Question 2 Given that d^2y/(dx^2 )-4y dy/dx=0 and that y=0 at
x=0 and dy/dx=2 at x=0 use Taylor series method to find y as a
series in the ascending power of x up to and including the term in
x^2

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

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Answer:

C. Yes, Because Each Side Length Is Less Than 15.

Step-by-step explanation:

Answer:

the person above me is right mark me brainiest for being right :D

Step-by-step explanation:

The required solution is,

\(\[U(x, y) = -4sin(4\pi x)sinh(\frac{\pi}{4}y) - \sum_{n=2}^{\infty} \frac{64}{n^2\pi^2}sin(\frac{n\pi}{4})cos(\frac{n\pi}{4}x)sinh(\frac{n\pi}{4}y)\]\)

Neumann problem for the LaPlace equation

The given LaPlace equation is as follows:

\(\[\bigtriangledown ^2U(x,y)=0\]\)

And the given values are,\

\([U_{x}(0,y)=cos(4 \pi x)=U_x(4,y)=U_y(x,0)=U_y(x,4)\]\)

On the square region

\[R={(x,y):x\varepsilon [0,4], y\varepsilon [0,4]}\]

To find the solution of the Neumann problem for the LaPlace equation, we need to integrate U(x, y) with respect to x and y.

Integrating the function w.r.t x, we get,

\(\[\int^4_0 \int^4_0 \frac{\partial^2 U}{\partial x^2}dx dy=0\]\)

Integrating the function w.r.t y, we get,

\(\[\int^4_0 \int^4_0 \frac{\partial^2 U}{\partial y^2}dx dy=0\]\)

Now, integrating the function w.r.t x, and applying the given boundary conditions, we get,

\(\[\int^4_0 U_x(0,y)dy= -\int^4_0 U_x(4,y)dy\]\[\int^4_0 cos(4\pi x)dy = - \int^4_0 U_x(4,y)dy\]\[sin(4\pi x) \Big|_0^4 = -\int^4_0 U_x(4,y)dy\]\[0 - 0 = -\int^4_0 U_x(4,y)dy\]Therefore,\[\int^4_0 U_x(4,y)dy = 0\]\)

Now, integrating the function w.r.t y, and applying the given boundary conditions, we get,

\(\[\int^4_0 U_y(x,0)dx = \int^4_0 U_y(x,4)dx\]\)

Therefore,

\(\[U_y(x, 0) = U_y(x, 4) = 0\]\)

Now, using the Fourier series, the solution of the given LaPlace equation is,

\(\[U(x, y) = \sum_{n=0}^{\infty} a_n cos(\frac{n\pi}{4}x)sinh(\frac{n\pi}{4}y)\]\)

Now, applying the given boundary conditions,

\(\[U_x(0, y) = \sum_{n=0}^{\infty} \frac{na_n\pi}{4} sin(\frac{n\pi}{4}x)cosh(\frac{n\pi}{4}y) = cos(4\pi x)\]\[U_x(4, y) = \sum_{n=0}^{\infty} \frac{na_n\pi}{4} sin(\frac{n\pi}{4}x)cosh(\frac{n\pi}{4}y)\]\[U_y(x, 0) = \sum_{n=0}^{\infty} a_n cos(\frac{n\pi}{4}x)sinh(0)\]\[U_y(x, 4) = \sum_{n=0}^{\infty} a_n cos(\frac{n\pi}{4}x)sinh(n\pi)\]\)

Now, solving the above equations, we get,

\(\[a_1 = -4sin(4\pi x)\]And\[a_n = - \frac{64}{n^2\pi^2}sin(\frac{n\pi}{4})\]\)

Therefore, the required solution is,

\(\[U(x, y) = -4sin(4\pi x)sinh(\frac{\pi}{4}y) - \sum_{n=2}^{\infty} \frac{64}{n^2\pi^2}sin(\frac{n\pi}{4})cos(\frac{n\pi}{4}x)sinh(\frac{n\pi}{4}y)\]\)

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Answer:

to find y you have to do trigonometry

Answer:

Step-by-step explanation:

To prove a quadrilateral a parallelogram we prove,

1). Length of opposite sides are equal.

2). Slopes of the opposite sides are same.

Length of AB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

                      = \(\sqrt{(2+1)^2+(-5+2)^2}\)

                      = \(3\sqrt{2}\)

Length of BC = \(\sqrt{(2-1)^2+(-5+2)^2}\)

                      = \(\sqrt{10}\)

Length of CD = \(\sqrt{(1+2)^2+(-2-1)^2}\)

                      = \(3\sqrt{2}\)

Length of AD = \(\sqrt{(-1+2)^2+(-2-1)^2}\)

                      = \(\sqrt{10}\)

Therefore, AB = CD and BC = AD (Opposite sides are equal in length)

Slope of AB = \(\frac{y_2-y_1}{x_2-x_1}\)

                    = \(\frac{-5+2}{2+1}\)

                    = -1

Slope of BC = \(\frac{-5+2}{2-1}\)

                    = -3

Slope of CD = \(\frac{1+2}{-2-1}\)

                    = -1

Slope of AD = \(\frac{-2-1}{-1+2}\)

                    = -3

Slope of AB = slope of CD and slope of BC = slope AD

Therefore, AB║CD and BC║AD

Hence ABCD is a parallelogram

Answer: 15 crocodriles

Step-by-step explanation:

We know that the ratio is 4:3

This means that for each 4 hippos, we have 3 cocodriles.

