Someone please help me

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

I think it might be A

Step-by-step explanation:

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Step-by-step explanation:

\(x + 3y = 1 \\ - 3x - 3y = - 15 \\ x = 1 - 3y \\ - 3(1 - 3y) - 3y = - 15 \\ - 3 + 9y - 3y = - 15 \\ - 3 + 6y = - 15 \\ 6y = - 15 + 3 \\ 6y = - 12 \\ y = - 2\)

\(y = - 2 \\x = 1 - 3y \\ x = 1 - 3( - 2) \\ x = 1 + 6 \\ x = 7\)

Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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Answer: 36=2547^3

Step-by-step explanation: calulat0r your welcome

Answer:

the "componential analysis" of the skill. This analysis breaks down the complete skill into its various components and determines the proportion of time required by each component during the performance of the skill. This can help in identifying the strengths and weaknesses of an individual's performance and improving their overall skill proficiency.

Step-by-step explanation:

Answer:

Step-by-step explanation:

√81 = √(9 * 9) = 9

√64 = √(8 * 8) = 8

√36 = √(6 * 6) = 6

In statistical hypothesis testing, the null hypothesis is the status-quo hypothesis, while the alternative hypothesis is the research hypothesis.

The Null Hypothesis is a statement that there is no significant difference between two or more populations, or no significant effect of an intervention or treatment.

This represents the current state of knowledge or understanding and assumes that any observed differences or effects are due to chance.

The Alternative Hypothesis is a statement that there is a significant difference between two or more populations, or a significant effect of an intervention or treatment. 0

This  represents the researcher's hypothesis, which they aim to test with the data.

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The given question is incomplete , the complete question is

Which hypothesis, the null or the alternative, is the status-quo hypothesis? Which is the Research hypothesis?

Answer:

630

Step-by-step explanation:

Given the system of equations:

we can solve it using elimination by directly adding both equations to get the following:

now that we have that x=3, we can find y using this value on any of the two equations:

therefore, the solution of the system is (3,0)

Answer:

80%

Step-by-step explanation:

The basic idea of this problem is to convert \(\frac{44}{55}\) into a percentage.  \(\frac{44}{55}\)  can be simplified to \(\frac{4}{5}\) which is also 80%.

Answer:

Step-by-step explanation:

44 out of 55

divide :44/55=0.8

to convert it to decimal  you multiply by 100 and put percentage next to it

0.8*100=80

%80

Answer:5.83

Step-by-step explanation:

Answer:

x = 3

x + 3 = 6

√45

Step-by-step explanation:

the general theorem is

a^2 + b^2 = c^2

Givens

a = x

b = x + 3

c = √45

Solution

x^2 + (x + 3)^2 = (√45)^2          Substitute

x^2 + x^2 + 6x + 9 = 45             Expand the brackets. Square √45  

2x^2 + 6x + 9 = 45                    Subtract 45 from both sides

2x^2 + 6x - 36 = 0                     Divide by 2

x^2 + 3x - 18 = 0                        Factor

(x + 6)(x - 3) = 0                         x+ 6 has no meaning in the real world.

x - 3 = 0

x = 3                                          

Answer

a) 3

b) 6

c) √45

Answer:

root of 45

Step-by-step explanation:

When chemist mixes Chemical A and Chemical B to make a solution

Part A

When the quantity of chemical B = 48 ml, then the quantity of chemical A = 4 ml

Part B

When the quantity of chemical A = 9 ml, then the quantity of chemical B = 108 ml

A chemist mixes Chemical A and Chemical B to make a solution

She uses the same ratio of chemicals for each batch

The solution A and B are in linear relationship

y = kx

Where y is the quantity of chemical A

x is the quantity of chemical B

k is the constant

Substitute the values in the table and find k

36 = k × 3

k = 36 /3

k = 12

Part A

When chemical B = 48 ml

48 = 12 × x

x = 48 / 12

x = 4 ml

Part B

When chemical A = 9 ml

y = 12 × 9

y = 108 ml

Therefore, when Chemical B = 48 ml, chemical B is 4ml . When chemical A = 9 ml, Chemical B = 108 ml

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Answer:

\(y=-\frac{2}{3}x+1\)

Step-by-step explanation:

Parallel means same slope.

\(y=-\frac{2}{3}x+b\)

\(5=-\frac{2}{3} (-6)+b\)

5 = 4 + b

b = 1

\(y=-\frac{2}{3}x+1\)

Answer:

Point A' (-1, -2) Point B' (-5,-4) Point C' (-3, -5)

Step-by-step explanation:

There are 4 different variations in rotations: 90; 180; 270; 360
They are diversified by clockwise and counterclockwise rotations.

When doing rotations it depends on what they ask:
90 degrees requires moving to one next quadrant
180 degrees requires moving to two more quadrants
270 three
360 etc

This rotation is requiring a 90-degree counterclockwise rotation.

Your original shape is a triangle with 3 points.
These points are  Point A (-2,-1); Point B (-4,-5); Point C (-5,-3).

You need to dilate them.
The rule requires that the x and y values shall be switched where the y value shall be negative.

Point A' (-1, -2) Point B' (-5,-4) Point C' (-3, -5)




 

The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.

The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.

Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.

In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

it is fair to say that the ucr is: group of answer choices

A. A mutually exclusive measure

B. Not a truly reliable measure

C. An exhaustive measure

D. All of the above

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Answer:

x = 39

Step-by-step explanation:

In a parallelogram the opposite angles are congruent , then

3x - 15 = 2x + 24 ( subtract 2x from both sides )

x - 15 = 24 ( add 15 to both sides )

x = 39

Answer:

16 and 5

Step-by-step explanation:

Hope that helps! :)

The time it would take Michael Scott to ship all the boxes is 4 hours.

In order to determine the hours it would take to ship all the boxes, divide 48 boxes by the number of boxes shipped per hour.

Division is the mathematical process that is used to group a number into equal parts using another number. The result of the division process is known as quotient. The sign that is used to represent division is ÷. Other operations that are used in mathematics include addition, multiplication and subtraction.

Time it would take to ship all the boxes of paper = total number of of boxes / boxes shipped per hour

48 / 12 = 4 boxes per hour

Here is the complete question:

Michael Scott has 48 boxes of paper and 12 boxes are shipped out of his warehouse every hour. How many hours would it take to ship all the boxes?

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The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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Answer:

4/20

Step-by-step explanation:

The average length by which finger nails will grow in 12 months will be 60mm, considering that they grow by an average of 5mm every month.

As per the question statement, there is no information provided about the average monthly growth of fingernails, and we required to calculate the average length by which finger nails will grow in 12 months.
To solve this question, we assumed that, the fingernails grow by an average of 5mm every month.

Now, using the unitary method, we can form a series of Mathematical statements to solve this question, which goes as follows:

If the average monthly growth of fingernails is 5mm,

It means that, fingernails grow in 1 month, by an average of 5mm.

Therefore, they will grow in 12 months, by an average of (5 * 12) = 60mm.

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

Answer:

the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.

Step-by-step explanation:

To evaluate the Riemann Sum for the function $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points, we first need to determine the width of each subinterval. Since we have four subintervals to cover the interval $[0, 2]$, each subinterval has a width of $\Delta x = \frac{2-0}{4} = \frac{1}{2}$.

Next, we need to choose a sample point from each subinterval to evaluate the function. Since we are using right-hand endpoints as the sample points, we choose the endpoint of each subinterval as the sample point. The four subintervals are:

$[0, \frac{1}{2}]$, with sample point $x_1 = \frac{1}{2}$

$[\frac{1}{2}, 1]$, with sample point $x_2 = 1$

$[1, \frac{3}{2}]$, with sample point $x_3 = \frac{3}{2}$

$[\frac{3}{2}, 2]$, with sample point $x_4 = 2$

The Riemann Sum is then given by:

∑i=14f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(12)2⋅12+2(1)2⋅12+2(32)2⋅12+2(2)2⋅12=12+2+92+4=152i=1∑4​f(xi​)Δx​=f(x1​)Δx+f(x2​)Δx+f(x3​)Δx+f(x4​)Δx=2(21​)2⋅21​+2(1)2⋅21​+2(23​)2⋅21​+2(2)2⋅21​=21​+2+29​+4=215​​

Therefore, the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.

The Riemann Sum is 15/2 or 7.5.

To evaluate the Riemann Sum for the function f(x) = 2x^2 on the interval [0, 2] using 4 equal subintervals and right-hand endpoints, follow these steps:

1. Determine the width of each subinterval:
  Δx = (b - a) / n = (2 - 0) / 4 = 0.5

2. Identify the right-hand endpoints of each subinterval:
  x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2

3. Evaluate the function at each right-hand endpoint:
  f(x1) = 2(0.5)^2 = 0.5
  f(x2) = 2(1)^2 = 2
  f(x3) = 2(1.5)^2 = 4.5
  f(x4) = 2(2)^2 = 8

4. Calculate the Riemann Sum using these values:
  Riemann Sum = Δx * (f(x1) + f(x2) + f(x3) + f(x4))
  Riemann Sum = 0.5 * (0.5 + 2 + 4.5 + 8)
  Riemann Sum = 0.5 * (15)
  Riemann Sum = 7.5

The Riemann Sum for the given function using 4 equal subintervals and right-hand endpoints is 7.5, which is not among the provided options. However, the closest answer choice would be 15/2 or 7.5.

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