Can someone please help me

Answer:

57 and 64

Step-by-step explanation:

x = smaller number

x + x + 7 = 121

2x = 114

x = 57

The solution is:

y(t) = (1/2)×cos(t) - (1/2)tsin(t) + (1/2)×∫[0,t] sin(τ)×cos(τ)dτ

What is the variation of parameters?

A typical approach for finding a specific differential equation solution involves replacing the constants in the answer to a related (homogeneous) equation with functions and figuring out these functions in such a way that the original differential equation is satisfied.

Here, we have

Given:  the differential equation d²y/dt² + y = cos(t) with initial conditions y(0) = 0 and y'(0) = 0 can be found using the method of Variation of Parameters.

Where the integral represents the convolution of the functions cos(t) and sin(t) with Green's function of the differential equation, which is sin(t).

The first two terms are the homogeneous solution of the differential equation, while the third term is the particular solution obtained using the method of Variation of Parameters.

To obtain this solution, we first find the homogeneous solution by assuming y(t) = Acos(t) + Bsin(t) and substituting it into the differential equation. We then solve for the constants A and B using the initial conditions.

Next, we use the method of Variation of Parameters to find the particular solution, which involves finding two functions u(t) and v(t), and using them to construct the particular solution.

Finally, we add the homogeneous and particular solutions to obtain the general solution to the differential equation.

Hence, y(t) = (1/2)×cos(t) - (1/2)tsin(t) + (1/2)×∫[0,t] sin(τ)×cos(τ)dτ

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When an English-language survey questionnaire is converted into a Korean version for usage in south Korea and then translated back into English to ensure accuracy.

Given statement;

When a survey questionnaire in English is translated into Korean for use in south Korea and then translated back into English to check its accuracy.

It can be described as back translation,

Back Translation:

Back translation, also known as reverse translation, is the process of literally translating text back into the source language from the target language. Translations from English to Swedish not affect would also include a reverse translation into English so that the meaning of the translated option could be clearly understood. Back translations have no effect on the translator's translation memory or other tools, such as glossaries.

It is described as a back translation.

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The outcome is random if we know the possible values it can have, but not which particular value it takes.

Randomness refers to the property of a process or system where the outcome is uncertain, unpredictable, and not predetermined. In a random process, we know the set of possible outcomes.

But we cannot determine which particular outcome will occur until it actually happens. For example, when flipping a fair coin, the possible outcomes are heads or tails.

But we do not know which one will come up until the coin is flipped. Randomness is a fundamental concept in probability theory and is used to model and analyze a wide range of phenomena.

Including games of chance, genetics, and quantum mechanics.

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The dimensions that will maximize the total area enclosed by the rectangular plot is; 12.5 m by 8.33 m

Let W represent the Width of the rectangular plot

Let L represent the Length with 3 pieces.

The total length will be 2W + 3L

The Area is L*W

Thus;

A = L*W

2W + 3L = 50

Solve for L

3L = 50 - 2W

L = (50 - 2W)/3

Put (50 - 2W)/3 for L in the Area equation to get;

A = ((50 - 2W)/3)*W

A = (50W - 2W²)/3

A = 50W/3 - 2W²/3

The maximum Area will occur at dA/dW = 0

dA/dW = 50/3 - 4W/3

At dA/dW = 0, we have;

50/3 - 4W/3 = 0

4W = 50

W = 50/4

W = 12.5 m

L = (50 - 2(12.5))/3

L = (50 - 25)/3

L = 25/3 = 8.33 m

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Answer:

x=4 y=1 or (4,1)

Step-by-step explanation:

Answer:

3,989.240

Step-by-step explanation:

Answer:

3,989.240

Step-by-step explanation:

hope dis helps :/

The y as a function of t if 8y″+28y=0, y(0)=3,y′(0)=4. then y(t) = (3√2 cos(2√2 t) + 2√2 sin(2√2 t))

To find the solution for the given second-order linear homogeneous differential equation, we can assume a solution of the form y(t) = e^(rt), where r is a constant to be determined. Plugging this into the equation, we get the characteristic equation:

8r^2 + 28 = 0

Simplifying the equation, we have:

r^2 = -28/8 = -7/2

Since the problem does not handle complex numbers, we express the solution in terms of sines and cosines instead of using e to a complex power. The complex roots of the equation are ±i√(7/2).

