It is important to understand that integral equations also arise from problems in differential equations. (a) For example, write the initial value problem dx = f(t, x), x(to) = xo dt as an integral equation and indicate what kind of equation it is. (b) Show that an initial value problem d²x dt² = f(t, x), x(to) = xo, x'(to) = x₁ involving a second order differential equation can be transformed into a Volterra integral equation

The 40th term of the arithmetic sequence (a) will be -183 and the 60th term of the arithmetic sequence (b) will be 242

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

a) Given that, an arithmetic sequence has a 2nd term equal to 7 and 8th term equal to -23, we need to find the term of the sequence that has value -183.

We know that,

aₙ = a+(n-1)d

Where, aₙ = nth term, d = common difference, a = first term and n = number of terms.

Therefore,

7 = a+(2-1)d

7 = a+d

a = 7-d....(i)

Similarly,

-23 = a+(8-1)d

-23 = a+7d

a = -7d-23....(ii)

Equating the RHS of the equations,

7-d = -7d-23

30 = -6d

d = -5

Put d = -6 in eq(i)

a = 7-(-5) = 12

Now,

-183 = 12+(n-1)(-5)

-183 = 12-5n+5

-183-17 = -5n

n = 40

Therefore, 40th term will be -183

b) Given that, an arithmetic sequence has a 6th term equal to 26 and 9th term equal to 38, we need to find the 60th term

We know that,

aₙ = a+(n-1)d

Where, aₙ = nth term, d = common difference, a = first term and n = number of terms.

26 = a+5d

a = 26-5d...(i)

38 = a+8d

a = 38-8d....(ii)

Equating the RHS of the equations,

26-5d = 38-8d

3d = 12

d = 4

Put d = 4 in eq(i)

a = 26-5(4)

a = 6

Therefore,

a₆₀ = 6+(60-1)(4)

= 242

Hence, the 40th term of the arithmetic sequence (a) will be -183 and the 60th term of the arithmetic sequence (b) will be 242

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The surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

Here, we are given a rectangular prism and a cube as shown in the figure below.

The three sides of the prism are- 2, 3 and 6

Thus, the total surface area of the cube will be-

2 [(2*3) + (3*6) + (6*2)]

= 2[6 + 18 + 12]

= 2*36

= 72 cm square

Now, the side of the cube is 3 cm

Thus, the total surface area of the cube will be-

6( 3*3 )

= 6*9

= 54 cm square

Thus, the difference between the surface area of prism and cube is = 72 - 54

= 18 cm square.

Thus, the surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

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Your question was incomplete. Check for the missing figure below.

Answer:

c

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

5+5=10+2x+x+2x=10+5x

Answer:since <BAD ≅ <DCB

<B≅<D

<A≅<C

<D≅<B

∴ AB≅CD

HOPE THIS WAS HELPFUL

Answer:

d

Step-by-step explanation:

Step-by-step explanation:

simply take the average of the x and y coordinates

Answer:

3600

Step-by-step explanation:

Answer: 45

Step-by-step explanation:

Jimmy's age = (serena age + tyler age) - 1

The solution to the given problem is given by

(a) x = 202.2921 USD

(b) y = 95.8132 USD

To solve for the values of x and y in the given arbitrage strategy, let's analyze each step:

1. Borrow x USD at 1.91% today, with a total loan repayment obligation after one year of (1+1.91%)x USD.

2. Convert y USD into CAD at the spot rate of 1.49. This gives us an amount of y * 1.49 CAD.

3. Lock in the 3.79% rate on the deposit amount of 1.49y CAD. After one year, the deposit will grow to \((1+3.79\%) * (1.49y) CAD.\)

4. Simultaneously, enter into a forward contract that converts the full maturity amount of the deposit into USD at the one-year forward rate of USD = 1.41 CAD.

The strategy generates 100 USD today and nothing otherwise. We can set up an equation based on the arbitrage condition:

\((1+1.91\%)x - (1+3.79\%) * (1.49y) * (1/1.41) = 100\ USD\)

Simplifying the equation, we have:

\((1.0191)x - 1.0379 * (1.49y) * (1/1.41) = 100\)

Now we can solve for x and y by rearranging the equation:

\(x = (100 + 1.0379 * (1.49y) * (1/1.41)) / 1.0191\)

Simplifying further:

\(x = 99.0326 + 1.0379 * (1.0574y)\)

From the equation, we can see that x is dependent on y. Therefore, we cannot determine the exact value of x without knowing the value of y.

To find the value of y, we need to set up another equation. The total amount in CAD after one year is given by:

\((1+3.79\%) * (1.49y) CAD\)

Setting this equal to 100 USD (the initial investment):

\((1+3.79\%) * (1.49y) * (1/1.41) = 100\)

Simplifying:

\((1.0379) * (1.49y) * (1/1.41) = 100\)

Solving for y:

\(y = 100 * (1.41/1.49) / (1.0379 * 1.49)\\\\y = 100 * 1.41 / (1.0379 * 1.49)\)

\(y = 95.8132\ USD\)

Therefore, the values are:

(a) \(x = 99.0326 + 1.0379 * (1.0574 * 95.8132) ≈ 99.0326 + 103.2595 ≈ 202.2921\ USD\)

(b) \(y = 95.8132\ USD\)

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Answer:

The area is 36m^2

Step-by-step explanation:

6×6=36

Answer:

6 x 6 = 12

Step-by-step explanation:

area is length x width and all sides on a square are congruent ( so all of the sides are 6)

Step-by-step explanation:

"The difference of twice of a # and 10 is  = to 12

We're gonna do this like statement reason because I don't want to write a paragraph lol

2x-10=12             Given

2x=24                 Simplify (+10 to each side cancels on left, adds on the right)

x=12                    Simplify (divide by 2)

Yay!

Also if you have 2 chances maybe try -1? but I think 12 is right

Answer:

x = (5/3 , 7)

Step-by-step explanation:

Answer:

your annual interest rate will be 5%.

Step-by-step explanation:

brainliest please?

It was 120 dollars over the span of 2 years, so we divide 120 by 2.

120/2=60

So the loan costed $60 per year

---

hope it helps

Answer:

76.8

Step-by-step explanation:

Im assuming that R24 stands for 24 rupees

We can set up a fraction:

\(\frac{24}{250} = \frac{x}{800}\)

Now cross multiply:

\(19200 = 250x\)

Solve for x:

\(x = 76.8\)

Answer:

Yes

Step-by-step explanation:

I know that is right.

A corner point, is at (a,b).Then a=band b=a. The absolute minimum of f(x, y) within D is 0,The absolute maximum is 16.

To find the critical point of f(x, y)  to the boundary of D, to consider the boundary curve of D. In this case, the boundary curve is given by the line y = x, where 0 ≤ y ≤ x ≤ 4.

First,  the function f(x, y) in terms of a single variable, either x or y. Let's express it in terms of y:

f(x, y) = x²2 - xy + y²2 - 4x + 4y

Substituting y = x, we have:

f(x, x) = x²2 - x²2 + x²2 - 4x + 4x

= x²2

Now,  to find the critical points of f(x, x) = x²2 within the interval 0 ≤ x ≤ 4. To find the critical points,  differentiate f(x, x) with respect to x and set it equal to zero:

f'(x) = 2x = 0

Solving 2x = 0,  find x = 0. This critical point occurs at the corner point (0, 0), which is not on the boundary curve y = x.

Since there are no critical points of f(x, y) restricted to the boundary curve y = x that are not at a corner point, that there are no critical points (a, b) within the given conditions.

The absolute minimum and maximum of f(x, y) within the region D, to consider the function values at the corners of D.

The corners of D are (0, 0), (4, 0), and (4, 4). Evaluating f(x, y) at these points:

f(0, 0) = 0²2 - 0 × 0 + 0²2 - 4 × 0 + 4 × 0 = 0

f(4, 0) = 4²2 - 4 × 0 + 0²2 - 4 × 4 + 4 ×0 = 0

f(4, 4) = 4²2 - 4 × 4 + 4²2 - 4 ×4 + 4 × 4 = 16

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The solution of the given initial value problem, x'' + 33.64x = 4cos(6t), with x(0) = x'(0) = 0, can be expressed as a sum of the homogeneous solution and the particular solution.

