The complementary for
is y" — 2y" — y' + 2y = e³x,
Yc = C₁е¯x + C₂еx + С3е²x.
Find variable parameters u₁, U2, and u3 such that
Yp = U₁(x)e¯¤ + U₂(x)eª + Uz(x)e²x

is a particular solution of the differential equation.

The average radius of the Crab Nebula in the year 2019 was 4.56 x 107 R_(sun).

As per the given question, the average velocity of the Crab Nebula is 1,500 km/s, and it has been expanding since the year 1054. We are supposed to find the average radius in the year 2019.

To find the average radius in the year 2019, we need to find out the time period between 1054 and 2019.

Time difference, t = 2019 - 1054= 965 years

Then we need to convert this time into seconds.

Since 1 year = 365 days and 1 day = 24 hours and 1 hour = 3600 seconds,965 years = 965 x 365 x 24 x 3600 seconds = 3.04 x 1010 seconds

Now we can use the formula:

v = d/t

Where v is velocity, d is distance, and t is time distance of the crab nebula is the radius of the crab nebula, and the time is 3.04 x 1010 seconds.

v = 1500 km/s

Let r be the average radius of the Crab Nebula in the year 2019.

r = v x t = 1500 km/s x 3.04 x 1010 seconds = 4.56 x 1013 km = 4.56 x 107 R_(sun)

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Answer:

21

Step-by-step explanation:

Because 9 + 12 equals 21 and when you're adding negative numbers you don't add the negative part So it's going to be 21 by itself

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

x = 9 units

Step-by-step explanation:

\(\frac{x}{54}\) = \(\frac{8}{48}\)

x = \(\frac{54*8}{48}\) = 9 units

Answer:

centre : (4;-5)

radius : 2

The second smallest positive x-value where the graph of f(x) has a horizontal tangent line is (1/3) * (π - arccos(1/9)).

To find the second smallest positive x-value where the graph of the function f(x) = x + 3sin(3x) has a horizontal tangent line, we need to find the points where the derivative of the function is zero.

First, let's find the derivative of f(x) with respect to x. Applying the derivative rules, we have:

f'(x) = 1 + 3cos(3x) * (3) = 1 + 9cos(3x).

To find the points where the derivative is zero, we set f'(x) = 0 and solve for x:

1 + 9cos(3x) = 0.

Subtracting 1 from both sides and then dividing by 9, we get:

cos(3x) = -1/9.

Now, we can use the inverse cosine function to solve for x:

3x = arccos(-1/9).

Dividing both sides by 3, we have:

x = (1/3) * arccos(-1/9).

Since we are looking for the second smallest positive x-value, we can use the periodicity of the cosine function to find the exact value.

The cosine function has a period of 2π, which means it repeats every 2π. The smallest positive value for arccos(-1/9) occurs at the principal value of arccos(-1/9), which is between 0 and π. Let's denote this value as θ.

Therefore, the second smallest positive x-value occurs when:

x = (1/3) * θ.

To express this value exactly, we need to determine the exact value of θ. Since cos(θ) = -1/9, we can use the Pythagorean identity for cosine:

sin(θ) = √(1 - \(cos^2\)(θ)) = √(1 - \((-1/9)^2\)) = √(1 - 1/81) = √(80/81) = √80 / 9.

Thus, the exact value of θ is:

θ = arccos(-1/9) = π - arccos(1/9).

Therefore, the second smallest positive x-value where the graph of f(x) has a horizontal tangent line is:

x = (1/3) * θ = (1/3) * (π - arccos(1/9)).

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Try to use this to help

Hopefully this helps you

The paintball will hit the disc after around 2.16 seconds.

To find the time it takes for the paintball to hit the disc, we need to find the common value of t when the height of the disc and the path of the paintball are equal.

Setting the two functions equal to each other, we get:\(5t^2 - (149/5)t + 1 = 0\).

Rearranging the equation, we have:\(5t^2 - (149/5)t + 1 = 0\).

This is a quadratic equation. By solving it using the quadratic formula, we find that t ≈ 2.16 seconds.

Therefore, it will take approximately 2.16 seconds for the paintball to hit the disc.

In conclusion, the paintball will hit the disc after around 2.16 seconds.

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The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Answer:

11.571

Step-by-step explanation:

Answer:

(A) - B

(B) - DC

The idea is to sort the array in descending order and then return the second element which is not equal to the largest element from the sorted array.

In order to have as few implementation dependencies as feasible, Java is a high-level, class-based, object-oriented programming language.

