Write the given second order equation as its equivalent system of first order equations

Nag basa nito walang jõwa

The Laplace transformation of given equation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

According to the statement

we have given that the equation and we have to find the Laplace transformation of that equation.

So, For this purpose, we know that the

Laplace transformation is an integral transform that converts a function of a real variable to a function of a complex variables.

And the given equation is

y'' − 6y' + 13y = 0, y(0) = 0, y'(0) = −9

To convert into the Laplace transformation

firstly find the single derivative of given equation in the Laplace transformation and put y = -9 in this.

And now find second derivative of given equation in the Laplace transformation.

And and put y = 0 in the given equation.

After the Laplace transformation give value as a Laplace transformation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

So, The Laplace transformation of given equation is [tex]y=-\frac{9}{2}e^{3t}\sin \left(2t\right)[/tex].

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With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:

A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)

A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²

A = 276 cm²

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

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#1

The unit is pounds

#2

So

#3

We shall use cups

#4

We should use pints

Answer:

1. pounds (lb)

2. pints (pt)

3. teaspoon (tsp)

4. cups (c)

Step-by-step explanation:

Liquid

128 fl oz = 16 cups = 8 pints = 4 quarts = 1 gallon

Mass

32000 ounces = 2000 pounds = 1 ton

1.  The best US standard unit in which to measure pumpkin with a mass of 1.2 kg would be pounds (lb).

⇒ 1 kg ≈ 2.205 lb

⇒ 1.2 kg ≈ 1.2 × 2.205 = 2.65 lb

2. The best US standard unit in which to measure stock with a volume of 1.5 L would be pints (pt).

⇒ 1 L ≈ 2.133 pt

⇒ 1.5 L ≈ 1.5 × 2.113 = 3.17 pt

3. The best US standard unit in which to measure sugar of 5 mL would be teaspoon (tsp).

⇒ 5 mL = 5 g ≈ 1 teaspoon

4.  The best US standard unit in which to measure yogurt with a volume of 0.25 L would be cups (c).

⇒ 1 L ≈ 4.167 c

⇒ 0.25 L ≈ 0.25 × 4.167 =  1.04 c

The answer is 0.

The expression in algebraic form is :

We know subtracting a term from its equivalent term will be 0.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

“[tex]\textsf{x minus x}[/tex]”

[tex]\huge\textbf{Simplifying it: }[/tex]

[tex]\textsf{x minus x}[/tex]

[tex]\mathsf{= x - x}[/tex]

[tex]\mathsf{= 1x - 1x}[/tex]

[tex]\mathsf{= 0x}[/tex]

[tex]\mathsf{= 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak 0}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The value of x is $30.

From the question, it can be deduced that Jeremy's investment account earns a compound interest. Compound interest is when the amount invested and the interest that has already accrued increases in value anytime interest is paid.

The formula that can be used to determine the value of x is:

x = FV / (1+r)^t

X = 480 / (2^4) = $30

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[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]

Answer:

8000/100+80/100=80+0.8=80.8

Step-by-step explanation:

hope this helps (❁´◡`❁)

The trigonometric values we require :

[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]

Now, let's solve for x.

tan 45° - cos 60° = x (sin 45°)

[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]

[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]

[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]

[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]

The value of x is 1/√2.

I hope it helped you solve the problem

Good luck on your studies!

Answer:

A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5.

Answer:

The second function (second graph and choice)

Step-by-step explanation:

If you look at the second function you will see that within the closed interval [-3,-2] the graph y  values are positive

First choice is incorrect since at x = -2  the y value is negative

Third choice incorrect since at x = -2, y value is negative

Fourth choice incorrect since y value is negative for x = -2

There are 7 ones on the left and only 2 on the right. The two sides need to be even, or balanced.

7 = 2 + r

r = 5

Hope this helps!

Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are given by:

n = 100, p = 0.88.

Hence the mean and the standard deviation for the approximation are:

The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:

Z = (89.5 - 88)/3.25

Z = 0.46

Z = 0.46 has a p-value of 0.6772.

1 - 0.6772 = 0.3228.

0.3228 = 32.28% probability that at least 90 cars pass inspection.

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A cell's expected frequency can be defined as the number of people in its row divided by the total number of people, multiplied by the number in its column and is therefore denoted as option C.

This is defined as the number of occurrences of a repeating which takes place per unit time.It also helps to measure how frequent something occurs when counted or observed and is also used in the calculation of the  different types of statistical data present or given.

This type of frequency is theoretical and are values which will most likely be in an experiment. it is calculated by multiplying the number in its column by the number of people in the row and dividing by the total number of people in this context.