To find the solution, we start by solving the homogeneous equation, x'' + 33.64x = 0. The characteristic equation associated with this homogeneous equation is \(r^2 + 33.64 = 0\), which yields the roots

r = ±i√33.64. Thus, the homogeneous solution can be expressed as

x_h(t) = A*cos(√33.64*t) + B*sin(√33.64*t),

where A and B are constants determined by the initial conditions.

Next, we need to find the particular solution for the forced oscillation. Since the right-hand side of the equation is of the form Acos(ωt), where ω = 6, we assume a particular solution of the form x_p(t) = C*cos(ω*t + φ), where C and φ are constants to be determined. Taking the derivatives, we have x_p''(t) = -ω^2*C*cos(ω*t + φ) and x_p'(t) = -ω*C*sin(ω*t + φ). Substituting these into the original equation, we obtain -ω^2*C*cos(ω*t + φ) + 33.64*C*cos(ω*t + φ) = 4*cos(ω*t).

To satisfy this equation, the coefficient of the cosine term must be 4, while the coefficient of the sine term must be zero. This gives us two equations: -ω^2*C + 33.64*C = 4 and -ω*C = 0. Solving these equations, we find C = 4/(33.64 - ω^2) and φ = 0. Therefore, the particular solution is x_p(t) = (4/(33.64 - ω^2))*cos(ω*t).

Finally, we combine the homogeneous solution and the particular solution to obtain the complete solution:

x(t) = x_h(t) + x_p(t) = A*cos(√33.64*t) + B*sin(√33.64*t) + (4/(33.64 - ω^2))*cos(ω*t).

By substituting the initial conditions x(0) = x'(0) = 0 into this equation, we can determine the values of A and B. With the obtained values, the final solution for the initial value problem can be expressed in terms of the given constants and the trigonometric functions involved.

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Answer:

A

Step-by-step explanation:

the middle angle has to be equal to make the entire angle equal

Answer:

I think the answer would be $21

Step-by-step explanation:

On a calculator you type 108.53 then divide it by six and add 18%.

Answer:

113.142 mm

Step-by-step explanation:

Easy.

Formula:

pi x radius x radius

Solution: 3.141592654 or 22/7 for pi

22/7 x 6 x 6 = 113.142 mm

According to the question the method of undetermined coefficients to find a particular solution is The particular solution to the given system is

\(\(x_p = -2 e^{kt}\)\) , \(\(y_p = e^{kt}\)\).

To apply the method of undetermined coefficients, we assume a particular solution of the form:

\(\(x_p = A e^{kt}\)\\\(y_p = B e^{kt}\)\)

where \(\(A\) and \(B\)\) are undetermined coefficients to be determined and \(\(k\)\) is a constant.

Differentiating the assumed forms of \(\(x_p\) and \(y_p\):\)

\(\(x'_p = Ak e^{kt}\)\\\(y'_p = Bk e^{kt}\)\)

Substituting these into the given system of equations:

\(\(Ak e^{kt} = 7(A e^{kt}) - 10(B e^{kt}) + 12\)\\\(Bk e^{kt} = 2(A e^{kt}) - 5(B e^{kt}) - 4e^{-3t}\)\)

Simplifying the equations:

\(\((Ak - 7A + 10B) e^{kt} = 12\)\)

\(\((Ak - 2A + 5B) e^{kt} = -4e^{-3t}\)\)

Since these equations must hold for all \(\(t\)\), the coefficients multiplying \(\(e^{kt}\)\) must be equal to 0:

\(\(Ak - 7A + 10B = 12\)\)

\(\(Ak - 2A + 5B = 0\)\)

Solving these equations for \(\(A\) and \(B\):\)

\(\(A = -2\)\)

\(\(B = 1\)\)

Therefore, the particular solution to the given system is \(\(x_p = -2 e^{kt}\)\) , \(\(y_p = e^{kt}\)\).

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The hypothesis test to conduct in this situation is a two-sample test for

means, specifically a paired-sample t-test.

This is because the same group of workers is being tested twice, under

two different conditions: without exercise breaks and with exercise breaks.

The two sets of data are dependent because they are coming from the

same group of individuals, and the goal is to determine if there is a

statistically significant difference in their well-being between the two

conditions.

A paired-sample t-test is appropriate because it can compare the means of

two related samples, and it takes into account the correlation between the

data points in each sample.

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