.10. Use the Laplace transform to solve the given IVP. y"+y' - 2y = 3 cos(3t) — 11sin (3t), y(0) = 0, - y'(0) = 6. Note: Write your final answer in terms of your constants. DON'T SOLVE FOR THE CONSTANTS.

Answer:

17.85

Step-by-step explanation:

just times 5.95 by 3

Tienes la tarea en Ingles? Yo solo puedo hacer mathematics en ingles.  Gracias.

Answer:

Hope it helps you,

Step-by-step explanation:

As the figure can be split in to 3 geometric figure,

Rectangle , Triangle and Semi circle ,

So first find the area of these figures then add up them ,

Area of rectangle = Length * width

Length = 20m m  and  width  = 14 mm

hence

Area of rectangle = 20*14  = 280 mm^2

Now ,

Are of  Circle  =  \(\\ \pi *d^{2} /4\)

Then Area of semi circle = \(\\ \pi *d^{2} /8\)

Hence we have d= 20mm

Putt in semi circle formula we get,

Area of Semi Circle= (3.14)*400/8  = 157 mm^2

Now area of triangle = 1/2 * length*width

length =32-20 = 12 mm

width = 14 mm

putt in the formula we get ,

Area of triangle = 1/2*12*14 = 84 mm^2

Now add these 3 Areas to get total Area,

To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.

Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:

P(z < 2.67) ≈ 0.9960

P(z < -0.15) ≈ 0.4404

To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:

P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)

≈ 0.9960 - 0.4404

≈ 0.5556

Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.

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Answer:

x = 36

∠M = 36

∠P = 71

∠N = 73

Step-by-step explanation:

Answer:

14?

Step-by-step explanation:

So sorry if I got it wrong-

Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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Answer:

33.33%

Step-by-step explanation:

600/3 is 200 which means 1/3 of it is rebated

To find the amount in the account after 25 years, we can use the formula for compound interest which is given by;A = P (1 + r/n)^(nt) where;A = the final amount P = the principal or initial amount of dollarsr = the annual interest rate as a decimaln = the number of times the interest is compounded per yeart = the number of years So, for the given question;P = 3400 dollarsr = 8.25% per annum = 0.0825n = 1 (annually)t = 25 yearsSubstituting the values in the formula;A = 3400(1 + 0.0825/1)^(1×25) = 3400(1.0825)^25 = 3400 × 4.27022 = 14531.746 dollarsTherefore, the amount in the account after 25 years, to the nearest cent is $14531.75.

To calculate the future value of the account after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (future value)

P = Principal amount (initial deposit)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

In thiS case, the principal amount (P) is $3400, the annual interest rate (r) is 8.25% or 0.0825 as a decimal, the number of times interest is compounded per year (n) is not specified, so we will assume it is compounded annually (n = 1), and the number of years (t) is 25.

Plugging in these values into the formula:

A = 3400(1 + 0.0825/1)^(1*25)

Simplifying the expression:

A = 3400(1.0825)^25

Calculating the value using a calculator or computer:

A ≈ 3400(3.368599602) ≈ $11,458.83

Therefore, to the nearest cent, the amount in the account after 25 years will be approximately $11,458.83.

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Given the following data: An initial amount of $3400 is placed in an account with an annual interest rate of 8.25%. We are to determine the amount in the account after 25 years, to the nearest cent.

Therefore, the amount in the account after 25 years, to the nearest cent is $23956.35.

The formula for the compound interest is given by;

\(P(1 + r/n)^{nt}\)

Where; P is Principal amount (the initial amount you borrow or deposit), r is Annual interest rate (as a decimal), n is Number of times the interest is compounded per year (in this case, it's annual, therefore n = 1), t is Number of years.

Hence, the amount in the account after 25 years is;

\(P(1 + r/n)^{nt} = $3400(1 + 0.825 / 1)^{1 \times25}\)

\(=  3400(1.0825)^{25}\)

\(= $3400 \times  7.04567\)

= $23956.35

Therefore, the amount in the account after 25 years, to the nearest cent is $23956.35.

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Answer: 54, inequality would be 2.50x+40>or=175 i think

Step-by-step explanation:175-40=135 divided by 2.50=54

Answer: 54, inequality would be 2.50x+40>or=175 i think

Step-by-step explanation:175-40=135 divided by 2.50=54

Answer:

The first term as 2.

Pattern: Multiply the previous term and 2 to get the next term.

Step-by-step explanation:

The pattern is every term is 2× the previous term.

The sequence of the differences, 2, 4, 8, 16, 32, … is geometric. The pattern is every term is 2 times the previous term.

The geometric series is a series in which the ratio of two consecutive numbers is constant.

The sequence of the differences, 2, 4, 8, 16, 32, … is geometric.

So, The ratio of two consecutive numbers is constant.

r = 4/2 = 2

r = 8/4 = 2

Thus, The pattern is every term is 2 times the previous term.

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The interest rate, to the nearest hundredth of a percent, that would be required in order for Mohal to end up with $1,110 would be = 4.2%

The interest rate of an investment is defined as the rate at which an individual receives stipulated amount of money for a period of time over the investment made.

The amount for investment (P) = $830

The time for investment(T) = 8 years

The simple interest yield(SI) = $1,110 -830 = 280

The rate(R) = x%

using the formula;

Simple interest = P×T×R/100

Make R the subject of formula;

R= SI ×100/P×T

R= 280×100/830×8

R= 28000/ 6,640

R= 4.2%

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Answer:

Answer Answer

(x+1) • (x-1) • (2x-1)

Answer:

\(f(-7) = 20\)

Step-by-step explanation:

Given:

\(f(x) = 2(3 -x)\)

Solving for \(f(-7)\):

\(f(-7) = 2(3 -(-7)) \\ f(-7) = 2(3 +7) \\ f(-7) = 2(10) \\ f(-7) = 20\)

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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If you have more than $250,000 to deposit, you should consider spreading your money across multiple accounts or banks to ensure that your funds are fully insured by the FDIC (Federal Deposit Insurance Corporation).

If you have more than $250,000 to deposit, you can safely store your deposits by spreading them across multiple accounts and/or banks. This strategy is commonly referred to as "deposit insurance coverage" and is provided by the Federal Deposit Insurance Corporation (FDIC). In this way, if any one bank fails, you will still have access to your insured funds through the other banks.

A second option is to use the CDARS program. The Certificate of Deposit Account Registry Service is a program that can be utilized by investors to deposit their funds in CDARS member banks. The service allocates these deposits across multiple banks to guarantee that the funds are fully insured.

The third option is to seek the services of an FDIC-insured bank that offers deposit insurance coverage beyond the $250,000 limit. These banks may provide higher deposit insurance coverage, and you can inquire with your bank to determine if they offer this service.

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Answer:

slope = 2 : 8 or 1:4

Step-by-step explanation:

a(-3, 4)

b(5, 6)

slope = rise / run

slope (6-4, 3+5))

slope = 2 : 8 or 1:4

Answer:

Slope =¼

Step-by-step explanation:

\((-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6\)

\(m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} \)

The correct value of ''n'' in this equation will be -5/8.

To solve this equation, we're going to isolate ''x'', and then we're going to subtract the two fractions.

But to subtract the two fractions with different denominators, let's represent the fractions with the least common multiple of the denominators, being 8.

\(\large \sf \dfrac{3}{4} +x=\dfrac{1}{8}\)

\(\large \sf x= \dfrac{1}{8} -\dfrac{3}{4}\)

\(\large \sf x= \dfrac{1-6}{8}\)

\(\large \sf x= \dfrac{-5}{8}\)

\(\boxed{\boxed{{\large \sf x=-\dfrac{5}{8} }}}\)

So we can conclude that the value of ''x'' in this equation will be -5/8.

Five integers that are congruent to 4 mod 13 are 4, 17, 30, 43, and 56.

To find integers congruent to 4 mod 13, you can follow these steps:

Step 1: Understand the congruence. Two numbers are congruent mod 13 if their difference is divisible by 13. In this case, we are looking for integers x such that x ≡ 4 (mod 13).

Step 2: Generate the first integer. The first integer is simply 4 because 4 ≡ 4 (mod 13).

Step 3: Add 13 to the previous integer. Adding 13 to the previous integer will give you the next integer in the sequence because (x + 13) - 4 = x - 4 + 13 is also divisible by 13.

Step 4: Repeat step 3 four times. Starting with 4, we get:
4 + 13 = 17
17 + 13 = 30
30 + 13 = 43
43 + 13 = 56

Thus, the five integers are 4, 17, 30, 43, and 56.

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we have shown that if {u1, u2, ..., ud} is linearly independent and c1, c2, ..., ct are non-zero scalars, then {c1u1, c2u2, ..., ctut} is also linearly independent.

To prove that the set {c1u1, c2u2, ..., ctut} is linearly independent, we need to show that the only solution to the equation c1u1 + c2u2 + ... + ctut = 0 is when c1 = c2 = ... = ct = 0.

Assume that there exist non-zero scalars c1, c2, ..., ct such that c1u1 + c2u2 + ... + ctut = 0. We can rewrite this equation as c1u1 + c2u2 + ... + ctut + 0u(t+1) + ... + 0un = 0, where u(t+1), u(t+2), ..., un are vectors in V.

Since the set {u1, u2, ..., ud} is linearly independent, it follows that c1 = c2 = ... = ct = 0. Otherwise, if any ci is non-zero, we could express one of the vectors u1, u2, ..., ut as a linear combination of the others, contradicting the linear independence of {u1, u2, ..., ud}.

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In order to solve a differential equation in the form of a power series, one uses a general power series solution. It is especially helpful in situations where there is no other way to find an explicit solution.

For the differential equation y' - 2xy = 0, we can assume a power series solution of the following type in order to get the general power series solution centred at xo = 0.

y(x) = ∑[n=0 to ∞] cnx^n

where cn are undetermined coefficients.

By taking y(x)'s derivative with regard to x, we get:

y'(x) = ∑[n=0 to ∞] ncnx = [n=1 to ] (n-1) ncnx^(n-1)

When we enter the differential equation with y'(x) and y(x), we obtain:

∑[n=1 to ∞] cnxn = ncnx(n-1) - 2x[n=0 to ]

With the terms rearranged, we have:

[n=1 to]ncnx(n-1) - 2x(cn + [n=1 to]cnxn) = 0

When we multiply the series and group the terms, we get:

∑[n=1 to ∞] (ncn - 2)x(n- 1) - 2∑[n=1 to ∞] cnx^n = 0

We obtain the following recurrence relation by comparing the coefficients of like powers of x on both sides of the equation:

For n 1, ncn - 2c(n-1) = 0.

The recurrence relation can be summarized as follows:

ncn = 2c(n-1)

By multiplying both sides by n, we obtain:

cn = 2c(n-1)/n

We can see that the coefficients cn can be represented in terms of c0 thanks to this recurrence connection. Starting with an initial condition of c0, we may use the recurrence relation to compute the successive coefficients.

As a result, the following is the universal power series solution for the differential equation y' - 2xy = 0 with its centre at xo = 0:

c0 = y(x) + [n=1 to y] (2c(n-1)/n)x^n

Keep in mind that the beginning condition and the precise interval of interest affect the value of c0 and the series' convergence.

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The result of the division of dividend 3 1/6 by divisor 1 3/8 is computed as 76/33.

For the stated question;

The dividend is  3 1/6, which is given in mixed fraction.

In proper fraction; 3 1/6 = 19/6.

The divisor is  1 3/8 = 11/8.

Thus,

= 19/6 / 11/8

= 19*8 / 6*11

= 76/33

Thus, the result of the division of dividend 3 1/6 by divisor 1 3/8 is computed as 76/33.

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Answer:

x=-22

Step-by-step explanation:

Let's substitute the number you are thinking of with x

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

3x+12=2x-10

x+12=-10

x=-22

Answer:

look at explanation k=3

Step-by-step explanation:

5×3=15 15-5=10 10+6=16

Therefore, the roots of the polynomial equation \(x^4 - x^3 = 4x^2 + 4x\) are infinite, and it is not possible to find them precisely using a graphing calculator or a system of equations.

To find the roots of the polynomial equation \(x^4 - x^3 = 4x^2 + 4x\), we can utilize a graphing calculator and a system of equations. Here's how you can proceed: Rewrite the equation to bring all terms to one side:

\(x^4 - x^3 - 4x^2 - 4x = 0\)

Enter the equation into a graphing calculator or any equation-solving software. Look for the x-intercepts or roots of the equation on the graphing calculator. These are the values of x where the graph intersects the x-axis. Alternatively, we can solve the equation using a system of equations. Let's set up the system:

Consider the original equation:\(x^4 - x^3 = 4x^2 + 4x.\)

Rearrange the equation to bring all terms to one side:

\(x^4 - x^3 - 4x^2 - 4x = 0\)

Introduce a new variable, y, to create a system of equations:

\(x^4 - x^3 - 4x^2 - 4x = 0 (Equation 1)\)

\(y = x^4 - x^3 - 4x^2 - 4x (Equation 2)\)

Now, we can solve this system of equations by eliminating y. Subtract Equation 2 from Equation 1:

0 = 0

The result is always true, indicating that there is an infinite number of solutions. This suggests that the equation has infinitely many roots.

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Subtract the height of the dive from

The total distance he dove:

15 - 9 = 6

The pool is 6 meters deep

Answer:

A

Step-by-step explanation:

I have attached a photo with working.

Answer:

y=-5x+9

Step-by-step explanation:

Answer:

y=-5x+-9

Step-by-step explanation:

If you notice is says that the line HAS to go through (1,4) but if you need it to go through (-1,4) it would be y=-5x+-1

Answer:

pretty sure its (-6, -4)

Step-by-step explanation:

in the ||| quadrant so I know they are both negative.

The point is 6 units to the left and 4 units down.

Hope this helps! Good luck!

The probability that a randomly chosen plant is detected incorrectly is 0.02965 = 2.965%.

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

Using the above as a guide, we have the following:

Probability = 2% * 3.5% + 3% * 96.5%

Evaluate

Probability = 0.02965

Rewrite as

Probability = 2.965%

Hence, the probability is 2.965%.

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Question

The test to detect the presence of a certain protein is 98% accurate for corn plants that have the protein and 97% accurate for corn plants that do not have the protein.

If 3.5% of the corn plants in a given population actually have the protein, the probability that a randomly chosen plant is detected incorrectly is