Solve the non-homogeneous IVP: y'(t)=-X(t) (x(0)= 1,7(0) = 0 a. using the matrix exponential method, b. using any other method of your choice. . Find a Fundamental Matrix 0(t) and solve the IVP: x'= 3y 1 y' = 3* (x(0) = 1, y(0)=0 , for x(t) and y(t).

Answer:315

Step-by-step explanation:

441 divide by 7 then what u get multiply by 5

The percent error in Mark's estimate of the distance from his house to his school is approximately 6.9%. This value represents the difference between Mark's estimate and the actual distance, relative to the actual distance, expressed as a percentage.

To calculate the percent error, we first find the absolute difference between the estimate and the actual value: |15.5 - 14.5| = 1. Then, we divide this difference by the actual value and multiply by 100 to express it as a percentage: (1/14.5) * 100 ≈ 6.9%.

In summary, Mark's estimate has a percent error of approximately 6.9%, indicating that his estimation is about 6.9% higher than the actual distance between his house and school.

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Answer:

i think 60 miles

Step-by-step explanation:

I just added the 100+40 then

200-140

Answer:

  1 3/7 hours

Step-by-step explanation:

The planes are closing the 200 mile separation distance at a rate of (40 +100) = 140 miles per hour. The time it takes for that distance to be closed is ...

  time = distance/speed

  time = (200 mi)/(140 mi/h) = 200/140 h = 10/7 h = 1 3/7 h

The planes will meet after 1 3/7 hours, about 1 hour 25 minutes 43 seconds.

The exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

To find a model for P(t), representing the U.S. population in 1960, we need to determine the growth or decay rate over time. Without additional information or assumptions about the population growth, we cannot provide an exact model. However, we can explore two common models: exponential growth and linear growth.

1. Exponential Growth Model:

If we assume that the U.S. population experienced exponential growth, we can use the formula P(t) = P₀ * e^(rt), where P₀ represents the initial population, r is the growth rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

Using the given information that the U.S. population in 1960 was 181 million, we can write the equation as follows:

181,000,000 = P₀ * e^(r * 1960)

2. Linear Growth Model:

Alternatively, if we assume that the U.S. population grew linearly, we can use the formula P(t) = mt + b, where m is the slope (rate of change) and b is the y-intercept.

Using the given information, we can form an equation as follows:

181,000,000 = m * 1960 + b

Without further information or data points, we cannot determine the exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

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Answer:

there's nothing in step 1

it's not clear enough

Answer:

1st option.

0 to 100 miles per hour

Step-by-step explanation:

as we can see the question states that a particular car' s gas mileage DEPENDS upon its speed.

Since, the independent variable is the domain of the function the speed of the car will act as the domain of the given function.

out of all the option option 1 gives us values of speed( cause its unit is miles/ hour - unit of speed).

so the domain is

0 to 100 miles per hour.

Answer:

(A) 0 to 100 miles per hour

Step-by-step explanation:

The domain is the independent variable, or the input. The speed is the independent variable because the gas mileage DEPENDS on it. That means the gas mileage is the dependent variable.

The only answer that is related to the speed is the first answer choice.

Hope that helps (●'◡'●)

Answer:

Forth term of the sequence is 61

Step-by-step explanation:

Let's just go from a1 to a4:

a1 = 5

a2 = 2x5+3 = 13

a3 = 2x13+3 = 29

a4 = 2x29+3 = 61

Answer:

0

Step-by-step explanation:

1. Distribute:  6x-12 - 6x+12

2. Combine like terms:  0

Answer:

0

Step-by-step explanation:

First you want to do distributive properties, so multiply 2 and -4 by 3. leaving you with 6x-12-6x+12. then we have to combine all the like terms. so you can either add 6x to the negative 6x or take away 6x from the positive 6x. Same with the 12's. so once you've combined all the like terms you should be left with 0. Thus, your answer would be 0.

Answer:

x1 = 2 and x2 =7/2 or 3.5 yeah it says I need 20 word but I'm done so bye good luck!

The solutions of the given equation are 2 or -2

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, x²+2 = 6

x²+2 = 6

Solving we get,

x²+2 = 6

x² = 6-2

x² = 4

x = ±2

Hence, there are two solutions of the equation 2 or -2

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Part A: The common difference is 4.

Part B: The 4th term is 17 and the 5th term is 21  of this sequence.

What do you mean by arithmetic sequence?

The difference between each term in an arithmetic sequence is a constant. To put it another way, we just add the same value repeatedly, indefinitely.

According to the given question,

We have the given information:

The arithmetic sequence:

5, 9, 13,...

Now, we need to find the common difference and we will find it in this way,

The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.

d = t2 - t1

= 9-5 = 4

So, the common difference is 4.

Then, we need to find the 4th and 5th terms of this sequence,

t4 = t3 + d

= 13+4

= 17

t5 = t4 + d

=17 + 4

=21

Therefore, the 4th term is 17 and the 5th term is 21.

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The common difference of this arithmetic sequence is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.

Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a geometric sequence is raised by either multiplying by or dividing by a certain constant, k.

Part A:

The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.

Therefore, the common difference (d) is equal to 9 - 5 = 4.

The 4th and 5th terms of this sequence are

Part B:

Using Arithmetic progression formula,

aₙ = a + (n- 1)d

where

n = nth term

a (first term = 5

d = common difference = 4

4th term of the sequence

a₄ = a + (n- 1)d

a₄ = 5 + (4 - 1)4

a₄ = 17

5th term of the sequence

a₅ = a + (n- 1)d

a₅ = 5 + (5 - 1)4

a₅ = 21

Hence the 4th and 5th term of this arithmetic sequence is 17 and 21.

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If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h =  [(5^(x - 3))(5^(h) - 1)]/h

We are given the function as;

j(x) = 5^(x - 3)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 5^(x - 3 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

5^(x - 3 + h) = 5^(x - 3) × 5^h

Therefore;

[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h

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Answer:

578.05 inch²

Step-by-step explanation:

Calculating the circumference of the base and the area of the sides and adding them together will get the surface area of a cone.

A=πr², where r is the circle's radius, is the formula for calculating a circle's area. To calculate the area of the circular base, we utilize this formula.

The sector, or side, of the cone, is essentially a segment of a circle. The ratio of the cone's radius to its slant height, or r/s, determines the sector's size.

We take the area of the circle's section to get the sector's size.

A=πr²⋅s/r

this simplifies to πrs.

Then, we multiply the to determine the area of the side of the cone.

the total surface area of the cone =bottom face +side

                                                          =πr²+ πrs

                                                           = πr(r+s)

                                                            =π8(8+15) =578.05 inch²

Answer:

The amount of material used is about 628.32 square inches.

Step-by-step explanation:

so here we have the formula to find area of cone

A= πr(r+ (h²+r²))

r=8 in and h=15in

The all values have been obtained.

As per data function is:

f(x, y, z) = xe + 4z cos'(Inx)

To find: Directions in which f(x, y, z) increases and decreases most rapidly at P(1, In2, 1/2) and Rates of change in these directions.

Let's first calculate the gradient vector,

∇f(x, y, z) = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k,

∂f/∂x = eˣ + 4z cos'(lnx) * 1/x

∂f/∂y = 0

∂f/∂z = 4cos'(lnx)

Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of vector,

v = ai + bj + ck is given by

D_vf(P) = ∇f(P).v

Now we need to find a unit vector in the direction of increasing f(x, y, z) and another unit vector in the direction of decreasing f(x, y, z) most rapidly.

Let's find the unit vector in the direction of increasing f(x, y, z) by taking

v = ∇f/|∇f| and the unit vector in the direction of decreasing f(x, y, z) most rapidly by taking

v = -∇f/|∇f|.

For increasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + 4²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v1

     = (1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v1 = (1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

   = (1/sqrt(45))(e + 4k)

For decreasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + (-4)²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v2

     = (-1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v2 = (-1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

    = (-1/sqrt(45))(e + 4k)

Now, we need to find the rates of change in the directions v1 and v2. Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v1 is,

D_v1f(P) = ∇f(P).v1

             = (1/sqrt(45))(e + 4k).(e + 4k)

            = (1/sqrt(45))(e² + 16)

            = (1/sqrt(45))(e² + 16)

For the direction of v2,Rates of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v2 is,

D_v2f(P) = ∇f(P).v2

              = (-1/sqrt(45))(e + 4k).(e + 4k)

              = (-1/sqrt(45))(e² + 16)

              = -(1/sqrt(45))(e² + 16)

Therefore, Direction of increasing is (1/sqrt(45))(e + 4k), direction of decreasing is (-1/sqrt(45))(e + 4k), rates of change in the direction of increasing is (1/sqrt(45))(e² + 16) and rates of change in the direction of decreasing is -(1/sqrt(45))(e² + 16).

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TRUE.

The Lorenz curve is a graphical representation of income distribution within a population. It plots the cumulative percentage of income received against the cumulative percentage of the population. The closer the Lorenz curve is to the diagonal line, the more evenly distributed income is within the population.

Conversely, if the curve is further from the diagonal, the greater the degree of income inequality. This is because a curve that is further from the diagonal indicates that a smaller percentage of the population holds a larger percentage of the income.

Therefore, if the Lorenz curve is closer to the diagonal, it suggests that the distribution of income is more equal within the population. In contrast, a curve that is further from the diagonal shows that income inequality is more pronounced.

Policymakers can use the Lorenz curve to evaluate the level of income inequality within a population and implement policies that aim to reduce the disparities between income earners.

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Answer:

The expression is not factorable with rational numbers

Step-by-step explanation:

The Simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

The simplest form of the square root of 1,764 is 42.

To understand why, it's helpful to know what a square root is. A square root is a mathematical operation that finds the number which, when multiplied by itself, gives a certain number. For example, the square root of 25 is 5, because 5 multiplied by itself equals 25.

In the case of the square root of 1,764, we want to find the number that, when multiplied by itself, equals 1,764. To do this, we can use a calculator or do it manually by trial and error. One way to do it manually is to start with a number and square it until we get 1,764.

For example, we could start with 10 and square it to get 100. Then we could try 20, which gives us 400. Continuing in this way, we eventually find that 42 multiplied by itself equals 1,764.

So, the simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

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Simple linear regression is a statistical technique used to model the relationship between two variables by fitting a straight line to the data. It provides a way to predict or estimate the value of one variable (dependent variable) based on the value of another variable (independent variable).

In simple linear regression, the relationship between the independent variable (x) and the dependent variable (y) is represented by a straight line. The goal is to find the best-fitting line that minimizes the differences between the observed values of the dependent variable and the predicted values from the regression line.

A graph illustrating simple linear regression includes the scatterplot of the data points, the regression line, and the residuals. The scatterplot shows the individual data points with the independent variable on the x-axis and the dependent variable on the y-axis. The regression line is the line that best fits the data, minimizing the sum of the squared residuals.

Residuals are the vertical distances between the observed data points and the regression line. They represent the differences or errors between the actual values and the predicted values. By examining the residuals, we can assess how well the regression line fits the data. If the residuals are randomly scattered around zero, it suggests that the linear regression model is appropriate. If there is a pattern or systematic deviation in the residuals, it indicates that the model may not be capturing the underlying relationship accurately.

The regression line is constructed by minimizing the sum of the squared residuals, which is known as the least squares method. This ensures that the line represents the best linear approximation of the relationship between the variables.

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Answer:

80 seconds

Step-by-step explanation:

rate x time = gallons

\(\frac{.7}{2}\)t = 28  Multiply both sides by  \(\frac{2}{.7}\)

t =  80

18.42 years will it take to exhaust her annuity, i.e., run the account down to zero

Given the following information,

PV = $610,000

i = 6.5%

PMT = $40,000/year

The number of years for Ruth to exhaust all her funds from the account is 18.42

Using the financial calculator, we can easily find the value of n equals to 18.42 years in which the account finishes to zero.

n = 18.42 years

An annuity is a contract between you and an insurance company that requires the insurer to make payments to you, either incontinently or in the future. You buy an subvention by making either a single payment or a series of payments.

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According to the theory of comparative advantage, if the United States and Mexico increase their trade with each other, the two countries will experience an increase in their standards of living.

The theory of comparative advantage suggests that countries can benefit from specializing in the production of goods and services in which they have a lower opportunity cost compared to other countries. By focusing on producing what they are relatively more efficient at, countries can achieve higher levels of productivity and output.

When countries engage in international trade based on comparative advantage, they can access a wider range of goods and services at lower costs. This leads to increased efficiency, greater market competition, and access to a larger consumer base. As a result, both the United States and Mexico can enjoy the advantages of trade, such as lower prices, increased variety, and access to new markets.

By leveraging their respective comparative advantages and engaging in trade, the United States and Mexico can enhance their productivity, economic growth, and overall standards of living. The specialization and exchange of goods and services allow countries to allocate resources more efficiently, leading to higher living standards for their populations.

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L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

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Answer:

45.7 inches

Step-by-step explanation:

The perimeter uses 3 sides of the square, so 3 x 10 = 30. We'll add that later.

Then we need to find the circumference of the half-circle. We know the diameter is 10, because that's the side of a square.

Circumference = pi x diameter

C = 3.14 x 10 = 31.4

But that's for the whole circle. We only have a half.

31.4 /2 = 15.7 is the perimeter for the half circle. Add this to the 3 sides of the square

30 + 15.7 = 45.7

Answer:

i believe 6

Step-by-step explanation:

no need hon u got this

Answer:

10 yards

Step-by-step explanation:

The mean of the sample means (H) is 20 and the standard deviation of the sample means (σ) is 1. These values represent the expected values for the means of samples of size 25 drawn from a population with a mean of 20 and a standard deviation of 5.

To find the mean and standard deviation for samples of size n = 25 from a population with a mean μ = 20 and standard deviation σ = 5, we can use the formulas for the sampling distribution.

The mean of the sampling distribution (also known as the expected value or the population mean of sample means) is denoted as μx and is equal to the population mean, which is μ = 20 in this case. Therefore, H (the mean of the sample means) is 20.

The standard deviation of the sampling distribution (also known as the standard error) is denoted as σx and is equal to the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation σ is 5, and the sample size n is 25. Therefore, the standard deviation of the sample means, o (sigma), is calculated as:

σx = σ / √n = 5 / √25 = 5 / 5 = 1

Hence, the mean of the sample means (H) is 20 and the standard deviation of the sample means (σ) is 1. These values represent the expected values for the means of samples of size 25 drawn from a population with a mean of 20 and a standard deviation of 5.

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Answer:

13

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the points (-3, 6) and (-8, -6) as follows:

d = sqrt((-8 - (-3))^2 + (-6 - 6)^2)

= sqrt((-5)^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

Therefore, the distance between the two points in simplest radical form is 13.

Answer:

-2.75

Step-by-step explanation:

-4w-2=6w+20

-20-2=6w+4w

-22 = 8w

w = -2.75