hello! Could Someone help me I am stuck ? Will name brainliest if correct answer :D

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

21x

Step-by-step explanation:

i think the expression should be x ×21 =21x

Answer:

m+10

Step-by-step explanation:

We know that yesterday, eric had m baseball cards. Thus, we can denote that the total number of baseball cards he had yesterday is m.

We know that he got 10 more today. Since he is receiving more, he is adding to his collection. Since he is getting more, we have to add 10 to how many baseball cards he used to have. He used to have m baseball cards, so today he has m+10 baseball cards.

This is the answer as we cannot combine 10 and m. Since m is a variable with no set value as of now, and 10 is a constant number that has no variable, they are not like terms and cannot be added. So the answer is m+10 baseball cards.

I hope this helped.

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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Answer:

10(6)

Step-by-step explanation:

Hope it's right.....

Answer:

Will can buy 8 pounds of granola with $10.

Step-by-step explanation:

If it is $3.75 for 3 pounds of granola then it is $1.25 for 1 pound of granola.

1.25 * x = 10

this equation will allow us to find a number that will add up to 10.

Another way to write this equation is:

10/1.25 = x

10/1.25 = 8

Now check your work:

1.25 * x = 10

1.25 * 8 = 10

10 = 10

Final Answer:

Will can buy 8 pounds of granola with $10.

Answer:

i think its 3

Step-by-step explanation:

Follow the formula and do the steps

Answer:

slope m=--3/-2=-3/2 is required slope

Answer:

m = -3, b = -2

Step-by-step explanation:

The equation is written in the form of slope-intercept, where m = slope and b = y-intercept.

The slope is the number before x. For the equation y = -3x - 2, it's -3.

The y-intercept is the constant. For the equation y = -3x - 2, it's -2.

Hence, m = -3, and b = -2.

\(\rule{350}{4}\)

\(\frak{-Dream-}\)

Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs is 0.0596.

\(\sigmaT = \sigma / \sqrtn = 1.25 / \sqrt15 = 0.3227\)

\(= P[(9 - 10) / 0.3227 < (T - \muT ) / \sigmaT < (9.5 - 10) / 0.3227)]\)

= P(-3.10 < Z < -1.55)

= P(Z < -1.55) - P(Z < -3.10)  

= 0.0606 - 0.001

=  0.0596

Probability that a random sample of 15 bags will have a mean between 9 and 9.5 kgs = 0.0596

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The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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Answer:

-13 11/20 = -271/20

Step-by-step explanation:

-4 3/4 - 8 4/5 =

= -4 15/20 - 8 16/20

= -12 31/20

= -13 11/20 = -271/20

Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

Answer:

5/2.5

Step-by-step explanation:

Answer: -3/4 < -1/2 < 1/2 < 3/4

Step-by-step explanation:

Answer:

\(y - 9 = 3(x - 5)\)

Explanation:

y=3x+5

If you want the equation parallel, then the slope will be: 3

Point Slope Form: \(y - y_{1} = m( x - x_{1})\)

Since we have everything we need for this equation, we just need to fill in the blanks:  \(y - 9 = 3(x - 5)\)

Answer: The length of the hypotenuse is  25

Step-by-step explanation:

Hi, to answer this question we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (the longest side) and a and b are the other legs of the triangle (vertical and horizontal leg)

Replacing with the values given:  

c^2 = 7^2 + 24^2  

c^2 = 49+576

c^2 = 625

c = √625

c = 25  

Feel free to ask for more if needed or if you did not understand something.  

Answer: -3/2

Step-by-step explanation:

rise / run . the line is decreasing vertically by 3 and increasing horizontally by 2.

Answer:

x=3 and y=4

Step-by-step explanation:

Answer:

all real numbers

x = 0

y = 1

Step-by-step explanation:

-2x + y = 1

-2x + (2x + 1) = 1

-2x + 2x + 1 = 1

x + 1 = 1

x = 0

-----------------------------------

y = 2x + 1

y = 2(0) + 1

y = 0 + 1

y = 1

Answer:

2.4/3

8 Feet of yarn

This is because we're asking of one third of the original amount so we divide it by three.

Answer:

Step-by-step explanation:

Yes these pairs are a function because no two numbers are the same in any of the (x,y) pairs

The statement that f has a simple zero at z=0 and vanishes nowhere else in |z|≤1 implies that the function f is non-vanishing and has a derivative that does not vanish at z=0.

