Which gives; \(\displaystyle {2\cdot \pi = \frac{C}{r} }\)

The relationship is a proportional relationship, and the constant of proportionality is 2·π.

Therefore, points on the graph includes (0, 0), and as the value of r increases, the value of C, increases proportionately.

(a) The range, which is the possible output values, which is the possible values of the circumference is; 0 ≤ C < ∞ which is [0, ∞)

Range: 0 ≤ C < ∞

(b) The value of the circumference depends on the radius, therefore, the input variable is the radius and the output variable is the circumference, which gives, the domain as the possible values of the radius, and therefore;

Domain = 0 ≤ r < ∞ which using interval notation is [0, ∞)

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One of three different floors each day during a 4-day work week in 12 different ways, can be assigned to the nursing student.

To find the number of ways a nursing student can be assigned to one of three different floors each day during a 4-day work week, we need to use the multiplication principle of counting.

First, we need to determine the number of options the nursing student has for each day. Since she can be assigned to one of three different floors, she has 3 options each day.

To find the total number of ways she can be assigned over the 4-day work week, we multiply the number of options she has for each day by the number of days in the week:

3 options per day x 4 days = 12 total ways

Therefore, the nursing student can be assigned to one of three different floors each day during a 4-day work week in 12 different ways.

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The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.

However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.

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The inequality  for speed is s<270.

Inequality shows relation between two expression which are not equal to each others.

Given that,

Most of the helicopters fly at speed of less than 270 kilometers,

Let the speed in denoted by s,

s is less than 270,

Use inequality to solve this data,

s<270

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Answer:

∠V = 33°

∠W = 90°

∠X = 57°

Step-by-step explanation:

In a right triangle, the sum of the acute angles is 90 degrees

(2x+3) + (3x+12) = 90

combine like terms

5x + 15 = 90

5x = 75

x = 15

∠V = 2x+3, x=15

2(15) + 3

30 + 3

33°

∠X = 3x+12, x=15

3(15) + 12

45 + 12

57°

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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The encryption method that combines a random value with the plain text to produce the cipher text is: One-time pad.

The one-time pad encryption technique is a form of symmetric encryption where a random key, known as the one-time pad, is combined with the plain text using a bitwise XOR operation. The one-time pad should be at least as long as the plain text and should never be reused.

In this method, each character of the plain text is combined with a corresponding character from the one-time pad, resulting in the cipher text. The one-time pad acts as a random key stream, making the encryption extremely secure if implemented correctly.

Steganography is a different technique that involves hiding information within other seemingly innocuous data, such as images or audio files, without necessarily encrypting it.

Transposition is a method of encryption where the characters of the plain text are rearranged or shuffled without changing the actual characters themselves.

Elliptic Curve is not an encryption method but rather a mathematical framework used in public-key cryptography systems, such as Elliptic Curve Cryptography (ECC), which provide secure communication channels but do not involve combining random values with the plain text to produce the cipher text.

Therefore, the correct answer is: One-time pad.

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Answer:

Abby will earn $510 if she works 60 hours.

Step-by-step explanation:

8 hrs --> $68

1 hr --> 68 × 1/8 = $8.5

So, 60 hrs

= 8.5 × 60

= $510

Answer:

\(30\)

Step-by-step explanation:

\(6(3 + 2) \\ = 6(5) \\ = 30\)

The probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

The event of getting a "2" and the event of getting a "5" on the first roll of a die are mutually exclusive events because they cannot both occur in the same trial. The probability of either of these events occurring is P(A) = 0.16, and the probability of both events occurring at the same time is P(A ∩ B) = 0.00.

The event of getting a "2" on the first roll and the event of getting a "5" on the second roll of a die are independent events. This can be confirmed using the formula P(A ∩ B) = P(A)P(B). The probability of getting a "2" on the first roll is P(A) = 0.16 and the probability of getting a "5" on the second roll is P(B) = 0.16. Thus, the probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

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Answer:

Complementary angels are basically two angles that add up to 90 degrees. Supplementary angles are two angles that add up to 180 degrees.

Step-by-step explanation:

(self-explanatory)

I hope this helps, have a nice day.

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

The given argument can be considered as formally invalid because it contains a logical fallacy. In particular, the fallacy involved is known as the affirming the consequent fallacy, which is a type of non sequitur.

This fallacy occurs when a conclusion is drawn that affirms the consequent of a conditional statement, without considering other factors. In this case, the argument starts with a conditional statement (if Felix is a bachelor, then he is not married) and then proceeds to the conclusion that Felix is not a bachelor based solely on the fact that he is married.

However, this conclusion does not necessarily follow from the conditional statement because it is possible for someone to be married without being a bachelor, such as if they were previously married and then divorced. Therefore, the argument is not valid.

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Answer: It is B. RuthAnn will meet her annual goal of $32,523 for retirement with an excess of $20,791.60.

Step-by-step explanation:

Im pretty sure the answer is A but if not then it is C

This is bcuz B doesn’t make sense because the graph doesn’t say anything close to 100 rides and D doesn’t make sense either.

Hope this helped.

Answer: Fries = $1.50 Hamburger = $2

Step-by-step explanation:

   so since the first person payed 11 for 4 burgers and 2 fries and the second person got 2 more fries than the first person and spent 14 and there is a 3 dollar difference which 3 divided by 2 is 1.5 which means that the fires a 1 dollar and 50 cents. so 3 dollars subtracted from 11 equals 8 and 8 divided by 4 is 2 dollars leaving you with hamburgers being 2 dollars and fries being 1 dollar and 50 cents

The total cost function for manufacturing at Factory X and Factory Y is given by C(x, y) = 4x^2 + xy + 8y^2 + 3200. To minimize the total monthly cost of production while producing 1,700 units per month, we need to determine the optimal quantities to produce at each factory, x and y.

To minimize the total monthly cost, we need to find the values of x and y that minimize the cost function C(x, y) while satisfying the constraint that the total quantity produced is 1,700 units per month.

To solve this problem, we can use optimization techniques such as partial derivatives. We differentiate the cost function with respect to x and y and set the resulting equations equal to zero to find the critical points. Solving these equations will give us the optimal values of x and y.

After obtaining the optimal values of x and y, we round them to the nearest whole units since the problem specifies rounding to whole units.

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The ship moved 2 km to the west, then 1 km to the east, and finally 6 km to the west. So, the total distance covered by the ship is 2 + 1 + 6 = 9 km.

To move the ship according to the given signals, we need to follow the instructions for each signal received. Let's go step by step:

1. The ship moves 2 km to the west. So, we start at the initial position and move 2 km to the west.
2. The ship moves 1 km to the east. Since we are currently 2 km to the west, we need to move 1 km back towards the east.
3. No signal is given, so the ship stays in its current position.
4. No signal is given, so the ship stays in its current position.
5. No signal is given, so the ship stays in its current position.
6. The ship moves 6 km to the east. As there were no previous signals to affect our position, we move 6 km east from the initial position.
7. The ship moves 6 km to the west. Since we moved 6 km east in step 6, we need to move back 6 km to the west.

After following this sequence of signals, the ship returns to its initial position.

In total, the ship moved 2 km to the west, then 1 km to the east, and finally 6 km to the west. So, the total distance covered by the ship is 2 + 1 + 6 = 9 km.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

75 = 5x

x = 15

Step-by-step explanation:

These angles are equal!

75 = 5x

Now, if the next question is to solve for x:

75 = 5x

Divide both sides by 5

75/5 = x

x = 15

Answer: corsehero is the way to go

Step-by-step explanation: