plsase help meeeeeee​

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Answer:

45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

Applying the tangent ratio, the length of n in simplest form is: n = 3.

One of the ratios of the trigonometric ratios that is used to solve a right triangle is the tangent ratio, which is:

tan ∅ = opposite side length/adjacent side length, where ∅ is the reference angle.

Given the following:

Substitute

tan 60 = 3√3 / n

Multiply both sides by n

n(tan 60) = (3√3/n)(n)

n(tan 60) = 3√3

Divide both sides by tan 60

n(tan 60)/tan 60 = 3√3/tan 60

n = 3√3/tan 60

n = 3√3 / √3 [Note: tan 60 = √3]

n = 3

Therefore, applying the tangent ratio, the length of n in simplest form is: n = 3.

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The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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Answer: 43.21 if you're rounding it two decimal places, 0.08642998 if you're multiplying 43.21499 by 0.002, and 0.8642998 if you're multiplying 43.21499 by 0.02.

Answer:  The correct answer is (#3) this is a ssa situation, only one triangle is possible.

Step-by-step explanation:  Confirmed correct using the Law of Cosines.

Answer:

84.48

Step-by-step explanation:

Formula = Number x 100

Percent = 49 x 100

58 = 84.48

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

\(\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}\)

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

\(\dfrac{s}{C}=\dfrac{A}{360^{\circ}}\)

Cross multiply:

\(360^{\circ} \cdot s=C \cdot A\)

Now, divide both sides by A to isolate C:

\(\dfrac{360^{\circ} \cdot s}{A}=C\)

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

\(\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}\)

Answer:32

Step-by-step explanation:

i think the answer will be 32 feet

The sum of the angles of the triangle expressed in two ways are x + 1/2x + 3/2x and 2x + x + 3x/2

It is important to note that the sum of the angles of a triangle is equal or equivalent to 180 degrees.

We have the angle measurements as;

Substitute the values

x + 1/2 x + 3/2x = 180

Find the lowest common multiple

2x + x + 3x /2 = 180

Add the numerators

6x/2 = 180

cross multiply

6x = 360

x = 60

Hence, the expression is x + 1/2x + 3/2x and 2x + x + 3x/2

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Answer:it will be D

Step-by-step explanation: because $100 + 4%=$100.4

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

Note that in the above problem where a marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore, note that the width of the oil spill is 20m. See the proof below.

In ΔABC and ΔDEC, Note that since

DC = BC; and

EC = AC

It means that ∠DCE = ∠ACB (Diagonal Equality)

⇒ ΔABC ≅ ΔDEC

Therefore:

DE = AB

Since AB = 20m,

DE is also = 20m.

Thus, it is correct to state that the width of the oil spill is 20m.

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Answer:

The image of P on the curve is (0,-3).

Step-by-step explanation:

On the curve with equation y=f(x)-1

On this curve, the output is subtracted by 1 from the original function.

The point P(0,-2) lies on the curve with equation y=f(x).

Input: 0, output: -2

-2 -1 = -3

So

The image of P on the curve is (0,-3).

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

Hundreds Thousands Place

Step-by-step explanation:

It is the 6th digit, therefore making it the hundreds thousands place...

Answer:

A - C(-3, -2), D(1, -2)

Step-by-step explanation:

The tower, the flagpole and Jeff's position form similar triangles

The tower is 54 feet's tall

Using the attached figure as an illustration, we have the following highlights

So, we have the following equivalent ratios

\(AB:BE = CD:CE\)

Where:

BE = BC + CE

So, we have:

\(AB:BC + CE = CD:CE\)

This gives

\(h:40 + 20 = 18:20\)

\(h:60 = 18:20\)

Express as fraction

\(\frac{h}{60} = \frac{18}{20}\)

\(\frac{h}{60} = 0.9\)

Multiply through by 60

\(h= 54\)

Hence, the tower is 54 feet's tall

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The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

We have,

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart.

Because of this, it is also known as an equiangular quadrilateral.

The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

the points (-1 , 2) and (3 , 2 ) form one the of the rectangle

w = √ 16

  = 4

The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5)            

                = √9 + 36

                 = √45 = 3√5

The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit

The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

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complete question:

Find the area and perimeter of a rectangle with vertices at (-1, 2), (3, 2),

(3.-5), and (-1,-5).

Answer:

x = -2/5

x = 3/4

Step-by-step explanation:

Factoring:

20x²-7x-6=0

20x²+8x - 15x - 6 = 0

4x * (5x + 2) - 3 * (5x + 2) = 0

(5x + 2) * (4x - 3) = 0

Cases:

5x + 2 = 0

4x - 3 = 0

x = -2/5

x = 3/4

Answer:

20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120

Step-by-step explanation:

now,

20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)

5x(4x-3) +2(4x-3)=0

(5x+2) (4x-3)=0

Either 5x=-2

X=-2/5

Or

4x=3

X=3/4

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.

There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.

One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.

A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.

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Step-by-step explanation:

\(4\left(3\cdot \:8-x\right)=4\)

\(\mathrm{Divide\:both\:sides\:by\:}4\)

\(\frac{4\left(3\cdot \:8-x\right)}{4}=\frac{4}{4}\)

\(Simplify\)

\(24-x=1\)

\(\mathrm{Subtract\:}24\mathrm{\:from\:both\:sides}\)

\(24-x-24=1-24\)

\(Simplify\)

\(-x=-23\)

\(\mathrm{Divide\:both\:sides\:by\:}-1\)

\(\frac{-x}{-1}=\frac{-23}{-1}\)

\(Simplify\)

\(x=23\)

Answer:

\(x=23\)

Step-by-step explanation:

\(4(3\cdot8-x)=4\)

Divide both sides by 4:

\(\implies 3\cdot8-x=1\)

Add x to both sides:

\(\implies 3\cdot8=x+1\)

Multiply 3 × 8:

\(\implies 24=x+1\)

Subtract 1 from both sides:

\(\implies 23=x\)

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Answer:

only 5 points ;(

Step-by-step explanation: