solve the following differential equation using method of undetermined coefficients
y" +49 y = 2x² + 5cos 7x

The value of x and y in the algebra (3x - y, 2) = (2, x + y) ​ are 1 and 1 respectively.

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Given the algebra:

(3x - y, 2) = (2, x + y) ​

Therefore, equation:

3x - y = 2        (1)

Also:

x + y = 2        (2)

From both equations, solving simultaneously:

x = 1, y = 1

The value of x and y are 1 and 1 respectively.

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Answer:

See attachment

PS:

Can I have Brainliest?

The correct statement is  BC equals to AC times CE all over CD.

We have, If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. this is known as the triangle proportionality theorem.

Given, DE and AB are parallel

So,   \(\frac{BC}{CE} =\frac{AC}{CD}\)

\(BC = \frac{AC\times CE}{CD}\)

Therefore in statement form we say that BC equals to AC times CE all over CD.

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Answer:

-128

Step-by-step explanation:

hope it helps srry if its wroung:>

Solution a needed 70 ounces and solution b needed 50 ounces

What does "1 ounce" mean?

One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.

One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.

So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:

50% * x + 20% * (100-x) = 41% * 100

Dropping the ‘%’ we get

50x + 2000 - 20x = 4100

30x = 2100

x = 2100/30 = 70

Hence 70 ounces will be needed

Solution a = 70 ounces

Solution b = 50 ounces

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Answer:

7+(5 3/10+ 2 2/10) = 12 5/10

The mathematical expression will be;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 145/10

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Now,

Since, The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Hence, We can formulate;

The mathematical expression as;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 7 + (53/10 + 22/10)

⇒ 7 + (75/10)

⇒ (70 + 75) / 10

⇒ 145/10

Thus, The value of the expression is,

⇒ 145/10

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\(\log^8 x -4 \log^8 x\\\\=-3 \log^8 x\)

Answer:

$6

Step-by-step explanation:

System of equations

x+y = 18

0.03x+0.06y = 5% of 18 = 0.9

(0.03x+0.06y=0.9)*100 = 3x+6y=90

(3x+6y=90)÷3 = x+2y=30

Substract (1)-(2)

x+2y=30 ... (1)

x+y=18 ... (2)

y=12

x+12=18

x=6

Thanks.

Answer:

Rise is vertical, run is horizontal

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

First thing you do is set up your equation:

y-17= -37

+17   +17        Next you add 17 to both sides

-------------        Follow your integer rules

y= -20

We can check this by putting it back into the solution

-20-17= -37  Integer Rules

                     You use KCC aka Keep Change Change

= -20+ -17= -37

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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To find the p-value for this test, we need to calculate the probability of observing at least 154 successful observations (assuming H0 is true) using the cumulative binomial distribution.

Given:

H0: p = 0.8

Ha: p > 0.8

Sample size (n) = 177

Number of successful observations = 154

We will use the binomial distribution to calculate the probability of observing at most 154 successful observations and subtract it from 1 to get the probability of observing at least 154 successful observations.

Using a statistical software or calculator, the p-value is found to be 0.0002 (rounded to four decimal places).

Since the p-value (0.0002) is less than the significance level (α = 0.005), we reject the null hypothesis (H0).

Therefore, the final conclusion is that there is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.8.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

I'm not sure but I think the awnser is

4 C

8 R

5 D

and 7H

Using the data given in the question, given below is the frequency table for the movie genres liked by the students.

Movie genre      Number of students

  Action                             6

  Comedy                          4    

  Horror                             7

  Drama                             5

  Romance                        8    

A frequency table lists a set of values and how often each one appears. Frequency is the number of times a specific data value occurs in your dataset.

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Answer:

The triangles are lined up with their correct pairs already.

Step-by-step explanation:

The leg that is the base is always seen as the bottom, and the leg to the side of it that makes the right angle will always be the height. Though if the base is at the hypotenuse as it is seen in the last photo, the height will be from the point of which the two legs of the triangle meet down to the hypotenuse.

The reasonable estimate for limStartFraction 2 x squared minus x + 15 Over x cubed minus 5 x minus 12 EndFraction as x approaches 3 is \(\dfrac{1}{2}\)

Given the limit of a function expressed as:

\(\lim_{x \to 3}\frac{2x^2-x+15}{x^3-5x-12}\)

First, we need to substitute x = 3 into the function to have:

\(=\frac{2(3)^2-3+15}{3^3-5(3)-12}\\=\frac{18-3+15}{27-15-12}\\=\frac{0}{0} (indeterminate)\)

Apply l'hospital rule on the function:

\(=\lim_{x \to 3}\frac{\frac{d}{dx} (2x^2-x+15)}{\frac{d}{dx} (x^3-5x-12)}\\=\lim_{x \to 3}\frac{4x-1}{3x^2-5}\\\)

Subtitute x = 3 into the result

\(=\frac{4(3)-1}{3(3)^2-5}\\=\frac{12-1}{27-5}\\=\frac{11}{22}\\=\frac{1}{2}\)

Hence the reasonable estimate for limStartFraction 2 x squared minus x + 15 Over x cubed minus 5 x minus 12 EndFraction as x approaches 3 is \(\dfrac{1}{2}\)

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Answer:

1/2

Step-by-step explanation:

i am in your walls

Answer:

f(x) = x – 3

Step-by-step explanation:

The equation that is written in function notation, with x as the independent variable is D. f(x) = x – 3

To write the equation as an independent variable, we simply need to isolate y.

The next step would be to subtract x from both sides:

-y = 3 - x

To eliminate the -ve sign in y, we would divide both sides by -1

y= -3+x

If we rearrange, the answer would be:

f(x) = x – 3

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Using the percentage method, we know that the original price of the TV set was $400.

Percentages are just fractions with a denominator of 100.

To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the percentage is always out of 100.

Then we automatically know that:

100% - 15% = 85%

We know:
85% = $340

15% = ?

Now, calculate the reduced price as follows:
85/340 = 15/x

85x = 15(340)

85x = 5,100

x = 5100/85

x = $60

Original price of the TV set:

Sold cost + Reduced cost

$340 + $60

$400

Therefore, using the percentage method, we know that the original price of the TV set was $400.

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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True, zero divergence imply zero circulation

If a vector field has zero divergence throughout a region where the conditions of Green's theorem are satisfied, then it is indeed true that the circulation on the boundary of that region is zero.

Green's theorem establishes a relationship between the circulation (line integral) of the vector field along the boundary and the flux (double integral) of the divergence of the vector field over the region.

When the vector field has zero divergence, it means that the net flow of the vector field into or out of any closed surface within the region is zero. This implies that the flux is also zero.

Consequently, based on Green's theorem, the circulation along the boundary of the region must be zero as well.

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Answer:

7.62

Step-by-step explanation:

Using Phythagoras' theorem...

Hyp^2 = a^2 + b^2

that is:

8^2 = 11^2 + r^2

64 = 121 + r^2

64-121 = r^2

58 = r^2

therefore r = sqrt of 58

NB: Not sure but there you go.

Answer:

r ≈ 3.6

Step-by-step explanation:

∠ OAB is right ( angle between tangent and radius at point of contact )

then Δ OAB is a right triangleΔ

using Pythagoras' identity in the right triangle

with hypotenuse OB = r + 8 , then

OB² = OA² + AB² , that is

(r + 8)² = r² + 11²

r² + 16r + 64 = r² + 121 ( subtract r² from both sides )

16r + 64 = 121 ( subtract 64 from both sides )

16r = 57 ( divide both sides by 16 )

r = \(\frac{57}{16}\) ≈ 3.6 ( to the nearest tenth )

Answer:

y=4

Step-by-step explanation:

parallel lines have the same slope, y=6 has a slope of 0

so the function will be in the form of

y=0 × x +b

substitute x and y values with (3,4)

4= 0 ×3 +b

b=4

y=4

Note that

a) f'(x) = 0.0xe^(-0.06x) + 0.1e^(-0.06 x) thousands donations per hours.

b) the rate of change of donations is zero at approximately 51.24 hours after the major disaster

c) donation level in part (B) is 1.58.

(a) The rate of change of donations can be found by taking the derivative of the function f (x )  .....

f'(x  ) = (0.1 x)(-0.06)e^(-0.06 x) + e^(-0.06 x)(0.1)

Simplifying:

f'(x) = 0.01e^( -0.06x )(10  - x)

So the expression for the rate of change in donations is f' ( x) = 0.01e^( -0.06x)( 10 - x).

