Find the slope of the line passing through the two points.

(12, 1), (36, 42)

Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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Two normal-curves with similar forms but distinct spreads will have the same mean but different standard deviations.

Since the centre of a normal distribution is determined by the mean, the centre of both curves on the horizontal axis will be the same. The spread of a normal distribution is, nevertheless, determined by its standard deviation. A smaller standard deviation indicates that the distribution is more tightly concentrated around the mean, whereas a bigger standard deviation indicates that the distribution is more dispersed.

Since extreme values are more likely to occur, the normal curve with the larger standard deviation will have more area under the curve in the tails. Extreme values are less likely to occur for the normal curve with the smaller standard deviation, which will have less area under the curve in the tails.

When compared to a normal curve with a smaller standard deviation, the larger standard deviation normal curve will visually appear wider and flatter. Both curves will have a bell-shaped curve with the highest point at the mean that is symmetrical around the mean.

Similarities:

The mean of both normal curves, which symbolises the distribution's centre, will be the same.

The mean will be the centre of symmetry for both normal curves.

The area under the curve for both normal curves will be equal to one.

Differences:

Greater standard deviation results in a wider normal curve than smaller standard deviation does.

The data will be more dispersed over the normal curve with a higher standard deviation, whereas the data will be more firmly grouped along the normal curve with a smaller standard deviation.

The peak of the normal curve with a higher standard deviation will be flatter than the peak of the normal curve with a lower standard deviation.

Overall, the two normal curves are comparable in that they both have the same mean, but they differ mostly in terms of their standard deviation, which has an impact on both their spread and the possibility of extreme values.

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The value of x in the geometric sequence is -3.

Option (A) is correct.

To find the value of x.

A progression of numbers with a constant ratio between each number and the one before .A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. For example, the sequence 1, 2, 4, 8, 16, 32… is a geometric sequence with a common ratio of r = 2.

Given that:

The geometric sequence are x, 3, -1/3.......

Let x  = a be  the first term

3 = a*r = x *r , is second term

r is the common ratio,

r =3/x

- 1/3 = ar^2 = x r^2

substitute r, and solve for x:

-1/3 = x*3*3/x*x

cancel out the x term from numerator and denominator we have,

-1/3=9/x

By cross multiplication,

x=-9/3

By simplifies

x=-3

first term is x = -3

So, the value of x in the geometric sequence is -3.

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Answer:

missing angle <60 and side lengths 5, 5\(\sqrt{3}\)

Step-by-step explanation:

we understand from the given information that  the triangle in question is a special right triangle

and since this is a special triangle the side lengths follows :

the side length that sees <90 is represented by 2x

the side length that sees <60 is represented by x\(\sqrt{3}\)

and the side length that sees <30 is represented by x

2x = 10 so x = 5 and  x\(\sqrt{3}\) = 5\(\sqrt{3}\)

Answer:

See attached

Step-by-step explanation:

Refer to attachment

One relation is a linear function

Second one is a graph of non-functional relation

Answer:

below

Step-by-step explanation:

For the first graph, we can use a linear function as it means "straight" lines so when we use the vertical lines test, it passes it (shown below).

We can use a U shaped line so it when we use the vertical line test, it passes through two points to resemble its not a function (shown below).

Best of Luck!

The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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The probability that if a random person is chosen from the group of lawyers, the person will be a liar is 38/45, or 0.84.

As a fraction: The probability is given as 38/45, which means that out of 45 people chosen randomly from the group of lawyers, 38 of them are expected to be liars.

As a decimal: To express the probability as a decimal, we divide the numerator (38) by the denominator (45):

38 ÷ 45 ≈ 0.8444444444444444

Rounded to two decimal places, this would be approximately 0.84.

As a percentage: To express the probability as a percentage, we multiply the decimal form by 100:

0.8444444444444444 * 100 ≈ 84.44%

Rounded to two decimal places, this would also be approximately 84.44%.

So, the probability that if a random person is chosen from the group of lawyers, the person will be a liar can be expressed as 38/45 as a fraction, approximately 0.84 as a decimal, or approximately 84.44% as a percentage.

This can be expressed as a fraction, decimal, or percentage, whichever is more helpful.

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Answer:

a) 1/2

b) y = 0.5x + 2,5

c) k = -3

Step-by-step explanation:

Given are points T(3, 4) and U(7,6).

To find the gradient of TU, you look at the incline in value in the y-direction, divided by the incline in value in the x-diretion.

(Uy- Ty) / (Ux- Tx)

substitute the values given and you get:

(6-4) / (7-3)

2 / 4

This gives you the answer on question a) The gradient of TU = 1/2

Any line is of the form y = ax + b with a = the gradient found in answer a) an b is the the value on the y-coordinate on the y axis, where the line TU intersects with the y-axis.

The whole next part is my attempt to explain to you something about getting the answer for b. Sorry if it is so long, but please take the time to read the explanation, and I hope it will help you to understand what is going on.

The gradient of TU = 1/2 which means that if you start on any point on the line, and then you go 2 units to the right and 1 up you will end upon another point on the line. That is because the quotient is the same. 2/4 = 1/2 = 0,5/1

The last quotient, 0,5/1 , also has the resulting value of 0,5.

This means that if you start on any point on the line, and then you go 1 unit to the right and 0.5 up, you will be on another point on the line.

ATTENTION : This means also, that if you start on any point on the line TU, and then you go 1 unit to the LEFT and 0.5 DOWN, you will be on another point on the line TU. If you understand this, than you have learned something important!

We need to know where the line TU intersects with the y-axis, and now we can use this to find that value?

Since point T(3,4) lies 3 units to the right of the y-axis, we need to go 3 units to the LEFT. But remember the incline of 0.5/1 ... For every unit you go to the left you need to go 0,5 unit DOWN to remain on the line.

If you go 3vunits to the left, how many units do you need to go down?

3 * 0.5 units which is 1.5.

Point T has an y coordinate of 4 so ... what will the y coordinate be if you go 3 units to the left?

4 - (1.5) = 2.5

So now finally we can write down the answer to question b).

y = 0.5x + 2,5

c) (k, k+ 8) lies on the line TU. So substitute that in y = 0.5x + 2,5

y = 0.5 * ( x ) + 2,5

k+8 = 0.5 * ( k + 8 ) + 2,5

k+8 = 0.5*k + 4 + 2,5

Bring all k values to the left of the equality sign, and all number values to the right.

k - 0.5*k = 4 + 2,5 - 8

0.5*k = 6,5 - 8

0.5*k = -1,5

multiply left and right of the = sign by 2 and you get your answer on question c).

k = -3

Answer:

A coupon for 30%

Step-by-step explanation:

A coupon takes the a certain percentage of a price and subtracts it (a discount). A coupon for 30% off takes 30% of the price which is $60 and subtracts it, same goes for the $20 off coupon. Because a greater percentage is being taken off of the price, the 30% off coupon would save someone more money.

    \(\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}\)

  2x+2<14?

  \(\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}\)

When solving an equation/inequality, We need to make sure that all numbers are on one side, And all variables are on the other.

Since we have numbers on both sides, we need to move them to one side (usually the right-hand side, RHS)

So, let's start ~

Subtracting 2 on both sides:-

\(\sf{2x < 12}\)

Now, Dividing by 2 on both sides:-

\(\sf{x < 6}\)

So numbers less than 6 will make this inequality true.

It's always a good idea to make sure our solution's correct.

In order to check whether or not our solution's correct, we need to plug it into our original inequality.

Let's take any number less than 6; Let's take 5:-

\(\sf{2(5) < 14}\)

Simplifying,

\(\sf{10 < 14}\)

Is 10 less than 14? Yes. Henceforth, Our solution's correct.