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Answer:

Width is 11 inches

Step-by-step explanation:

I am not sure what the question is.  I think you might be looking for the width length.  The perimeter is the distance around a rectangle.  If the whole distance around is 48.  We have 2 lengths and 2 widths.  They tell us that the length is 13.  We have two lengths so the lengths add up to 26.  We can subtract that from 48 and that leaves us with 22 (48-26)  This is the total for the 2 widths.  Since the 2 widths are the same length we divide that number by 2 to get 11.

11 + 11+ 13 + 13 = 48

She has 38 nickels

N as the number of nickels, D as the number of dimes, and Q as the number of quarters.

She has 140 coins in total, so we can writen:

N + D + Q  = 140.

And the total value is $19.00

Then we have:

N*0.05 + D*0.10 + Q*0.25 = 19

And "The difference in the number of dimes and the number of quarters is 10."

D - Q = 10.

So we have a system of 3 equations and 3 variables:

N + D + Q  = 140

N*0.05 + D*0.10 + Q*0.25 = 19

D - Q = 10.

First, let's isolate one of the variables in the third equation, i will isolate D.

D = 10 + Q.

Now we can replace this in the other two equations:

N + (10 + Q) + Q = 140

N*0.05 + (10 + Q)*0.10 + Q*0.25 = 19.

Now we can isolate Q in the first equation:

N + 10 + 2*Q = 140

2*Q = 140 - 10 - N

Q = 130/2 - N/2. = 65 - N/2

Now we can replace this in the other equation:

N*0.05 + 10*0.10 + Q*(0.10 + 0.25) = 19

N*0.05 + 10*0.10 + (65 - N/2)*( 0.35) = 19

Now we can find the number of nickels.

N*0.05 + 1 + 22.75 - N*0.175 = 19

23.75 - N*(0.175 - 0.05)  = 19

23.75 - 19 = N*0.125

4.75/0.125 = N

38 = N

She has 38 nickels

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Using the median concept, it is found that:

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

Researching the problem on the internet, we have that there are 21 5th grade students. It is an odd number, hence the median is the 11th element, as (21 + 1)/2 = 11. Looking at the dot plot, the median is of 13.

There are 23 5th grade students. It is an odd number, hence the median is the 12th element, as (23 + 1)/2 = 12. Looking at the dot plot, the median is of 17.

The relationship is that 7th grade students have a higher median than 5th grade students.

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Answer: [tex]\Large\boxed{\angle DAB=62^\circ}[/tex]

Concept:

Here, we need to know about the idea of a cyclic quadrilateral.

In a cyclic quadrilateral, the sum of either pair of opposite angles is supplementary, which means they add up to 180°.

Please refer to the attachment below for a graphical explanation

Solve:

Given information

∠DAB = 2x + 4

∠ABC = 4y + 4

∠BCD = 4x + 2

∠CDA = 3y + 8

Derived formula from the concept

∠DAB + ∠BCD = 180°

∠ABC + ∠CDA = 180° (Not Important)

Substitute values into the formula that includes ∠DAB

∠DAB + ∠BCD = 180°

(2x + 4) + (4x + 2) = 180

Combine like terms

2x + 4 + 4x + 2 = 180

2x + 4x + 4 + 2 = 180

6x + 6 = 180

Subtract 6 on both sides

6x + 6 - 6 = 180 - 6

6x = 174

Divide 6 on both sides

6x / 6 = 174 / 6

x = 29

Substitute values into the angle expression of ∠DAB

∠DAB = 2x + 4

∠DAB = 2 (29) + 4

∠DAB = 58 + 4

[tex]\Large\boxed{\angle DAB=62^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).

The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.

In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)

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Correct match for the quadratic equation are:

A. {-4, 4}

B.  {-5, 5}

C.  {-8, 8}

D.  {-11, 11}

E.  {3,-3}

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

2x² - 32 = 0

Adding thirty-two to both sides of the equation:

2x² = 32

Dividing between two on both sides of the equation:

x² = 322

x² = 16

Applying square root to eliminate the exponent:

x =  ±√16

x =  ±4

4x² - 100 = 0

Adding hundred to both sides of the equation:

4x² = 100

Dividing between four on both sides of the equation:

x² = 100/4

x² = 25

Applying square root to eliminate the exponent:

x = ±√25

x = ±5

x² - 55 = 9

Adding fifty-five to both sides of the equation:

x² = 9 + 55

x² = 64

Applying square root to eliminate the exponent:

x = ±√64

x =  ±8

x² - 140 = -19

Adding one- fourty to both sides of the equation:

x² = -19 + 140

x² = 121

Applying square root to eliminate the exponent:

x = ±√121

x = ±11

2x² - 18 = 0

Adding eighteen to both sides of the equation:

2x² = 18

Dividing between two on both sides of the equation:

x² = 182

x² = 9

Applying square root to eliminate the exponent:

x = ±√9

x = ±3

Correct match for the quadratic equation are: A. {-4, 4},B.  {-5, 5},

C. {-8, 8},D.  {-11, 11},E.  {3,-3}

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I understand that the question you are looking for is:

Match each quadratic equation with its solution set.

A. 2x2 - 32 = 0  {-8, 8}

B. 4x2 - 100 = 0  {-4, 4}

C. x2 - 55 = 9          {-5, 5}

D. x2 - 140 = -19         {-11, 11}

E. 2x2 - 18 = 0  {3,-3}

Answer:

$40/unit?

Step-by-step explanation:

I'll assume the the fixed and variable costs are for 2000 units.

Fixed Costs = $35,000

Variable Costs = $45,000

Tota Costs = $80,000

The selling price can be anything. Free and we lose $80,000; $40 each, net profit of $0; $100 each for a net profit of $120,000.

In the absence of any infoprmation regarding selling price (e.g., 50% profit margin), I'd select the $40/unit selling price since that is breakeven.

The probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex] .

According to the question

we roll one fair six-sided die, and flip six coins

i.e

The Total Outcomes is the product of the sample spaces for the dice and the coins.  

sample spaces for the dice = 6

sample spaces for the coins = 2⁶

S = 6.2⁶

S = 384

Now, The  probability is

Therefore, the Favorable Outcomes

Consider the number of ways to get each total of heads from 1 to 6.

= 2⁶-1 (as TTT is excluded )

= 63

The probability that the number of heads is equal to the number showing on the die

As

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

By substituting the values in the formula

Probability(Event) = [tex]\frac{63}{384}[/tex]

Probability(Event) = [tex]\frac{21}{128}[/tex]

Hence, the probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex]

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Answer: (-4, 0) and (4, 8)

Step-by-step explanation:

Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)

The probability of event A and event B IS  15/91.

What is the probability?

Probability determines the odds that a random event would occur. The odds lie between 0 and 1.

The probability of event A  = number of brown marbles / total number of marbles

= 6/14

The probability of event B = number of orange marbles / total number of marbles -1

= 5/13

P(A and B) =6/14 x 5/13

                 = 30/182

                 = 15/91

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Answer:

B.) 5/13

Step-by-step explanation:

15/3=5

91/7=13

5/13

BRAINEST IS VERYYYY APPRECATED

I assume that 0.53 with a bar means the decimal fraction in which 3 is repeating.

24/45, 8/15, and 48/90 all result in the same decimal value. Thus, we are simply looking for the one that is fully simplified.

The correct answer is 8/15.

Hope this helps!

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the volume of each chocolate. Hence:

6 * volume of each chocolate = (380 - 300) ml

6x = 80

Divide both sides of the equation by 6:

x = 13.33 ml

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

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The value of x that would make ABCD a parallelogram is x = 5

A parallelogram, opposite sides are equal and parallel, which means opposite interior angles are equal.

Opposite sides of a parallelogram are congruent and parallel

Therefore,

5x - 3 = 14x - 48

subtract 5x from both sides

5x - 5x - 3 = 14x - 5x - 48

-3 = 9x - 48

add 48 to both sides

-3 + 48 = 9x - 48 + 48

45 = 9x

x = 45 / 9

x = 5

Therefore, the value of x that would make ABCD a parallelogram is x = 5

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The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

We are given;

Total number of objective questions = 5 questions

Number of choices of first 2 questions = 3 choices

Number of choices of last 3 questions = 4 choices

Number of ways of answering the first 2 questions = 3 * 3 = 9 ways

Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways

Total number of ways of answering the five questions = 9 * 64 = 576 ways

Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.

Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144

Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192

The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

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Answer:

a) 175 m

b) 20 cm

Explanation:

scaled size → actual size

1 cm represents 25 m

a)

In the scaled size on the map, the distance from church to village is 7 cm.

Then actual size,

1 cm → 25 m

7 cm → (25 × 7) m

7 cm → 175 m

b)

half a kilometer = 0.5 km = 500 m

Then scaled size,

25 meter → 1 cm

500 meter → 500/25 cm = 20 cm

The percent is the new value of the house of the price they paid 20 years ago is 216.67%.

percent is the new value of the house = New price / Old price

= 520,000 / 240,000 × 100

= 2.16666666666666

= 216.666666666666%

Approximately,

percent is the new value of the house = 216.67%

Therefore, the percent is the new value of the house of the price they paid 20 years ago is 216.67%.

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Considering the given box plots, we have that:

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for class A, we have that:

Then:

Hence, for class B, we have that:

Then:

Hence the correct options are given as follows:

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