Solve the initial value problem below using the method of Laplace transforms. y" - 12y' + 72y = 40 e 4 y(0) = 1, y'(0) = 10

Answer:

C. 8, H. 6x^2+43x+55

Step-by-step explanation:

You're looking for a value that will make x-2=6, since you add exponents. So W^8/W^-2 is equal to 1/W^6. Since 8-2=6.

A= length * width

(2x+11)(3x+5), foil it out by taking 2x(3x+5), then 11(3x+5).

6x^2+10x+33x+55, combine like terms

6x^2+43x+55

Answer:

26. H: \(6x^2+43x+55\)

Step-by-step explanation:

\(( 2x + 11 ) ( 3x + 5 )\)

\(6x^2+43x+55\)

Answer:

For the first one if solving for y, y=−8x−16. If solving for x,

x= −1/8y-2

For the second one if solving for y, y=3x−5 and if solving for x,

x=1/3y +5/3

Answer:

60/200

Step-by-step explanation:

credit to pawlossolomon

There are 600 different combinations of 2 students that can be chosen from a class of 25, where the order of selection does not matter.

The number of different combinations of 2 students that can be chosen from a class of 25, where the order of selection does not matter, can be calculated using the concept of combinations.

The formula to calculate combinations is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of students and r is the number of students to be chosen.

In this case, we have 25 students and we want to choose 2 students. Plugging these values into the formula:

C(25, 2) = 25! / (2!(25-2)!)

Simplifying further:

C(25, 2) = 25! / (2! * 23!)

Since 2! equals 2 and 23! equals 23 * 22 * 21 * ... * 2 * 1, many terms in the numerator and denominator will cancel out:

C(25, 2) = (25 * 24) / (2 * 1)

C(25, 2) = 600

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Answer:

450+120w

will be the expression

Equation: 450+120w = x

The solution of the given inequality is h > 4.5 and it is shown by the blue-shaded line in the number line.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given inequality,

2 > 8 - (4/3)h

Subtract both sides by 2

0 > 8 - 2 - (4/3)h

0 > 6 - (4/3)h

Subtract 6 on both sides,

-6 > -(4/3)h

Multiply by -3/4

-6(-3/4) <-(4/3)(-3/4)h   (since inequality sign changes by multiplying with negative)

h > 18/4

h > 4.5

The plot of this region in the number line is shaded with a blue line.

Hence "The solution of the given inequality is h > 4.5 and it is shown by the blue-shaded line in the number line.".

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Answer:

Saleh is x years old. And 10 years ago he was 100 years old.

Suha is x years old. Saleh is 10 years younger than Suha. Saleh is 100 years old.

Answer:

20,000 per sq. km.

Step-by-step explanation:

In this question, the variable k represents the total number of people in a single square km. Since we are provided both the total number of the population and the total square kilometers of the land, we can calculate the value of k by dividing the population size by the total land. Therefore, the calculation would be the following...

\(\frac{10,400,000 people}{520km^{2} }\) = k

20,000 per sq. km. = k

Finally, we can see that the value of k is 20,000 per sq. km.

Answer:

1067/10000

Step-by-step explanation:

simple

The number of ways to select a simple random sample of size 5 from a population of 7 children in a family is equal to 21ways.

As given in the question,

Number of children in the family 'n' = 7

Number of simple random sample of size  = 5  ( without replacement )

Number of ways to select the children defines a population

= ⁷C₅

= ( 7! ) / ( 7 - 5 )! ( 5! )

= ( 7 × 6 × 5! )/ ( 2! ) ( 5! )

= 7 × 3

= 21 ways

Therefore, the number of ways to select children of simple random sample of size 5 is equal to 21ways.

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The critical value, tc, for a confidence level of c0.90 and sample size n=16 can be found using a t-distribution table. The degrees of freedom for this calculation is n-1, which in this case is 15. From the table, we find that the tc value is approximately 1.753. This means that if we take a sample of size 16 from a population and calculate a sample mean, we can be 90% confident that the true population mean falls within a range of ± tc multiplied by the standard error of the sample mean. The critical value tc is an important factor in calculating confidence intervals for sample means.

To find the critical value, we need to use a t-distribution table, which provides the t-scores for various levels of confidence and degrees of freedom. The degrees of freedom for this calculation is n-1, which is 16-1=15. We look for the row in the table that corresponds to 15 degrees of freedom and then find the column that corresponds to a confidence level of 0.90. The value at the intersection of this row and column is the critical value, which in this case is approximately 1.753.

The critical value tc for a confidence level of c0.90 and sample size n=16 is approximately 1.753. This value is important in calculating confidence intervals for sample means, which allows us to estimate the range within which the true population mean is likely to fall with a certain level of confidence.

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Answer:

+ x = 116/9

- x = 40

* x = -2/3 and x = 59/3

/ x =  -2/3

Step-by-step explanation:

Since it's unclear what operations here are all of them, plus, minus, multiply and divide. If you need Steps, let me know.

Answer:

D I did the test on Ed.......................................

To evaluate the line integral using Green's Theorem, we first need to find the curl of the given vector field. The vector field in this case is F(x, y) = (e^x cos(2y), -2e^x sin(2y)).

Using the partial derivative notation, we have:

∂F/∂x = (d/dx)[e^x cos(2y)] = e^x cos(2y)

∂F/∂y = (d/dy)[-2e^x sin(2y)] = -2e^x cos(2y)

Now, we can calculate the curl of F:

curl(F) = ∂F/∂x - ∂F/∂y = e^x cos(2y) + 2e^x sin(2y)

Next, we need to find the area enclosed by the curve C, which is described by the equation x^2 + y^2 = a^2, where 'a' is a constant representing the radius of the circle.

To apply Green's Theorem, we integrate the curl of F over the region enclosed by C. However, since the given curve C is a closed curve, the integral of the curl over this region is equal to the line integral of F around C.

Using Green's Theorem, the line integral is given by:

∮C F · dr = ∬R curl(F) · dA

Here, ∮C represents the line integral around the curve C, ∬R denotes the double integral over the region enclosed by C, F · dr represents the dot product of F with the differential element dr, and dA represents the area element.

Since the region enclosed by C is a circle, we can use polar coordinates to evaluate the double integral. Setting x = r cosθ and y = r sinθ, where r ranges from 0 to a and θ ranges from 0 to 2π, we have dA = r dr dθ.

Substituting the values into the line integral expression, we have:

∮C F · dr = ∫[0 to 2π]∫[0 to a] (e^(r cosθ) cos(2r sinθ) + 2e^(r cosθ) sin(2r sinθ)) r dr dθ

Evaluating this double integral will yield the final result of the line integral. However, due to the complexity of the expression, it may not be possible to find an exact closed-form solution. In such cases, numerical methods or approximations can be employed to estimate the value of the line integral.

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Answer:

F

Step-by-step explanation:

The smallest angle will be opposite the smallest side

F

The smallest angle is ∠DFE.

A polygon which has three sides and three vertices is called as triangle.

The sum of all the angles of the triangle is 180°.

Given:

Triangle DEF with sides d, e, and f opposite angles D, E, and F respectively.

And the side:

d=14, e = 12, and f = 10

To find the smallest angle:

The smallest angle is opposite to the smallest side.

And the smallest side is f = 10.

Let the angle opposite to f is ∠DFE.

Therefore, the smallest angle is ∠DFE.

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Answer:

boring

Step-by-step explanation:

To prove the given identity, we'll start with the left side and simplify it step by step until we obtain the right side of the equation:

We have:

((sec y - tan y)(sec y + tan y)) / sec y

Using the difference of squares, we can rewrite the numerator:

((sec y)^2 - (tan y)^2) / sec y

Recall the trigonometric identity: (sec x)^2 - (tan x)^2 = 1

Substituting this identity into our expression:

(1) / sec y

Using the reciprocal identity: sec x = 1 / cos x

We can rewrite the expression as:

1 / (1 / cos y)

Simplifying further by multiplying by the reciprocal:

cos y / 1

Which simplifies to:

cos y

Therefore, we have shown that the left side of the identity ((sec y - tan y)(sec y + tan y)) / sec y simplifies to cos y, which is the same as the right side of the equation.

Answer:

104°

Step-by-step explanation:

The principle to apply here is that angle subtended at the center of a circle is twice the angle at circumference.

  Angle subtended at arc  = 52°

  Angle at the center  = 2 x 52°  = 104°

Answer:

104°

Step-by-step explanation:

Answer:

The slope is -3 and the y intercept is 7

Step-by-step explanation:

3x+y = 7

We can write the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -3x+7

The slope is -3 and the y intercept is 7

Answer:

23/12

Step-by-step explanation:

5/6 + 3/4 + 1/3

=> 10/12 + 9/12 + 4/12

=> 23/12

Therefore, 23/12 is the answer.

Hoped this helped.

Answer:

16 boys total

8 girls total

Step-by-step explanation:

We know that Hillary invited 23 of her friends, including her, this lets us know there are 24 people total.

Given, we already know 8 of that 24 are boys, which leaves us with 16 people left.

24 - 8 = 16

We simply know there are 8 girls and 8 boys from this problem and on top we add 8 more boys because there are 8 more boys.

_______________________________

Total = 1 + 23 = 24

Girls:

x + (x + 8) = 24

2x = 16

x = 8

Boys:

x + 8 = 1b

Answer:

B, \(8\sqrt{2}\)

Step-by-step explanation:

Diagonals of a square are congruent so AC= 4

using pythagorean theorem we can then do \(x^{2} +x^{2}\)=\(4^{2}\)

\(2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}\)

Then for perimeter we times the \(2\sqrt{2}\) by 4 and get

\(8\sqrt{2}\)

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Answer:

A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.

Answer: 96$

Answer:

The washer costs $723 and the dryer $241.

Step-by-step explanation:

Represent the cost of the washer by w and that of the dryer as d.

Then w = 3d.

Since w + d + $964, we get 3d + d = $964, or 4d = $964, or d = $241.

Three times that is $723.

The washer costs $723 and the dryer $241.

Answer:

X=1/2, -2/5

Step-by-step explanation:

Solve the equation for X by finding a, b, and c of the quadratic then applying the quadratic formula.

Answer:

:) :) :) :) :) :) :0

Step-by-step explanation:

2/5 and 1/2

For part (a), we can use Cauchy's Integral Formula which states that for a function f(z) that is analytic inside and on a simple closed contour C, and a point a inside C, we have:   The value of the integral is 2πi i0^(m+1).


f^(m)(a) = (1/2πi) ∮ C f(z)/(z-a)^(m+1) dz

where f^(m)(a) denotes the m-th derivative of f evaluated at a, and the integral is taken counterclockwise around C.

In our case, we have f(z) = 1, which is analytic everywhere, and C is the circle {izl = r} with counterclockwise orientation. So we can write:

iizml dz = i(1/2πi) ∮ {izl = r} 1/(z-i0) dz

where i0 is any point inside the circle, and the integral is taken counterclockwise around the circle.

Using Cauchy's Integral Formula with a = i0 and m = 0, we get:

iizml dz = i

So the value of the integral is just i.

For part (b), we need to evaluate the derivative of the integral, which is:

d/dz (iizml) = -m iizm-1

Using Cauchy's Integral Formula with a = i0 and m = 1, we get:

iizmlldzl = i(-m) (1/2πi) ∮ {izl = r} z^(m-1)/(z-i0)^2 dz

Note that the only difference from part (a) is the z^(m-1) term in the integral. We can simplify this using the Residue Theorem, which states that for a function f(z) that has a pole of order k at z = a, we have:

Res[f(z), a] = (1/(k-1)!) lim[z->a] d^(k-1)/dz^(k-1) [(z-a)^k f(z)]

In our case, the integral has a simple pole at z = i0, so we have:

Res[z^(m-1)/(z-i0)^2, i0] = lim[z->i0] d/dz [(z-i0)^2 z^(m-1)] = i0^m

Therefore, we can write:

iizmlldzl = -2πi Res[z^(m-1)/(z-i0)^2, i0] = -2πi i0^m

Note that the minus sign comes from the fact that the residue is negative. So the value of the integral is -2πi i0^m.

For part (c), we need to evaluate the integral of z^m around the same circle. Again, we can use Cauchy's Integral Formula with a = i0 and m = -1, which gives:

izm dz = (1/2πi) ∮ {izl = r} z^(m+1)/(z-i0) dz

Using the Residue Theorem, we can find the residue at z = i0, which is:

Res[z^(m+1)/(z-i0), i0] = lim[z->i0] z^(m+1) = i0^(m+1)

Therefore, we can write:

izm dz = 2πi Res[z^(m+1)/(z-i0), i0] = 2πi i0^(m+1).

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Answer:

Its 3 square units

Step-by-step explanation:

The distinguishing feature of ecological economics is the concept of steady-state economies that neither grow nor shrink.

This concept recognizes the finite nature of natural resources and the need to balance economic activity with ecological limits.

Unlike traditional neoclassical economics, which assumes that growth is always desirable, ecological economics emphasizes the need for sustainable development that maintains ecological integrity while meeting human needs.

Additionally, ecological economics recognizes that environmental damage and benefits are external to the market system and must be internalized through policies like carbon taxes and cap-and-trade systems.

While cost-benefit analysis is an important tool in ecological economics, it is used within the framework of steady-state economics and sustainable development rather than as a justification for unlimited economic growth.

Finally, ecological economics rejects greenwashing as a means of increasing public acceptance of products, recognizing that true sustainability requires fundamental changes in economic and social systems.

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The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

When studying the incidence of rare phenomena, researchers should use "relatively large samples". Using a large sample corrects for bias. If bias has been eliminated, it is safe to assume that the sample is free of sampling errors." The effects of random sampling errors are predictable in the long run.

One of the most effective methods that can be used by researchers to avoid sampling bias is simple random sampling, in which samples are chosen strictly by chance. This provides equal odds for every member of the population to be chosen as a participant in the study at hand.

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

Non-probability sampling often results in biased samples because some members of the population are more likely to be included than others.

To avoid non-response bias, researchers should keep surveys as simple as possible, with clear wording and instruction and seek respondents who are relevant to the survey topic.

Therefore,

The prevalence of sampling errors can be reduced by increasing the sample size. As the sample size increases, the sample gets closer to the actual population, which decreases the potential for deviations from the actual population.

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Answer:

y =  ( c-ax)/b

Step-by-step explanation:

ax + by = c

Subtract ax from each side

ax-ax + by = c-ax

by = c-ax

Divide each side by b

by/b = ( c-ax)/b

y =  ( c-ax)/b

Answer:

Step-by-step explanation:

Yes it is correct. :)

Answer:

Yeah, You're correct

Step-by-step explanation:

Have a nice day