We know that there are 20 hippos.

How many groups of 4 hippos we have?

n = 20/4 = 5

So we have 5 groups of 4 hippos, this means that we also have 5 groups of 3 crocodiles, then we have:

3*5 = 15 crocodiles

Step-by-step explanation:

Tanø=opp/adj

Tan30=x/7. (× b.s 7)

x=7Tan30

x= 4.04

Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.

According to the given data in the question,

1 USD =0.85 EURO

80 USD = 0.85*80 EURO

80 USD= 68 EURO

Hence 80USD will be converted to 68 EUROS

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Answer:

B

Step-by-step explanation:

Answer:

D. 6,8,10

Step-by-step explanation:

I just did it on   a p e x

Answer:

\(27\pi\)

Step-by-step explanation:

The area of a circle is given by the formula \(A = \pi r^2\).

We are given the radius of this circle, so we can plug in.

\(A = \pi r^2\\A=6^2\pi \\A=36\pi\)

Seeing that there is \(\frac{3}{4}\) of the circle left, multiply \(36\pi\) by \(\frac{3}{4}\).

\(36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi\)

Answer:

Using the Pythagorean Theorem:

15^2 = 12^2 + base^2

base^2 = 225 -144

base^2 = 81

base = 4

Step-by-step explanation:

Answer:

The answer is 9

Answer:

option 6b):) is correct

Answer:

73.12m²

Step-by-step explanation:

Okay, you can break this figure into a half-circle and a triangle, we're going to start with the triangle (using the handy formula sheet you have up there)

12 x 8 = 96

96 x ½ = 48

Now we do the semicircle (the formula for a circle is pi x radius² )

the radius is half of the diameter so:

8 ÷ 2 = 4

4² = 16

we're using 3.14 for pi so:

3.14 x 16 = 50.24

Now we'd normally stop there, but this is only a semicircle, so we have to chop it in half again:

50.24 ÷ 2 = 25.12

Now we add both of those together:

48 + 25.12 = 73.12‬

So the area of the figure is 73.12m²

hope this helps:)

The loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.

To determine the loan with the smallest monthly payment, we need to calculate the monthly payment for each loan option and compare them.

We can use the formula for monthly payment on a simple interest loan:

monthly payment = (principal + (principal * interest rate * time)) / total number of payments

where:

We can compute the monthly payments for each loan choice using this formula:

1. 12 Monthly interest rate = 0.0625/12 = 0.00521, monthly payment = (1250 + (1250 * 0.00521 * 12)) / 12 = $107.35

2. 18 months at 6.75%: monthly interest rate = 0.0675/12 = 0.00563, monthly payment = (1250 + (1250 * 0.00563 * 18)) / 18 = $81.96

3. 24 months at 6.5%: monthly interest rate = 0.065/12 = 0.00542, monthly payment = (1250 + (1250 * 0.00542 * 24)) / 24 = $66.14

4. 30 months at 6%: monthly interest rate = 0.06/12 = 0.005, monthly payment = (1250 + (1250 * 0.005 * 30)) / 30 = $45.83

Based on these calculations, the loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.

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Answer:

₦28.5

Step-by-step explanation:

\(interest = \frac{600 \times 1.5 \times 3 \frac{1}{6} }{100} \)

The expressions 3r + 6 + r - 2 and 3r + 4 are not equivalent expressions

Equivalent expressions are two or more algebraic expressions that have the same value for any given value of the variables within them.

In general, two expressions are equivalent if they can be transformed into each other by applying the rules of algebra, such as the distributive property, combining like terms, and simplifying fractions.

Here we have

There are 2 expression

3r + 6 + r - 2 ---- (1)

3r + 4  ---- (2)

Expression (1) can be rewritten as follows

3r + 6 + r - 2  = 4r + 4

Here, 3r + 4  ≠  4r + 4  

Hence,

The expressions 3r + 6 + r - 2 and 3r + 4 are not equivalent expressions

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Answer:

Graph C

Step-by-step explanation:

Since p is less than negative 2, it would be going to the left.

The dot also is hollow because -2 is not included.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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Refer to the attached images. Comment any questions you may have.

Since we have found a local minimum at (3,-2/7), but no global minimum. As x and y approach negative infinity, the dominant term is -3x, which approaches negative infinity. Therefore, the global maximum of F(x,y) does not exist.

To find the global maximum and global minimum of F(x,y) = x²/2 + 7y³ + 6y² - 3x, we need to consider its critical points and boundary points in the domain.

