find the general solution of the differential equation y⁽⁴⁾ + 18y'' + 81y = 0
y(t) =

The general solution to the differential equation is: y = -(3/2)x + C, where C is the constant of integration.

To solve the differential equation 6x dx + 4x dy = 0 using separation of variables, we need to rearrange the equation so that all the x terms are on one side and all the y terms are on the other side.

Let's start by dividing both sides of the equation by 4x:

(6x dx + 4x dy) / 4x = 0

(6x / 4x) dx + (4x / 4x) dy = 0

(3/2) dx + dy = 0

Now we can separate the variables by moving the dy term to the other side:

dy = -(3/2) dx

Integrating both sides with respect to their respective variables, we have:

∫ dy = ∫ -(3/2) dx

The integral of dy with respect to y is simply y, and the integral of -(3/2) dx with respect to x is -(3/2)x:

y = -(3/2)x + C

where C is the constant of integration. Thus, the general solution to the differential equation is:

y = -(3/2)x + C

This is the final solution using separation of variables.

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Answer:

It increases by 2.5

Step-by-step explanation:

yeah

The volume, in cubic inches, of the cylinder will be   [tex]\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches.

Cylinder is a [tex]3D[/tex] solid shape which holds two parallel bases joined by a curved surface, at a fixed distance. These bases are circular in shape and the center of the two bases are joined by a line segment.

Volume is define as capacity of cylinder.

Volume of cylinder [tex]=\pi r^{2} h[/tex]

We have,

Radius [tex]=3[/tex] inches

Height [tex]=5[/tex] inches,

Then,

Volume of cylinder [tex]=\pi r^{2} h[/tex]

                              [tex]=\frac{22}{7} *(3)^{2} *5[/tex]

                               [tex]=\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches

Hence, we can say that The volume, in cubic inches, of the cylinder will be     [tex]\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches

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Answer:

Only the mean increased.

Step-by-step explanation:

The mean is the total divided by the number of scores, and since adding 21 will increase the total score significantly, the mean increases.

The median is still 7.

The translation for this problem is classified as follows:

The four translation rules are defined as follows:

For this problem, we have a translation 2 units left, which is an horizontal translation, and then a translation 4 units down, which is a vertical translation.

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The number of iterations required is 6.

Given a starting guess of [90, yo] = [1, 2], Newton's method for optimization takes 6 iterations to find a minimum of the function f(x, y) = 12a^2 – 7x + 7 +10y – xy to a tolerance of 10^-8.Step-by-step explanation:

Newton's method is an iterative process to approximate the roots of an equation or optimization of a function.

To solve this problem, we need to apply Newton's method to the function f(x, y) = 12a^2 – 7x + 7 +10y – xy as follows:

Given a starting guess of [90, yo] = [1, 2], we can find the solution using the following formula:xn+1 = xn - f'(xn)/f''(xn)where xn is the current guess, f'(xn) is the derivative of f at xn, and f''(xn) is the second derivative of f at xn.

Here, f(x, y) = 12a^2 – 7x + 7 +10y – xy, so we have (x, y) = [-7 - y, 10 - x]f''(x, y) = [0, -1; -1, 0]

We need to apply this formula until the difference between xn and xn+1 is less than or equal to the tolerance of 10^-8.

This means that we need to keep iterating until |xn+1 - xn| <= 10^-8.

Given the assumption of quadratic convergence, we can also calculate the number of iterations required as follows:|xn+1 - xn| ≈ |xn - xn-1|^2/|xn+1 - 2xn + xn-1|

Using this formula, we can calculate the number of iterations required to reach the tolerance of 10^-8.

Here are the results of the first six iterations:x1 = [1, 2]x2 = [4.125, 2.9]x3 = [4.223382352941176, 2.979411764705882]x4 = [4.223639551849474, 2.979707510729614]x5 = [4.223639551862697, 2.979707510767132]x6 = [4.223639551862697, 2.979707510767132]

We can see that the difference between x5 and x6 is less than 10^-8, so we have found a solution to the desired tolerance.

Therefore, the number of iterations required is 6.

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There is no polynomial attached ; considering the hypothetival

Answer:

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Step-by-step explanation:

Considering an hypothetical situation ;

For any polynomial such as 2x³ + 3x + 1

The polynomial is represented as : ax³ + bx + c

Where a = leading Coefficient ;

x³ = leading term

c = constant term

Therefore ;

The leading term in this hypothetical question is :

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Answer:

The height of the kite from the ground is 13.617 feet  

Step-by-step explanation:

Given as :

The measure of the string = 30 feet

The angle of elevation from the boy to his kite = 27°

Let the height of the kite from ground = H feet

So, From Triangle

Sin angle =

Or, Sin 27° =  

or, H = 30 ×  Sin 27°

I.e H = 30 × 0.4539

∴ H = 13.617 feet

Hence the height of the kite from the ground is 13.617 feet   Answer

Answer:

37.999749573966

Step-by-step explanation:

Brainliest?

Divide total miles by number of days:

151.2 / 24 = 6.3 miles per day

Answer: $50 withdrawl $50 withdrawl and $65 deposite

Step-by-step : $50 withdrawl $50 withdrawl and $65 deposite

Answer:

50/100, simplified to 1/2

Step-by-step explanation:

50% means half of 1.

1/2=.5 which is half of 1.

1=100%

.5=50%

1/2=50%

Answer:

[tex] \displaystyle \frac{1}{2} [/tex]

Step-by-step explanation:

we are given a parcentage

we want to convert it into fraction

remember that,

[tex] \displaystyle \% = \frac{1}{100} [/tex]

therefore

substitute:

[tex] \displaystyle 50 \times \frac{1}{100} [/tex]

reduce fraction:

[tex] \displaystyle \cancel{50} \times \frac{1}{ \cancel{100} \: ^{2} }[/tex]

[tex] \displaystyle 1 \times \frac{1}{2} [/tex]

simplify multiplication:

[tex] \displaystyle \frac{1}{2} [/tex]

hence,

[tex] \displaystyle 50\% = \frac{1}{2} [/tex]

The lifetimes of a certain brand of photographic light are normally distributed with a mean of 210 hours and a standard deviation of 50 hours. We need to find the probability that a particular light will last more than 250 hours.

Given mean = μ = 210 hours. Standard deviation = σ = 50 hours. Let X be the lifetime of a photographic light. X ~ N (μ, σ) = N (210, 50). The probability that a particular light will last more than 250 hours can be calculated as follows: P(X > 250) = 1 - P(X < 250)Let Z be the standard normal variable.

Then, (250 - μ) / σ = (250 - 210) / 50 = 0.8P(X < 250) = P(Z < 0.8). Using the z-table, the probability that Z is less than 0.8 is 0.7881. Therefore, P(X > 250) = 1 - P(X < 250) = 1 - 0.7881 = 0.2119. Hence, the probability that a particular light will last more than 250 hours is 0.2119.

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Answer:

A would be the answer I would choose

I think it’s the third one. Hope that helps!

Answer:

the answers are B or C x>4/19

Answer:

d) population is divided into similar groups and a SRS is chosen from each group.

Step-by-step explanation:

Stratified random sampling

can be regarded as "proportional random sampling" and is method of sampling which entails division of a population to more simpler sub- groups, this sub- groups are regarded as " strata". This strata are been formed on the basis of shared attributes of the members. This attribute could be educational attainment as well as income. It should be noted that stratified random sample is population is divided into similar groups and a SRS is chosen from each group.

Answer:

what?

Step-by-step explanation:

The answer is b=18. To solve, multiply 6 by 3 to get 18. This is called doing the inverse operation. Since the equation is a division equation, we would have to multiply in order to find the missing variable.

The probability that a rider must wait between 1 minute and 1.4 minutes at the elevator can be determined by calculating the proportion of the uniform distribution that falls within this time interval.

The given information states that the waiting time at the elevator follows a uniform distribution between 30 and 200 seconds. To find the probability of waiting between 1 minute and 1.4 minutes, we need to convert these time values to seconds.

1 minute is equal to 60 seconds, and 1.4 minutes is equal to 84 seconds. Therefore, we are interested in finding the probability that the waiting time falls between 60 seconds and 84 seconds.

Since the waiting time follows a uniform distribution, the probability of waiting within a specific interval is equal to the length of that interval divided by the total length of the distribution.

The total length of the distribution is 200 seconds - 30 seconds = 170 seconds.

The length of the interval between 60 seconds and 84 seconds is 84 seconds - 60 seconds = 24 seconds.

Thus, the probability that a rider must wait between 1 minute and 1.4 minutes is 24 seconds / 170 seconds, which is approximately 0.1412 or 14.12%.

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13. k=3/4       14. a=23

15. p= 5 1/2    16. x=13

17. m=56         18. n=1 1/2

Answer:

13)

14)

15)

16)

17)

18)

Answer:

3/20

Step-by-step explanation:

1/1-1/4-3/5= (money spent)

1×4×5/(1×4×5)-1×1×5/(1×4×5)-3×1×4/(1×4×5)

20/20-5/20-12/20

(20-5-12)/20=3/20

Answer:

$y - $0.85

Step-by-step explanation:

y represents how much money he had.

[tex]\frac{3}{5}+\frac{1}{4} =\frac{17}{20}[/tex]

$y - $0.85

The 90% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is -21.3% to -16.1%, which represents the range of values within which the true difference is likely to fall.

To construct the confidence interval, we first calculate the sample proportions for Democrats and Republicans: p₁ = 644/700 ≈ 0.92 for Democrats, and p₂ = 323/850 ≈ 0.38 for Republicans.

Next, we calculate the standard error of the difference using the formula: SE = √((p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂)), where n₁ and n₂ are the sample sizes.

Using the given sample sizes, the standard error is approximately 0.019.

To determine the margin of error, we multiply the standard error by the z-score corresponding to a 90% confidence level, which is approximately 1.645.

Finally, we calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error from the difference in sample proportions: 0.92 - 0.38 ± (1.645 * 0.019).

The resulting confidence interval is approximately -21.3% to -16.1%, which represents the range within which we can estimate the overall difference in the percentages of Democrats and Republicans prioritizing environmental protection.

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The height of the radio tower to the nearest tenth of a metre is 6.9 m.

Let the height of the radio tower be h metresFrom Sun's point of view, the top of the radio tower is right-angled to the horizontal line through his eye. This implies that the length of the radio tower is opposite the angle of elevation.

Thus, the distance of Sun from the radio tower is equal to the length of the adjacent side of the right-angled triangle formed.

Thus, from the tangent ratio:tan 31° = h / 14.5 + 1.6 (since Sun's eye level is 1.6m above the ground)h = (14.5 + 1.6) tan 31° = 6.9 m (to one decimal place)From Natalia's point of view,

the radio tower makes an acute angle with the line of sight from her eye to the top of the radio tower. This implies that the length of the radio tower is adjacent to the angle of elevation.

Thus, the distance of Natalia from the radio tower is equal to the length of the hypotenuse of the right-angled triangle formed.

Thus, from the sine ratio:sin 89° = h / 14.5 - 1.6 (since Natalia's eye level is 1.6m above the ground)

h = (14.5 - 1.6) sin 89° = 12.9 m (to one decimal place)

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it is True ..............................................

Answer:

True

Step-by-step explanation:

2-72+3+4x=ax+b

73 + 4x = ax + b

Since there are 3 variables in this equation you need 3 equations. Since there is only 1 you cannot continue solving this equation after you simplified.

Hope this helps!

Answer: 45

Step-by-step explanation:

Answer:

46.08

Step-by-step explanation:

you have to make your percentage a decimal, which 60% will be .60 and 20% will be .20. you then multiply your initial number which is 36 by .60 and add that on because youre adding 60%. After that you will multiply that given number by .20 and you subtract what that product is from your last product you received (36x.60) which if im not mistaken will give you $46.08.

Answer:

C

Step-by-step explanation:

I took the test

Answer: May

Step-by-step explanation: 9 is greater than 8 don't worry about the signs

Answer:

$20

Step-by-step explanation: