When $720 is divided in the ratio 3:5, the larger share is

The natural response of the system is given by \(n(t) = A_1 e^{-2t} \sin(3t + \varphi) + A_2 e^{-2t} \cos(3t + \varphi)\),

The transfer function of a system describes the relationship between the input and output signals. It is defined as the Laplace transform of the system's impulse response. In this case, the transfer function is given as \(T(s) = \frac{3s - 12}{s^3 + 4s^2 + 13s}\).

To find the natural response of the system, we perform partial fraction decomposition. By decomposing the transfer function, we obtain \(T(s) = \frac{A}{s} + \frac{Bs + C}{s^2 + 4s + 13}\).

Multiplying both sides by \(s(s^2 + 4s + 13)\), we get \(3s - 12 = A(s^2 + 4s + 13) + (Bs + C)s\).

By substituting specific values of \(s\), we can determine the coefficients \(A\), \(B\), and \(C\).

Solving for \(A\), we substitute \(s = 0\) and obtain \(A = -\frac{12}{13}\).

For \(C\), we substitute \(s = -2\) and find \(C = -\frac{6}{13}\).

Finally, substituting \(s = 2\), we find \(B = \frac{9}{13}\).

Therefore, the transfer function \(T(s)\) can be written as \(T(s) = -\frac{12}{13s} + \frac{9s - 6}{s^2 + 4s + 13}\).

In summary natural response of the system with the given transfer function is characterized by the equation \(n(t) = A_1 e^{-2t} \sin(3t + \varphi) + A_2 e^{-2t} \cos(3t + \varphi)\).

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Answer:

y=6x+5  →equation 1

y=4x+5 → equation 2

you can either substitute equation 1 in 2 or equation 2 in 1

substituting equation 1 in 2,

y = 4x + 5

6x + 5 = 4x + 5

6x - 4x = 5 - 5

2x = 0

x = 0/2

x = 0

substituting x = 0 in equation 1, (to get y)

y = 6x + 5

y = 6(0) + 5

y = 0 + 5

y = 5

hope it helps you!!

The coefficient of variation is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit.

The coefficient of variation is a measure of relative risk that compares the standard deviation of a dataset to its mean. It is calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage. The formula for the coefficient of variation (CV) is as follows:

CV = (Standard Deviation / Mean) * 100

The coefficient of variation provides a standardized measure of risk per unit of mean. It is particularly useful when comparing the risk of different datasets or investments that have different scales or units of measurement. By dividing the standard deviation by the mean, the coefficient of variation allows for a comparison of the relative variability or riskiness of different datasets or investments.

In this sense, the coefficient of variation is considered a better measure of stand-alone risk than the standard deviation alone because it takes into account the magnitude of the mean. It provides a way to assess and compare the risk of different datasets or investments in a standardized manner, regardless of their scales or units of measurement.

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Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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Answer:

Volume of larger box: 480

Length of small box: 5

Width of small box: 4

Height of small box: 3

Volume of small box: 60

Ratio of small box to large box: 1/8

The resulting units are kilograms grams milligrams, mole grams liter, ft^2g mL ft gmL

To evaluate the given unit expressions, we can apply the rules of multiplying units similar to multiplying fractions.

(kilogram)(kilogram grams)(gram milligrams):

The units cancel out as follows:

(kilogram)(kilogram grams)(gram milligrams) = (kilogram)(grams)(milligrams)

Therefore, the resulting units are kilograms grams milligrams.

(mole)(mole grams)(gram liter):

The units cancel out as follows:

(mole)(mole grams)(gram liter) = (mole)(grams)(liter)

Therefore, the resulting units are mole grams liter.

(mL)(cmmg)(mLcm3):

The units cancel out as follows:

(mL)(cmmg)(mLcm3) = (mL)(cm mg)(cm^3)

Therefore, the resulting units are mL cm mg cm^3.

(f^2g)(mLft)(gmL):

The units cancel out as follows:

(f^2g)(mLft)(gmL) = (ft^2g)(mLft)(gmL)

Therefore, the resulting units are ft^2g mL ft gmL.

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y = f(x)

so f(14) = 11 means the input x = 14 leads to the output y = 11

The point (x,y) = (14,11) is on the f(x) curve.

Function f(14) = 11 implies that the outcome of a function at x = 14 the value of the function is 11.

Given that,
To specify what the function f (14) = 11 means.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f( 14 ) = 11
f( 14 ) = f( x )
x = 14
f( x ) = 11

Implies that,
f(x) = y
is function, when x = 14 the function gives y = 11 ,,means that for x = 14 the outcome of the function is 14.

Thus, function f(14) = 11 implies that the outcome of a function at x = 14 the value of the function is 11.

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Answer:43

Step-by-step explanation:

YOUR WECOME!!!!!

If that isnt the answer because i evaluated, try t=43/h :)

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The mean of the batting averages is 0.341125.

Mean is used to summarize a set of data, frequently to help determine the overall significance of the data set.

To find the mean of the batting averages, we need to sum up all the batting averages and divide by the total number of players.

Batting averages: .373, .360, .321, .321, .320, .312, .311, .311

Sum of batting averages = .373 + .360 + .321 + .321 + .320 + .312 + .311 + .311

Sum of batting averages = 2.729

Now, we divide the sum by the total number of players, which is 8:

Mean = Sum of batting averages / Total number of players

Mean = 2.729 / 8

Calculating the mean:

Mean ≈ 0.341125

The mean of the batting averages is approximately 0.341125.

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The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,

To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.

If the first letter is not 'a', we have the freedom to ch

oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.

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Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.

What are arithmetic operations?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.

3. Using pythagoras theorem, we get the equation as D² = 12² + 16².

⇒D² = 144 + 256

⇒D² = 400

⇒D = √400

⇒D = 20

4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.

So, the difference is 28-20= 8 miles

Hence, Jane travels 8 miles much farther than her trainer.

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Answer:

domain: (-∞,∞)

range: y=3

no x intercept

y intercept = (0,3)

The net operating income will be $ 5000.

The profitability of real estate assets that produce income is evaluated using a formula known as net operating income (NOI). NOI is the total revenue from the asset less all running costs that are deemed to be absolutely required.

Here we have  

A product has a selling price of $10 per unit, variable expenses of $6 per unit, and total fixed costs of $35,000.

In total 10,000 units are sold  

The net operating income will be computed by Subtracting all expenditures from all money collected on the product.    

Net operating income = ($10 - $6) × 10000 - $ 35000

= ($10 - $6) × 10000 - $ 35000  

=  $ 40000 - $ 35000

= $ 5000    

Therefore,

The net operating income will be $ 5000.

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\(\sf\purple{The\: square\: root \:of \:50\: is\: 5√2.}\)

\(\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}\)

Error made by Jaclyn ⤵

\( \sqrt{50} \)

\(\sf\red{=\:2√25}\) ❌

Correct way to solve it ⤵

\( \sqrt{50} \\ \\ = \sqrt{5 \times 5 \times 2} \\ \\ = \sqrt{ {5}^{2} \times 2} \\ \\ = \sqrt{ {5}^{2} } \times \sqrt{2} \\ \\ = 5 \sqrt{2} \\ \\ (∵ \sqrt{ {a}^{2} } = a)\)

\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)

Using Cooking measurements,

The value replacement for 3/4 cup is = 36 teaspoons or 12 tablespoons.

Cooking Measurements :

Calculate and determine the specific amounts of ingredients required using standard measuring equipment.

A measuring spoon, measuring cup, or measuring utensil.

Measuring Spoons come in a variety of sizes and materials. The smallest set of spoons measure smudges, pinches and dashes. Other sets include tsp (tsp) and tsp (tbsp)

we have given 3/4 cup and we want to replace it

Using the cooking measurement chart ,

1 cup = 16 tablespoons or 48 teaspoons

1/2 cup = 8 tablespoons or 24 teaspoons

we have 3/4 cup then

3/4 cup = 1 cup - 1/4 cup

1/4 cup = 4 tablespoons or 12 teaspoons

then , 3/4 cup = 16 tablespoons - 4 tablespoons

= 12 tablespoons or

3/4 cup = 48 teaspoons - 12 teaspoons

= 36 teaspoons

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i dont know ethrreer

Step-by-step explanation:

Answer:

Step-by-step explanation:The distributive property dictates that:

a(b + c) = ab + ac

Thus,

(0.7 x 0.7) + (0.7 x 0.9) + (0.7 x 0.2)

= 0.7(0.7 + 0.9 + 0.2)

follows the distributive property. The third option is correct.

overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

In two's complement representation, numbers are represented using a fixed number of bits. The most significant bit (MSB) is reserved to indicate the sign of the number, where 0 represents a positive number and 1 represents a negative number.

Overflow occurs in two's complement arithmetic when the result of an operation exceeds the range that can be represented with the available number of bits.

When overflow occurs, the result is truncated or wrapped around to fit within the bit representation. This wrapping around effectively causes the MSB to flip its value, changing the sign of the number. As a result, the number that was intended to be positive becomes negative in the two's complement representation.

For example, consider an 8-bit two's complement representation. The range for a signed 8-bit number is -128 to +127. If we add 1 to the maximum positive value of 127, overflow occurs because the result exceeds the range. The binary representation of 127 is 01111111, and adding 1 results in 10000000. Since the MSB changed from 0 to 1, the number is interpreted as -128 in two's complement representation.

In summary, overflow in two's complement arithmetic causes the wrap-around of the most significant bit, resulting in the representation of positive numbers as negative numbers.

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The conventional B/C ratio using the expected EUAC (Equivalent Uniform Annual Cost) can be computed as 1 / EUAC

To calculate the conventional B/C ratio using the expected EUAC, we need to determine the present value of costs and benefits over the project's life and then compare them.