#TogetherWeGoFar ~

\(\rule{300}{1}\)

The fourth question asks for the probability of the interarrival time between customers falling within a specific range. The fifth question introduces variables X and Y, where X represents whether a customer's interarrival time exceeds a target value, and Y represents the total number of customers with interarrival times exceeding the target value.

In order to calculate the probability of the interarrival time falling between 15 and 45 seconds (0.25 and 0.75 minutes), we need to know the specific distribution of the interarrival times. The given question refers to A ∼ Exponential(λ) as a reasonable representation of the times. However, without knowing the specific value of λ, we cannot calculate the probability.
Moving on to variables X and Y, X is defined as 1 if a customer's interarrival time exceeds 30 seconds (0.5 minutes), and 0 otherwise. X follows a Bernoulli distribution, as it takes on two possible values. The probability distribution of X can be represented as P(X = 1) = p and P(X = 0) = 1 - p, where p represents the probability of a customer's interarrival time exceeding the target value.
Y represents the total number of customers with interarrival times exceeding the target value. Y follows a binomial distribution since it counts the number of successes (customers exceeding the target value) in a fixed number of trials (n = 500 customers), assuming each customer's interarrival time is independent. The probability distribution of Y can be calculated using the binomial probability formula.
It's important to note that without additional information about the specific values of λ and p, we cannot provide exact calculations for the probability distributions of X and Y.

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The largest possible volume of such a box, V(x), is 3√6 cubic feet.

1. Let x be the side length of the square base, and h be the height of the box.

2. The surface area of the box (without the top) is given by A = x^2 + 4xh.

3. Since we have 18 square feet of material, the equation for the surface area is 18 = x^2 + 4xh.

4. Solve for h:

h = (18 - x^2) / (4x).

5. The volume of the box is given by V(x) = x^2h.

6. Substitute the expression for h from step 4:

V(x) = x^2((18 - x^2) / (4x)).

7. Simplify the equation: V(x) = (18x - x^3) / 4.

8. To find the maximum volume, take the derivative of V(x) with respect to x:

dV(x)/dx = (18 - 3x^2) / 4.

9. Set the derivative equal to 0 and solve for x:

(18 - 3x^2) / 4 = 0.

10. Multiply by 4:

18 - 3x^2 = 0.

11. Add 3x^2 to both sides:

18 = 3x^2.

12. Divide by 3:

6 = x^2.

13. Take the square root:

x = √6.

14. Plug x back into the equation for h:

h = (18 - (√6)^2) / (4√6).

15. Simplify:

h = (18 - 6) / (4√6) = 12 / (4√6) = √6 / 2.

16. Calculate the maximum volume:

V(√6) = (√6)^2 * (√6 / 2) = 6 * (√6 / 2) = 3√6 cubic feet.

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Answer:

Their down payment is 20% of the purchase price.

Step-by-step explanation:

The down payment is $30,000 and the purchase price is $150,000.

To find the percentage, we can divide the down payment by the purchase price and multiply by 100:

($30,000 / $150,000) x 100% = 20%

Therefore, the down payment is 20% of the purchase price.

Answer: 2 \(\;\frac{2}{3}\) inches

Step-by-step explanation:

      Since we have two pieces of wood that are 1 1/3 inches thick, we will multiply 1 1/3 by 2.

(1 1/3) * 2 = 2 2/3

     The thickness is 2 \(\;\frac{2}{3}\) inches

P(Y₁ < 3, Y₂ > 6) is 0.0108 by integrating the given joint density function. P(Y₁ + Y₂ = 7) is 0.4472by integrating the same joint density function over the appropriate region.

To find P(Y₁ < 3, Y₂ > 6), we need to integrate the joint density function over the region defined by Y₁ < 3 and Y₂ > 6

P(Y₁ < 3, Y₂ > 6) = ∫∫\(e^{-(Y_1 Y_2)}\) dY₁ dY₂, where the limits of integration are Y₁ from 0 to 3 and Y₂ from 6 to infinity.

Using the formula for the integral of exponential functions, we have:

P(Y₁ < 3, Y₂ > 6) =\(\int\limits^6_\infty\)\(\int\limits^0_3\) \(e^{-(Y_1 Y_2)}\)  dY₁ dY₂

=\(\int\limits^6_\infty\) [-1/Y₂ \(e^{-(Y_1 Y_2)}\) ] from 0 to 3 dY₂

=\(\int\limits^6_\infty\) [(-1/3Y₂) + (1/Y₂\(e^{3Y_2}\))] dY₂

= [(-1/3) ln(Y₂) - (1/9)\(e^{3Y_2}\)] from 6 to infinity

= (1/3) ln(6) + (1/9)e¹⁸

≈ 0.0108

Therefore, P(Y₁ < 3, Y₂ > 6) ≈ 0.0108.

To find P(Y₁ + Y₂ = 7), we need to first determine the range of values for Y₂ that satisfy the equation. If we set Y₂ = 7 - Y₁, then Y₁ + Y₂ = 7, so we have:

P(Y₁ + Y₂ = 7) = P(Y₂ = 7 - Y₁)

We can then integrate the joint density function over the region defined by this range of values for Y₁ and Y₂:

P(Y₁ + Y₂ = 7) = ∫∫\(e^{-(Y_1 Y_2)}\) dY₁ dY₂, where the limits of integration are Y₁ from 0 to 7 and Y₂ from 7 - Y₁ to infinity.

Using the substitution Y₂ = 7 - Y₁ and the formula for the integral of , we have

P(Y₁ + Y₂ = 7) = \(\int\limits^0_7\) \(\int\limits^{ \infty} _{7-Y_1\) \(e^{-(Y_1(7- Y_1)}\)) dY₂ dY₁

= \(\int\limits^0_7\) \(e^{7Y_1}\)/49 - 1/7 dY₁

= (7/6)(e⁷/49 - 1)

≈ 0.4472

Therefore, P(Y₁ + Y₂ = 7) ≈ 0.4472.

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--The given question is incomplete, the complete question is given below " Let Y₁ and Y₂ have the joint density function

f(y₁,y₂) = {e^-(Y₁ Y₂)   Y₁ > 0, Y₂> 0

             {0,  elsewhere_

What is P(Y₁ < 3, Y₂>  6)? (Round your answer to four decimal places:) (b) What is P(Y₁+ Y₂= 7)? (Round your answer to four decimal places:)"--

Answers:

=========================================================

Explanation:

Part (a)

We are given a two-sided stem-and-leaf plot.

The stems are along the middle column. We have two sets of leaves (one set per class).

The stems are 5,6,7,8,9. The stems represent the tens digit of the test score. Each leaf is a units digit of the test score, so it means each leaf represents a different student (there are 15+20 = 35 leaves total)

In the bottom row we have the stem 9 to represent all the scores in the 90s. In fourth period, only one leaf is shown and that is 8. The score 98 is the only score in the 90s for fourth period. There are more 90s scores for fifth period because we have the three leaves 2, 2, and 9. They correspond to the scores 92, 92, and 99. It's possible to repeat leaves.

Fifth period has more scores in the 90s

---------------------------

Part (b)

The data set for the fourth period class is

{51, 53, 56, 57, 59, 61, 66, 66, 70, 71, 71, 77, 77, 86, 98}

To get this data set, read off each stem with their corresponding leaf. Eg: in the first row we have a stem of 5 pair with the right-most leaf of 1 to form the score 51. You should have 15 scores in this set.

If the data set isn't sorted from smallest to largest, then make sure to do so. After doing that, cross off the first and last items to end up with this smaller set (two less items in it from the previous set listed above)

{53, 56, 57, 59, 61, 66, 66, 70, 71, 71, 77, 77, 86}

Repeat the last step. Cross off the first and last items to get

{56, 57, 59, 61, 66, 66, 70, 71, 71, 77, 77}

Repeat again

{57, 59, 61, 66, 66, 70, 71, 71, 77}

and again

{59, 61, 66, 66, 70, 71, 71}

we keep going until we reach either one or two values left

{61, 66, 66, 70, 71}

{66, 66, 70}

{66}

The last item remaining is 66, which is the middle-most item. This is the median of the fourth period class scores.

We follow the same steps to find the median of the fifth period class.

The original data set for the fifth period class is

{51,53,58,60,60,61,61,61,64,66,67,73,78,79,85,87,88,92,92,99}

After crossing off each pair of outer items, to reduce the set one step at a time, you should end up with these two items in the very middle: {66,67}

The median is the midpoint of those values, so it is (66+67)/2 = 66.5

Or another way you could do it is to note there are 20 scores in the fifth period class, so the middle is between slots 10 and 11. The 10 is from 20/2 = 10. The values in slots 10 and 11 are 66 and 67 respectively, so the midpoint here is 66.5

So we found:

We can see that the fifth period class had the higher median score.

---------------------------

Part (c)

Fortunately, this part isn't as lengthy as part (b). To get the range, you subtract the largest and smallest items.

The fifth period has a slightly higher range, so those scores are slightly more spread out. More spread out scores means less consistency.

The height of the building is approximately 27.62 feet. Rounded to the nearest hundredth, the answer is 27.62 feet.

In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.

Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It is used to determine the distance between any two objects, including heavenly bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.

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Domain of first function is {-6, -1, 0, 3}.

Domain of second function is {-7, -6, -2, -1, 0, 1, 3, 9}.

Domain: It is the set of possible values that we are allowed to input in our function. Basically, these set of values is the x values in a function.

Domain is nothing but it is the the input value or the value of x.

The first function domain is:

D = {-6, -1, 0, 3}

The second function domain is:

D = {-7, -6, -2, -1, 0, 1, 3, 9}

Domain of first function is {-6, -1, 0, 3} and the domain of second function is {-7, -6, -2, -1, 0, 1, 3, 9}

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The domain of the function is {x | x = -4, -1, 3, 5, 6}.

To determine the domain of a function, we need to identify all the possible values that the independent variable (usually represented by x) can take.

In this case, the given function is represented by a set of ordered pairs: {(3, -2), (6, 1), (−1, 4), (5, 9), (–4, 0)}. The x-coordinate of each ordered pair represents the independent variable.

By examining the set, we can identify all the unique x-values present in the ordered pairs:

-4, -1, 3, 5, 6

These are the values that the independent variable can take in the given function.

Therefore, the domain of the function is {x | x = -4, -1, 3, 5, 6}.

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What is the domain of the given function?

{(3,-2), (6, 1), (−1, 4), (5, 9), (–4, 0)}

Ox|x = -4,-1, 3, 5, 6)

Oyly=-2, 0, 1, 4, 9}

Ox|x = -4, -2, -1, 0, 1, 3, 4, 5, 6, 9)

Oyly=-4,-2, -1, 0, 1, 3, 4, 5, 6, 9)

Answer:

\(25\pi t^2\)

Step-by-step explanation:

After \(t\) seconds, the radius is \(5t\).

So, the area is \(\pi(5t)^2=25\pi t^2\).

All of the required trigonometric ratios are:

1) sin θ = 4/5

cos θ = 3/5

tan θ = 4/3

sec θ  = 5/3

cosec θ = 5/4

cot θ = 3/4

2) cos θ = 5/6

sin θ = (√11)/6

tan θ = (√11)/5

cosec θ = 6/√11

sec θ = 6/5

cot θ  = 5/√11

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) We are given:

sin θ = 4/5

Thus: cos θ = 3/5

tan θ = 4/3

sec θ = 1/(3/5) = 5/3

cosec θ = 1/(4/5) = 5/4

cot θ = 1/(4/3) = 3/4

2) cos θ = 5/6

sin θ = (√11)/6

tan θ = (√11)/5

cosec θ = 1/((√11)/6) = 6/√11

sec θ = 1/(5/6) = 6/5

cot θ = 1/((√11)/5) = 5/√11

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The equilibrium real output, Y, is approximately 1,460 (rounded to the nearest integer) in the given IS-LM model, using the provided IS and LM equations.

To find the equilibrium real output, we need to set the IS equation equal to the LM equation and solve for Y.

Given:

IS equation: Y = 1,586.27 - 3,145.45i

LM equation: i = 0.04

Substituting the LM equation into the IS equation:

1,586.27 - 3,145.45(0.04) = Y

Simplifying:

1,586.27 - 125.82 = Y

1,460.45 = Y

Therefore, the equilibrium real output, Y, is approximately 1,460 (rounded to the nearest integer).

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To construct a histogram of the estimates and compare it to the above estimates, follow these steps:
1. Compile the data and organize it into groups or bins.
2. Assign each group a height or frequency, usually the number of occurrences in the group.
3. Represent each group by drawing a bar with the corresponding height.
4. Connect the tops of the bars to form a histogram.

Comparing the histogram to the above estimates, if the histogram is similar in shape and spread, then the estimates are consistent.

The best estimate of the random modifier without examining the value is the mode of the data, which is the value that occurs most often.

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Answer:

30

Step-by-step explanation:

\(c^{2} = b^{2} + a^{2} \\\) =  formula

a = 24

b = 18

576+324 = 900

do \(\sqrt{900} \\\)

= 30

Answer:

x = 18311.61 m

Step-by-step explanation:

It is given that, An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. The distance from the observer (O) to the bird (B) is 15,000 ft. We need to find the distance between the bird and the nest. It is based on trigonometry. So,

\(\sin (35)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

Let x is the distance between the bird and the nest

So,

\(\sin (55)=\dfrac{15000}{x}\\\\x=\dfrac{15000}{ \sin(55)} \\\\x=18311.61\ m\)

So, the distance between the bird and the nest is 18311.61 m.

Answer:

8,604

Step-by-step explanation:

Answer:250

Step-by-step explanation:

Answer:

Step-by-step explanation:

i needs more iformation

Answer: $5,895

Step-by-step explanation:

First you want to add the earnings in order to find the total value being taxed.

17,500 + 15,250 = 32,750

We can then find the percent as a decimal by dividing it by 100:

\(\frac{18}{100} = .18\)

We can then multiply the total earnings by this decimal to find the total income tax:

\(32,750 * .18 = 5,895\)

Hope this helps

Answer:

20cm

Step-by-step explanation:

a square has 4 equally long sides.

when we know its perimeter, that means we know the sum of all 4 sides.

since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.

80/4 = 20cm

The Laplace transform of the given IVP yields the expression Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2), which can be further simplified using partial fraction decomposition. The inverse Laplace transform of this expression gives us the final solution for y(t), which is a combination of cosine and sine functions with exponential decay.

Taking the Laplace transform of the given IVP, we get:
s^2Y(s) - sy(0) - y'(0) + k^2Y(s) = E(s) / (s-k)
Substituting y(0) and y'(0) as 0, we get:
s^2Y(s) + k^2Y(s) = E(s) / (s-k)
Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2)
Using partial fraction decomposition, we can express Y(s) as:
Y(s) = 1 / (s^2 + k^2) - (s+10) / ((s-10)*(s^2 + k^2))
Taking the inverse Laplace transform, we get:
y(t) = cos(kt) - e^10t * cos(kt) / k + sin(kt) / k
In summary, the Laplace transform of the given IVP yields the expression Y(s) = E(s) / (s-k) * 1 / (s^2 + k^2), which can be further simplified using partial fraction decomposition. The inverse Laplace transform of this expression gives us the final solution for y(t), which is a combination of cosine and sine functions with exponential decay.

To know more about Laplace visit:

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