From this, we can use the Implicit Function Theorem which states that if f is holomorphic in a neighborhood of a point (a,b) and f(a,b)=0 and ∂f/∂y(a,b)≠0, then there exists an open neighborhood U of a and a unique holomorphic function g:U→R such that g(a)=b and (x,g(x)) is a solution of the equation f(x,y)=0 for all x in U.

In this case, since f(z) has a simple zero at z=0 and f'(0)≠0, by the Implicit Function Theorem, there exists an open neighborhood U of 0 and a unique holomorphic function h:U→C such that h(0)=0 and f(h(ϵ))=0 for all ϵ in U. Hence, fϵ(z) has a unique zero in |z|≤1.

Also, since f and g are holomorphic in a region containing the disc |z|≤1 and ϵ is continuous, it follows that fϵ is holomorphic in the same region. Thus, by the holomorphicity of fϵ and h, the mapping ϵ↦zϵ is continuous.

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Answer:

a = (d - c) / b

Step-by-step explanation:

ab + c = d

ab = d - c ( divide both sides by b to get the formula for a)

a = (d - c) / b

Answer:

T=2

Step-by-step explanation:

5x2=10

10+2=12

Could I please have BRAINLIEST.

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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Answer:

16.75

Step-by-step explanation:

Answer: I think its 32 meals

Step-by-step explanation:

Just divide 24 by 3/4

Answer:

24/0.75=32

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The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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Answer:

Step-by-step explanation:

Ten more than x x + 10

A number added to 5 5 + x

A number increased by 13 x + 13

5 less than 10 10 - 5

A number decreased by 7 x - 7

Difference between x and 3 x - 3

Difference between 3 and x 3 - x

Twice a number 2x

Ten percent of x 0.10x

Ten times x 10x

Quotient of x and 3 x/3

Quotient of 3 and x 3/x

Five is three more than a

number

5 = x + 3

The product of 2 times a

number is 10

2x = 10

One half a number is 10 x/2 = 10

Five times the sum of x and 2 5(x + 2)

Seven is greater than x 7 > x

Five times the difference of a

number and 4

5(x - 4)

Ten subtracted from 10 times a

number is

that number plus 5

10x - 10 = x

+ 5

The sum of 5x and 10 is equal

to the product of x and 15

5x + 10 =

15x

The sum of two consecutive

integers

(x) + (x + 1)

The sum of two consecutive

even integers

(x) + (x + 2)

The sum of two consecutive odd

integers

(x) + (x + 2)

Answer:

x=64

Step-by-step explanation:

5+(1/8)x=13

Subtract 5 to both sides to get (1/8)x=8

Multiply by the reciprocal of 1/8 (8) on both sides. The 1/8 and 8 cancel and the answer should be x=64

Using the inverse square law for light, the luminosity of Alpha Centauri A is 4.3 × 10^26 Watts.

The inverse square law for light states that the intensity of light (or brightness) decreases as the square of the distance from the source increases. This means that the apparent brightness of a star is related to its luminosity (total power output) and distance from Earth by the following formula:

apparent brightness = luminosity / (4π × distance^2)

We can rearrange this formula to solve for luminosity:

luminosity = apparent brightness × 4π × distance^2

Using the values given in the problem, we can substitute:

luminosity = (2.7 × 10^-8 Watts/m^2) × 4π × (4.4 light-years × 9.46 × 10^15 m/light-year)^2

Note that we need to convert the distance from light-years to meters by multiplying by the conversion factor 9.46 × 10^15 m/light-year.

Simplifying this expression, we get:

luminosity = 4.3 × 10^26 Watts

Therefore, the luminosity of Alpha Centauri A is approximately 4.3 × 10^26 Watts.

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The elements of Z3[x]/(x^2 - x) are of the form ax + b that is multiplication table, where a and b are elements of Z3.

The multiplication table is:

  | 0   1   x   1+x   2   2+x

-------------------------------

0 | 0   0   0    0   0   0

1 | 0   1   x   1+x  2  2+x

x | 0   x  2x  2+x   x  1+2x

1+x| 0  1+x 2+x   2  2+x  x

2 | 0   2   x   2+x  1  1+x

2+x| 0  2+x 1+2x  x  1+x 2

Note that in this table, we use the fact that x^2 - x = 0, which implies that x^2 = x.

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