(b) To find when the rate of change of donations is zero, we need to solve the equation f'(x) = 0:

0.01e^(-0.06x)(10 - x) = 0

10 - x = 0

x = 10

So the rate of change of donations is zero 10 hours after the major disaster strikes.

(c) To find the donation level at the time found in part (b), we substitute x = 10 into the original function f(x):

f(10) = 0.1(10)e^(-0.06(10)) = 0.635

So the donation level at 10 hours after the major disaster strikes is 0.635 thousand donations.

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The formula for determining the z score is expressed as

z = (data value - mean)/standard deviation

a) data value = 110

mean = 87

standard deviation = 11

z = (110 - 87)/11

z = 2.09

b) data value = 110

mean = 80

standard deviation = 11

z = (80 - 87)/11

z = - 0.64

The point on the line segment with endpoints (-7,7) such that its corresponding vector has components <14,16> is (7,23).

To find the point that lies on the line segment between the points (-7,7) and (7,-7) such that the vector from (-7,7) to this point has components <14,16>, we can use the following formula:

Point = (1-t)(-7,7) + t(7,-7)

where t is a scalar between 0 and 1 that represents the position of the point along the line segment. Since we know that the vector from (-7,7) to the point has components <14,16>, we can set up the following system of equations:

(7 - (-7))*t + (-7) = 14

(-7 - 7)*t + 7 = 16

Simplifying these equations, we get:

14t = 21

-14t = 9

Solving for t, we find that t = -9/14. Substituting this value back into the formula for the point, we get:

Point = (1 - (-9/14))(-7,7) + (-9/14)(7,-7) = (-17/7, 13/7)

Therefore, the x-coordinate of the point is -17/7 and the y-coordinate of the point is 13/7.

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It is more convenient to integrate with respect to y.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

To sketch the region enclosed by the curves y = 3x² and y = 5x - 2x² and determine whether to integrate with respect to x or y, we can analyze the intersection points and the shape of the curves.

First, let's find the intersection points by setting the equations equal to each other:

3x² = 5x - 2x²

Combining like terms:

5x² - 5x = 0

Factoring out x:

x(5x - 5) = 0

Solving for x:

x = 0 or x = 1

So the curves intersect at x = 0 and x = 1.

Next, we can analyze the behavior of the curves to determine the orientation of the region.

For y = 3x², we have a parabola that opens upwards. This curve lies below the x-axis and is symmetric with respect to the y-axis.

For y = 5x - 2x², we have a downward-opening parabola. This curve lies above the x-axis and is symmetric with respect to the y-axis.

Based on this information, we can sketch the region enclosed by the curves.

The region enclosed by the curves is bounded by the curves themselves and the x-axis. It is the area between the curves from x = 0 to x = 1.

To determine whether to integrate with respect to x or y, we can observe that the region is vertically oriented, meaning it extends vertically between the curves.

Therefore, it is more convenient to integrate with respect to y.

To draw a typical approximating rectangle, we can choose a small interval along the y-axis and draw a rectangle that spans between the curves for that particular y-interval. This rectangle will represent an approximation of the region's area.

Hence, it is more convenient to integrate with respect to y.

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Answer:

its undefined

Step-by-step explanation:

The final transformed function is: g(x) = 8/(x+1) + 8.

In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range. In simpler terms, a functiοn is a set οf rules that takes an input value and prοduces a cοrrespοnding οutput value.

Starting with the functiοn f(x) = 2/x, the transfοrmatiοn can be brοken dοwn intο three steps:

Translate οne unit left and 2 units up:

1. Tο translate the functiοn οne unit left and twο units up, we need tο substitute x+1 fοr x and add 2 tο the functiοn:

f(x+1) + 2 = 2/(x+1) + 2

2. Vertical stretch by a factοr οf 4:

Tο stretch the functiοn vertically by a factοr οf 4, we need tο multiply the functiοn by 4:

4 * (2/(x+1) + 2) = 8/(x+1) + 8

Therefοre, the final transfοrmed functiοn is:

g(x) = 8/(x+1) + 8

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