Using Euler's formula, we can write the complex roots in terms of sines and cosines:

r₁ = i√(7/2) = i√(7/2) = √(7/2) (cos(π/2) + i sin(π/2))

r₂ = -i√(7/2) = -√(7/2) (cos(π/2) + i sin(π/2))

The general solution of the differential equation is given by:

y(t) = c₁e^(√(7/2)t) cos(√(7/2)t) + c₂e^(√(7/2)t) sin(√(7/2)t)

To find the particular solution, we can substitute the initial conditions into the general solution:

y(0) = c₁ cos(0) + c₂ sin(0) = c₁ = 3

y'(0) = c₁(-√(7/2)) sin(0) + c₂(√(7/2)) cos(0) = c₂(√(7/2)) = 4

Solving the equations, we find c₁ = 3 and c₂ = 4/√(7/2) = 4√2/√7 = 4√2/√7 * (√7/√7) = 4√14/7.

Therefore, the solution to the differential equation is:

y(t) = 3 cos(√(7/2)t) + (4√14/7) sin(√(7/2)t)

Simplifying further:

y(t) = (3√2 cos(2√2 t) + 2√2 sin(2√2 t))

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Answer

Area of the real dining hall = 72 m²

Explanation

The area of any rectangular shape is given as

Area = L × W

where

L = Length of the rectangle

W = Width of the rectangle

For this question, we have been given the dimensions of the dining hall in the drawing and told that

5 cm in the drawing = 6 m in reality

So, if the real length of the dining is L

5 cm = 6 m

10 cm = L

We can write a mathematical relationship by cross multiplying

(5) (L) = (10) (6)

5L = 60

Divide both sides by 5

(5L/5) = (60/5)

L = 12 m

If the real width of the dining hall is W

5 cm = 6 m

5 cm = W

We can write a mathematical relationship by cross multiplying

(5) (W) = (5) (6)

5W = 30

Divide both sides by 5

(5W/5) = (30/5)

W = 6 m

So, for the real dining hall,

Length = 12 m

Width = 6 m

Area = Length × Width

Area = 12 × 6

Area = 72 m²

Hope this Helps!!!

Answer: around 63.3

Step-by-step explanation: you need to find how much they traveled first (380) & then divided that by the other number (6). then you get somewhere around 63.3 . :))

Answer:

63.3

Step-by-step explanation:

Answer:

yes it is true

Step-by-step explanation:

write the first five elements then write their cubes then write the cubes in the same form

for eg:

4³=16= 3×5+1= 3n+1

7³=49=3×16 +1= 3n + 1

and so on till the fifth element...

9514 1404 393

Answer:

  2

Step-by-step explanation:

y is the geometric mean of the segment lengths.

  y = √(4·1)

  y = 2

_____

You can also get there by considering the similarity of the triangles:

  short side / long side = y/4 = 1/y

  y^2 = 4 . . . . . . . multiply by 4y\

  y = √4 = 2 . . . . take the square root

Answer:

36 m

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

27 = b

45 = c

So let's solve

a² + 27² = 45²

a² + 729 = 2025

a² = 1296

√1296 = a

= 36

units = m

36 units

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

\(D\)

Step-by-step explanation:

\(2700*(1+x/100)=3200\)

\(1+x/100=3200/2700\)

\(1+x/100=32/27\)

\(x/100=32/27-1\)

\(x/100=5/27\)

\(27x=500\)

\(x=500/27\)

\(x=18.518518518518\)

To locate the discontinuities of the function y = ln(tan^2x), we need to find the values of x where the function is not continuous.

First, let's consider the domain of the natural logarithm, ln(x). It is defined only for positive values of x, so tan^2x must be greater than 0 for the function to be defined.

Next, let's consider the domain of tan(x). Tan(x) is undefined when its denominator, cos(x), is equal to 0. This occurs at x = (2n + 1)π/2, where n is an integer.

Since we have tan^2x, the square of tan(x) will always be non-negative. However, we need it to be positive (greater than 0) for ln(tan^2x) to be defined. Tan^2x will be equal to 0 when tan(x) is 0, which occurs at x = nπ, where n is an integer.

Thus, the discontinuities of the function y = ln(tan^2x) occur at two different sets of x values:

1. x = (2n + 1)π/2, where n is an integer, due to the undefined nature of tan(x).
2. x = nπ, where n is an integer, due to tan^2x being 0, which is not in the domain of ln(x).

There are infinitely many discontinuities because of the variable n.

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The y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y-intercept of line

Given a equation → y = 2.391x + 57.420 that models the taste rating of a cereal 'y' and 'x' represents the number of grams of sugar per serving.

The y-intercept of the equation represents the point at which the graph of the equation cuts the y - axis. Now, the coordinates of the y-intercept is of the form (0, y). Therefore, the x-coordinate will be 0. Now, the equation given is -

y = 2.391x + 57.420

Comparing it with the general equation of line -

y = 2.391x + 57.420

y =   mx     +    c

The y - intercept is c = 57.420

At x = 0, the equation becomes -

y = 2.391 x 0 + 57.420

y = 57.420

Now -

Number of grams of sugar per serving = 0

Taste rating of a cereal = y = 57.420

Therefore, the y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.

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The exponential regression equation for this set of data is y = \(14.129e^{(0.495x)\) and the number of bacteria present after 10 hours is approximately 24684.

The exponential regression equation for this set of data can use a calculator or spreadsheet software.

The equation will have the form y = abˣ a is the initial number of bacteria and b is the growth rate.
Using the given data can create a table of values for the equation:
x                y                   ln(y)
---------------------------------------
0              16                2.773
1               66               4.189
2             311                5.739
3            791                6.672
4          1553                7.349
5          2571               7.853

A regression tool can find that the equation is approximately y = \(14.129e^{(0.495x)\) rounded to three decimal places.

The initial amount of bacteria is approximately a = 14.129 and the growth rate is approximately b = 1.649.
The number of bacteria present after 10 hours can plug x = 10 into the equation:
y = \(14.129e^{(0.495\times 10)\)

= 24683.522
Rounding to the nearest whole number get that the number of bacteria present after 10 hours is approximately 24684.

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Answer:

-0.6 yards

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

  1st step

 To find the mean absolute deviation of the data, start by finding the mean of the data set.

  2nd step

 Find the sum of the data values, and divide the sum by the number of data values.

   3rd step

Find the absolute value of the difference between each data value and the mean: |data value – mean|.

   4th step

Find the sum of the absolute values of the differences.

   5th step

Divide the sum of the absolute values of the differences by the number of data values.

The rate of change of temperature at the point P(4,−1,4) in the direction towards the point (5,−4,5) is 0.

To find the rate of change of temperature at point P(4, -1, 4) in the direction towards the point (5, -4, 5), we need to calculate the gradient of the temperature function T(x, y, z) and then evaluate it at the given point.

The gradient of a function represents the rate of change of that function in different directions. In this case, we can calculate the gradient of T(x, y, z) as follows:

∇T(x, y, z) = (∂T/∂x) i + (∂T/∂y) j + (∂T/∂z) k

To calculate the partial derivatives, we differentiate each term of T(x, y, z) with respect to its respective variable:

∂T/∂x = 200e^(-x² - 5y² - 7z²) * (-2x)

∂T/∂y = 200e^(-x² - 5y² - 7z²) * (-10y)

∂T/∂z = 200e^(-x² - 5y² - 7z²) * (-14z)

Now we can substitute the coordinates of point P(4, -1, 4) into these partial derivatives:

∂T/∂x at P(4, -1, 4) = 200e^(-4² - 5(-1)² - 7(4)²) * (-2 * 4)

∂T/∂y at P(4, -1, 4) = 200e^(-4² - 5(-1)² - 7(4)²) * (-10 * -1)

∂T/∂z at P(4, -1, 4) = 200e^(-4² - 5(-1)² - 7(4)²) * (-14 * 4)

Simplifying these expressions gives us:

∂T/∂x at P(4, -1, 4) = -3200e^(-107)

∂T/∂y at P(4, -1, 4) = 2000e^(-107)

∂T/∂z at P(4, -1, 4) = -11200e^(-107)

Now, to find the rate of change of temperature at point P in the direction towards the point (5, -4, 5), we can use the direction vector from P to (5, -4, 5), which is:

v = (5 - 4)i + (-4 - (-1))j + (5 - 4)k

= i - 3j + k

The rate of change of temperature in the direction of vector v is given by the dot product of the gradient and the unit vector in the direction of v:

Rate of change = ∇T(x, y, z) · (v/|v|)

To calculate the dot product, we need to normalize the vector v:

|v| = √(1² + (-3)² + 1²)

= √(1 + 9 + 1)

= √11

Normalized vector v/|v| is given by:

v/|v| = (1/√11)i + (-3/√11)j + (1/√11)k

Finally, we can calculate the rate of change:

Rate of change = ∇T(x, y, z) · (v/|v|)

= (-3200e^(-107)) * (1/√11) + (2000e^(-107)) * (-3/√11) + (-11200e^(-107)) * (1/√11)

= 0

Since, the value of e^(-107) = 0.

Therefore, rate of change = 0.

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Answer:

2.5 hours

Step-by-step explanation:

60+2t=40+10t

hope this helps, have a great day :)

Answer:

C

Step-by-step explanation:

Geometrically: if we set a circle at the point of origin and it's radius is one of the points (I used L), then we simple rotate the point 180 degrees around the circle and discover our new coordinate.

doing this for all three points yields C.

Answer:

L (−4, −5)

M (0, −2)

N (2, 4)

Step-by-step explanation:

The rule for this particular rotation is: (x, y)→(−x, −y).

To visualize why this is the case, the rotation can also be seen as the 180°clockwise rotation of the x- and y- axes about the origin while the figure remains in place. This rotation changes all x distances into x distances of the opposite sign, and all y distances into y distances of the opposite sign.

Apply the rule to each of the vertices of the triangle.

L(4, 5) → L'(−4, −5)

M (0, 2) → M' (0, −2)

N (−2, −4) → N' (2, 4)

Therefore, the coordinates of the vertices of the rotated triangle are

L' (−4, −5)

M' (0, −2)

N' (2, 4)

Answer:    P(King AND King) = 1/221

Step-by-step explanation:

There are 4 Kings in a deck of 52 cards total

Probability of getting a King first time:

P(King) = 4/52                        > 4 Kings out of 52 total cards

P(King) = 1/13                          >reduced fraction by dividing top and

                                                bottom by 4

Probability of getting another king:

P(King) = 3/51                      > You took out a king so there are 3 left and 1

                                                 less to the total making 51

P(king) = 1/17                        >Reduced by dividing top and bottom by 3

Probability of getting king and then king again.  The second king is dependent on you getting a king the first time.  Because it is dependent, you multiply the 2 probabilities

P(King AND King) = (1/13)(1/17)

P(King AND King) = 1/221

Answer:

Step-by-step explanation:

The width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.

The problem states that the width of the basketball court (W) can be modeled by the equation:

W(A) = √(A/2)

where A is the area of the court in square feet.

Since the length (L) of the basketball court is twice the width (W), we can express it as:

L = 2W

Now, let's find the expression for the length (L) in terms of the area (A) of the court.

Step 1: Substitute the value of W from the given model into the expression for L:

L = 2 × √(A/2)

Step 2: Simplify the expression:

L = √(4A/2)

L = √(2A)

So, the expression for the length (L) of the basketball court in terms of its area (A) is given by L = √(2A).

To summarize, the width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.

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Complete question :- A community is building a new outdoor basketball court. The length of the court is twice the width. The width of the basketball court in feet can be modeled by w(A)= √A/2 where a is the area in square feet of the court.

Answer:

291

Step-by-step explanation:

Think of a triangle with vertices D (Dublin), L (London), and P (Paris).

Let x = DL

Let y = LP

Let z = DP

"The distance from Dublin to London is 78 more miles than the distance between London and Paris."

DL = LP + 78

x = y + 78

If the distance between Dublin and Paris is 504 miles, including the stop in London.

DL + LP = 504

x + y = 504

x = y + 78

x + y = 504

y + 78 + y = 504

2y = 426

y = 213

x = y + 78

x = 213 + 78

x = 291

Answer:

The distance between London and Paris is 213 miles, and the distance between Dublin and London is 291 miles.

Step-by-step explanation:

Let's assign variables to the unknown distances:

Distance from London to Paris = x

Distance from Dublin to London = x + 78

According to the given information, the distance between Dublin and Paris, including the stop in London, is 504 miles. Using these values, we can set up the equation:

Distance from Dublin to London + Distance from London to Paris = 504

(x + 78) + x = 504

Combining like terms:

2x + 78 = 504

Subtracting 78 from both sides:

2x = 426

Dividing both sides by 2:

x = 213

Therefore, the distance between London and Paris is 213 miles, and the distance between Dublin and London is 213 + 78 = 291 miles.

Answer:

y- intercept = \(\frac{1}{2}\)

Step-by-step explanation:

Given

f(x) = \(\frac{1}{2}\) \((6)^{x}\)

To find the y- intercept let x = 0 , then

f(0) = \(\frac{1}{2}\) \((6)^{0}\) [ \(6^{0}\) = 1 ]

      = \(\frac{1}{2}\) × 1 = \(\frac{1}{2}\) ← y- intercept

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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Answer:

7

Step-by-step explanation;

Rewriting our equation with parts separated:

4+1/7+2+6/7

Solving the whole number parts:

4+2=6

Solving the fraction parts:

1/7+6/7=7/7 (7/7 is a whole number) But first before simplifing, reduce the fraction, 7/7=1/1. Then 1/1=1.

Combining the whole and fraction parts:

(Solving the whole number parts - 6)

(Solving fraction parts - 1)

Comparing the calculated average (9.85 mg/dl) to the average associated with tetany (below 6 mg/dl), we can see that the patient's average total calcium level is within the normal range. This suggests that the patient's tetany may not be caused by a deficiency in total calcium levels.

To analyze the patient's total calcium test readings and determine if they are within the normal range, we can calculate the average and compare it to the average associated with tetany (below 6 mg/dl).

The total calcium test readings are as follows:

9.3, 8.8, 10.1, 8.9, 9.4, 9.8, 10, 9.9, 11.2, 12.1

To calculate the average total calcium level, we sum up all the readings and divide by the number of readings:

Average = (9.3 + 8.8 + 10.1 + 8.9 + 9.4 + 9.8 + 10 + 9.9 + 11.2 + 12.1) / 10

Average = 98.5 / 10

Average = 9.85 mg/dl

Comparing the calculated average (9.85 mg/dl) to the average associated with tetany (below 6 mg/dl), we can see that the patient's average total calcium level is within the normal range. This suggests that the patient's tetany may not be caused by a deficiency in total calcium levels.

It's important to note that while the average total calcium level is within the normal range, individual readings may still vary. Further evaluation by a healthcare professional is necessary to determine the underlying cause of the patient's tetany.

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