Cost Data:

Year 1: $10,000

Year 2: $8,000

Year 3: $6,000

Benefit Data:

Year 1: $15,000

Year 2: $12,000

Year 3: $9,000

Life Probability Distribution:

Year 1: 0.2

Year 2: 0.5

Year 3: 0.3

To calculate the present value of costs and benefits, we multiply each cash flow by the respective probability and discount it to present value. Assuming a discount rate of r%, the present value (PV) can be calculated using the formula:

PV = Cash Flow / (1 + r)^n

where n is the year of the cash flow.

Calculating the present value of costs:

PV(Costs) = ($10,000 / (1 + r)^1) + ($8,000 / (1 + r)^2) + ($6,000 / (1 + r)^3)

Calculating the present value of benefits:

PV(Benefits) = ($15,000 / (1 + r)^1) + ($12,000 / (1 + r)^2) + ($9,000 / (1 + r)^3)

The expected EUAC can be calculated as the sum of PV(Costs) divided by the sum of PV(Benefits), considering the probabilities:

EUAC = (PV(Costs) * 0.2 + PV(Costs) * 0.5 + PV(Costs) * 0.3) / (PV(Benefits) * 0.2 + PV(Benefits) * 0.5 + PV(Benefits) * 0.3)

Finally, the conventional B/C ratio is obtained by taking the inverse of the EUAC:

B/C ratio = 1 / EUAC

The conventional B/C ratio using the expected EUAC for the given cost, benefit data, and life probability distribution can be computed using the provided calculations. This ratio allows for a comparison between the present value of costs and benefits over the project's life, considering the probability distribution.

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Answer:

1. D

2. A

3. B

4. C

5. i am not sure

Step-by-step explanation:

Hope This Helps!!!

The inverse function of \(A(b) = 12 \cdot \frac{b + 9}2\) is b(a) = a/6 - 9

The function is given as:

\(A(b) = 12 \cdot \frac{b + 9}2\)

Divide 12 by 2

\(A(b) = 6 \cdot (b + 9)\)

Rewrite the function as

\(a = 6 \cdot (b + 9)\)

Divide both sides by 6

a/6 = b + 9

Subtract 9 from both sides

b = a/6 - 9

Express as a function

b(a) = a/6 - 9

Hence, the inverse function of \(A(b) = 12 \cdot \frac{b + 9}2\) is b(a) = a/6 - 9

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Answer:

\(\dfrac{-79}{126}\)

Step-by-step explanation:

The given expression is :

\(\dfrac{-2}{3}+\dfrac{5}{7}+\dfrac{-8}{9}+\dfrac{3}{14}\)

The LCM of 3,7,9 and 14 is 126

So,

\(\dfrac{-2}{3}+\dfrac{5}{7}+\dfrac{-8}{9}+\dfrac{3}{14}=\dfrac{42(-2)+18(5)+14(-8)+9(3)}{126}\\\\=\dfrac{-79}{126}\)

So, the value of the given expression is equal to \(\dfrac{-79}{126}\).

Answer: Domain is \([0,\infty)\) and range is [0,4000].

Step-by-step explanation:

It is given that, the set of ordered pairs (t,d), where

t = the time in seconds after  someone jumps out of a plane at  4000 meters to go skydiving

d = is the displacement above the  ground.

It means t is independent variable and it is represented on the x-axis.

d is dependent variable and it is represented on the y-axis.

We need to find the domain and Range.

Domain is the set of input values.

Here, input is time and time can not be negative.

Domain \(=0\leq t=[0,\infty)\)

Range is the set of output values.

Here, output is displacement above the  ground which can not be negative or more than 4000 meters.

Range \(=0\leq d\leq 4000=[0,4000]\)

Therefore, domain is \([0,\infty)\) and range is [0,4000].

Answer:

f( -5)  -=  f- 5

x ∈     ℝ

Step-by-step explanation:

Answer:

D = 01000100

A = 01100001

D = 01000100

B = 01000010

A = 01100001

S = 01110011

E = 01100101

1 = 00110001

6 = 00110110

Answer:

-5a+3b

Step-by-step explanation:

just adding and subtracting like terms

Answer:

3b-5a

Step-by-step explanation:

hope this helps:)

Answer:

The given function is k(t) = cos(2πt/3).

The general form of a cosine function is A*cos(Bx - C) + D, where:

Comparing this form to the given function, we can see that:

Therefore, the amplitude of k(t) is 1, the period of k(t) is 3, the phase shift of k(t) is 0, and the vertical shift of k(t) is 0.

A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, prediction, or entertainment.

The most suspicious set of outcomes for a simulated game of chess that is supposed to be biased in favor of player B winning 4 out of 5 times would be if player B won all 30 games. This outcome would be highly unlikely if the game was truly random and the bias towards player B was accurate. Other suspicious outcomes could include player B winning 29 out of 30 games or player B winning 28 out of 30 games with a high margin of victory in each game.

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Answer:

Step-by-step explanation:

Convert the given amount to the given unit.

6 yd; ft