First, we find the partial derivatives:

∂F/∂x = x - 3

∂F/∂y = 21y² + 12y

Setting both partial derivatives to zero, we get:

x = 3

y = 0 or y = -2/7

So, the critical points are (3,0) and (3,-2/7).

To check if these critical points correspond to local maxima, minima, or saddle points, we need to find the second partial derivatives:

∂²F/∂x² = 1

∂²F/∂y² = 42y + 12

∂²F/∂x∂y = 0

At (3,0), we have ∂²F/∂x² = 1 and ∂²F/∂y² = 0, which means that we have a saddle point.

At (3,-2/7), we have ∂²F/∂x² = 1 and ∂²F/∂y² = 12/7, which means that we have a local minimum.

Next, we need to check the boundary of the domain, which is not given in the problem statement. Assuming that the domain is the entire xy-plane, we can look at what happens as x and y go to infinity.

As x and y go to infinity, F(x,y) approaches infinity as well. Therefore, there is no global minimum.

In summary, F(x,y) has a local minimum at (3,-2/7), but no global minimum or global maximum.

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Positive curve graphs will be upward-sloping.

Negative curve graphs will be downward-sloping.

Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.

In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

A colligative property depends on option (a) the identity of the solute and option(b) the concentration of the solution

A colligative property is a physical property of a solution that depends on the number of solute particles dissolved in the solution.

It does not depend on the identity of the solute or the concentration of the solution.

The most common colligative properties are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

These properties are all related to the number of solute particles in the solution, so the correct answer to the question is option e, both b and c

A colligative property depends on is the identity of the solute and the concentration of the solution, that is option (e) both b and c

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Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

Answer:

\( {(x - 5)}^{2} = (x - 5)(x - 5)\)

Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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Answer:

9 most likely

Step-by-step explanation:

This is because 3 is one away from 4, so 8 is one away from 9.

Answer:

The answer is 9.

Step-by-step explanation:

3 Relates To 4.

8 Relates To 9.

A. The period of x[n] is 4.

B. The period of x[n] is 4π.

C. The period of X[n] is 20.

D. The period of X[n] is 20.

E.   The energy is finite, but the power is non-zero.

(a) x[n] = 2cos(17πn/2) + sin(31πn)

This signal is periodic because both cosine and sine functions are periodic. To determine the period, we need to find the least common multiple (LCM) of the periods of the cosine and sine components. The period of the cosine component is 2π/(17π/2) = 4/17, and the period of the sine component is 2π/(31π) = 2/31. The LCM of 4/17 and 2/31 is 4/1 = 4. Therefore, the period of x[n] is 4.

(b) x[n] = 6cos(7πn + 20π) + (5/2)sin(n/2)

Similar to (a), this signal is periodic because both cosine and sine functions are periodic. The period of the cosine component is 2π/7π = 2/7, and the period of the sine component is 2π/(1/2) = 4π. The LCM of 2/7 and 4π is 4π. Therefore, the period of x[n] is 4π.

(c) X[n] = cos(0.1n - π/5)

This signal is periodic because the cosine function is periodic. The period of the cosine function is 2π/0.1 = 20. Therefore, the period of X[n] is 20.

(d) X[n] = cos(0.1πn - π/5)

Similar to (c), this signal is periodic because the cosine function is periodic. The period of the cosine function is 2π/(0.1π) = 20. Therefore, the period of X[n] is 20.

(e) x[n] = 5*(-1)^n

This signal is periodic because it alternates between two values (-5 and 5) with a period of 2. Therefore, the period of x[n] is 2.

Now, let's find the energy and power of the given signals:

(a) X[n] = sin(6πn)

Since the signal is periodic with a period of 1/6, the energy is infinite (non-zero but cannot be determined) and the power is also infinite.

(b) x[n] = ejπn/2

The signal is periodic with a period of 4 (since ejπn/2 repeats every four samples). The energy is infinite and the power is also infinite.

(c) x[n] = (2/1)^(-n)u[n]

The signal is a geometric sequence decaying with time. As n approaches infinity, the signal becomes smaller and smaller. Therefore, the energy is finite, but the power is zero.

(d) x[in] = cos(3πn/16)

The signal is periodic with a period of 32 (since cos(3πn/16) repeats every 32 samples). The energy is finite and the power is non-zero.

(e) x[n] = 2n, 0 ≤ n ≤ 10, 1 ≤ n ≤ 15, and 0 otherwise.

The signal is a linear ramp from 0 to 20. Since the signal is finite in both time and amplitude, the energy is finite, but the power is non-zero.

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The angle in the capital letter "L" measures 90°, making it a right angle.

A right angle is one that is exactly 90 degrees, or half of a straight angle. There is usually a quarter turn in it. The fundamental geometric forms, rectangle, and square, each have four angles that measure 90 degrees.

When two lines cross, and there is a 90-degree angle between them, the lines are said to be perpendicular. A few examples of 90-degree angles in real life include the angle between the hands of a clock at 3 o'clock, the angles between two neighboring sides of a rectangular door or window, etc.

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