// Java program to find second largest element in an array

import java.util.*;

class GFG{

// Function to print the

// second largest elements

static void print2largest(int arr,int arr_size)

{

int i, first, second;

// There should be

// atleast two elements

if (arr_size < 2)

{

  System.out.printf(" Invalid Input ");

  return;

}

// Sort the array

Arrays.sort(arr);

// Start from second last element

// as the largest element is at last

for (i = arr_size - 2; i >= 0; i--)

{

  // If the element is not

  // equal to largest element

  if (arr[i] != arr[arr_size - 1])

  {

   System.out.printf("The second largest " +

                      "element is %d\n", arr[i]);

   return;

  }

}

System.out.printf("There is no second " +

                  "largest element\n");

}

// Driver code

public static void main(String[] args)

{

int arr[] = {12, 35, 1, 10, 34, 1};

int n = arr.length;

print2largest(arr, n);

}

}

The idea is to sort the array in descending order and then return the second element which is not equal to the largest element from the sorted array.

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Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation: It would be A because the factor is the denominator and it would be more units in size, so there are 60,000 inches in 5,000 feet.

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

again i can not see the given point

Step-by-step explanation:

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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a) The amplitude of the function is 4 feet.

b) The function that represents the situation is .

a) The amplitude (A), in feet, is equal to the difference between highest and lowest point (\(\left(y_{\max }, y_{\min }\right.\)), in feet, divided by 2. The period (T), in seconds, is the time taken by the bottle to complete one cycle. In this case, the period is the time between two maxima. Hence, we proceed to determine each variable:

Amplitude \(\left(y_{\max }=14 \mathrm{ft}, y_{\min }=6 \mathrm{ft}\right)\)

\(\begin{array}{l}A=\frac{14 f t-6 f t}{2} \\A=4 f t\end{array}\)

The amplitude of the function is 4 feet.

Period

The period of the function is 20 seconds.

b) The function that represents the situation is based on this model:

\(y(t)=y_{o}+A \cdot \sin \frac{2 \pi \cdot t}{T}\)  ........(1)

Where:

\(y_{o}\)- Average height of the bottle, in feet.

\(t\) - Time, in seconds.

\(y(t)\) - Current height, in feet.

If we know that \(A=4 \mathrm{ft}, y_{o}=10 \mathrm{ft} \text { and } T=20 \mathrm{~s}\) then the function that represents the situation is:

\(y(t)=10+4 \cdot \sin \frac{\pi \cdot t}{10}\) ......(2)

The function that represents the situation is \(y(t)=10+4 \cdot \sin \frac{\pi \cdot t}{10}\).

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Precalculus is an example here, since x=−2 is a vertical type line, there is no  y-intercept as well as the slope is undefined.

The slope is undefined and all of the factors on the road have an x-coordinate of that (a few number). For example, if x = -2, then all factors alongside this line can have an x-coordinate of -2, making it a vertical line. y=−2 is a flat line crossing the factor at (0,−2) consequently the gradient is 0 and the the y intercept is -2.

A terrible slope approach that variables are negatively related; that is, whilst x increases, y decreases, and whilst x decreases, y increases. Graphically, a terrible slope approach that as the road on the road graph movements from left to right, the road falls. The x-coordinate -2 is represented throughout. This is NOT a function.

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The total surface area of the new box is given by the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7).

To calculate the new total surface area of the box after increasing the height by 3.5 centimeters, we need to consider the dimensions of the box and how each side is affected by the increase.

Let's assume the original box has dimensions:

Length (L)

Width (W)

Height (H)

The total surface area of the original box is given by:

SA_original = 2(LW + LH + WH)

After increasing the height by 3.5 centimeters, the new height becomes H + 3.5. The other dimensions, length and width, remain the same.

The new total surface area of the box can be calculated as follows:

SA_new = 2(LW + (L(H + 3.5)) + (W(H + 3.5)))

Simplifying the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7)

Therefore, the total surface area of the new box is given by the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7)

To find the closest value to the total surface area of the new box, you would need to know the specific values of L, W, and H for the original box. With those values, you can substitute them into the equation to calculate the exact surface area.

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Answer:

27x7=189.

189x5= ***945cm***

Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

opposite angles of a llgrm are equal.

ABCD is a llgrm.

let angle A = 63 degree

so opposite angle of A is C is also 63.

let angle B=x degree =angle D

sum of all angles of a llgrm is 360 degree

angle A + angle B + angle C + angle D=360

63+x+63+x=360

126+2x=360

2x=360-126

x= 134/2

x=67

so the other angles are

A=63 B =67 C = 63 D = 67

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bijaymourya8114

Answer:

really hot❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

Answer:

YES yes YES!!!

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Step 1: combine like terms

Step 2: add x on both sides/move x to the other side

Step 3: combine x/combine variables

Step 4: subtract 13/move 13 to the other side of the equation

Step 5: combine like terms

Step 6: simplify/divide both sides by 2