Solve the follwing system of differential equations
dx/dt = -6x + 5y
dy/dt = -5x + 4y
x(0) = 1/3 ; y(0) = 0
B) Solve agin using variation of paremeters
Show all work

Answer:

the answer is c JUST guessing it might not be correct

Answer:

(A) The unshaded octagon is a reflection because it is a flip over a diagonal line.

Step-by-step explanation: Trust, rust, and pixie dust

Answer:

A is correct

The unshaded octagon is a reflection because it is a flip over a diagonal line.

i took the test

Answer:

Step-by-step explanation:

thats obtuse triangle, we just disscused that math equation last friday

Answer:

g(x) = x+2

Step-by-step explanation:

f(x) = x^2 + 1

fg(x) = x^2 + 4x + 5

Find the function g(x) so that when you put it into f(x) you get x^2 +4x + 5

g(x) = x+2

Answer:

\(x=60\degree\)

Step-by-step explanation:

Consecutive angles of a parallelogram are are supplementay.

\( \implies \: x + 2x = 180 \degree \\ \\ \implies \: 3x = 180 \degree \\ \\ \implies \: x = \frac{ 180 \degree }{3} \\ \\ \implies \: x =60 \degree\)

Answer:

See below.

Step-by-step explanation:

y^2 - 6y + 9 can be changed correctly into y^2 - 2(y)(3) + 3^2.

Up to here, it's correct.

The right side above shows a polynomial that is the square of a binomial.

It factors into (y - 3)^2.

The correct factorization is (y - 3)^2.

The incorrect factorization of the student's solution is the product of a sum and difference.

The product of a sum and a difference is the correct factorization for a difference of squares.

For example, y^2 - 9 is the same as y^2 - 3^2 and is a difference of squares.

It factors into (y + 3)(y - 3), a product of a sum and a difference.

The ratio in the form of 1 :n is 1:300.

Ratio of two number A and B is the comparison of A with respect to B and when two ratios are equal they are said to be in proportion.

It is given that a ratio is

6mm : 180cm

It has to be simplified in the form of

1:n

1 cm = 10mm

therefore

180 cm = 1800 mm

6mm:180cm = 6/ 1800

= 1/300

Therefore the ratio in the form of 1 :n is 1:300.

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Answer:

above sea level

Step-by-step explanation:

Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).

Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.

Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.

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Answer:

B. 0.03110

Step-by-step explanation:

Given

Probability of Hit = 60%

Required

Determine the probability that he misses at 6th throw

Represent Probability of Hit with P

\(P = 60\%\)

Convert to decimal

\(P = 0,6\)

Next; Determine the Probability of Miss (q)

Opposite probabilities add up to 1;

So,

\(p + q = 1\)

\(q = 1 - p\)

Substitute 0.6 for p

\(q = 1 - 0.6\)

\(q = 0.4\)

Next,is to determine the required probability;

Since, he's expected to miss the 6th throw, the probability is:

\(Probability = p^5 * q\)

\(Probability = 0.6^5 * 0.4\)

\(Probability = 0.031104\)

Hence;

Option B answers the question

Answer:

b) 0.03110

Step-by-step explanation:

Got it right on the test.

The significance of having an improper integral that converges versus an improper integral that diverges lies in the behavior and interpretation of the integral.

An improper integral is an integral that either has one or both of its limits of integration at infinity or contains an integrand that is not defined at certain points within the interval of integration.

When we talk about convergence and divergence of an improper integral, we are referring to whether the integral yields a finite value or tends to infinity/does not exist.

Converging Improper Integral: If an improper integral converges, it means that the integral evaluates to a finite value.

This implies that the area or total accumulated value represented by the integral is well-defined and finite.

It allows for precise calculations, interpretations, and predictions based on the integral's value.

Converging improper integrals are often associated with well-behaved functions or situations.

Diverging Improper Integral: On the other hand, if an improper integral diverges, it means that the integral does not converge to a finite value.

It can exhibit one of two types of divergence: unbounded divergence or oscillatory divergence.

Unbounded divergence occurs when the integral tends to positive or negative infinity, while oscillatory divergence occurs when the integral oscillates between positive and negative infinity without settling on a finite value.

Divergence suggests that the integral does not provide reliable calculations, interpretations, or predictions due to its unbounded or oscillatory behavior.

Diverging improper integrals often arise from functions or situations with rapid growth, singularities, or oscillations.

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The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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Answer: 1 & 2 are congruent

Step-by-step explanation:

They both have the same amount of space to get to the other point .

1.  AC is congruent to BD.

2. BD and CE are not congruent.

3. AD and BE are not congruent.

4.  BC and CE are not congruent.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

1. The segment AC is (1 - (-8)) = 9 units, and the line segment

BD is (3 -(-6)) = 9 units.

So, AC ≅ BD.

2. Line segment BD is 9 units and line segment CE is (7 - 1) = 6 units.

So, BD and CE are not congruent.

3. Line segment AD is (3 - (-8)) = 12 units and line segment BE is (7 - (-6)) = 13 units. (not congruent)

So, line segment AD and BE are not congruent.

4. Line segment BC is (1 - (-6)) = 7 units and line segment CE is (7 - 1) = 6 units.

So, Line segments BC and CE are not congruent.

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To solve this problem, we can use the fact that x + y = 3 for any two numbers x and y that add up to 3. Therefore, we can simply choose any five pairs of whole numbers that add up to 3.

What is whole number?

A whole number is a number that is not a fraction or a decimal, and it does not have a fractional or decimal part. Whole numbers include all the natural numbers (also known as positive integers) such as 1, 2, 3, 4, 5, ... and also include 0 and the negative integers such as -1, -2, -3, -4, -5, .... Whole numbers are a subset of the real numbers and are often used in counting and measuring quantities that cannot be divided into fractions or parts.

To solve this problem, we can use the fact that x + y = 3 for any two numbers x and y that add up to 3. Therefore, we can simply choose any five pairs of whole numbers that add up to 3. Here are five such pairs:

In each of these cases, when we add the two numbers to x, we get a total of 3. And in each case, solving for x gives us the solution x = 0.

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Average speed of the group for the two day event is 0.105 miles\min.

The average is defined as the mean value that is equal to the ratio of the total sum of the number of a given set of values to the total number of values present in that set.

Time taken on day 1 in minutes = 9x60 + 44

                                                   = 540 + 44 = 584 minutes.

Time taken on day 2 in minutes = 2x60 + 55

                                                   = 120 + 55 = 157 minutes

Now we will be applying speed-distance formula we get,

Speed= Distance/time

On day 1,

\(Speed_{1}\)= 28/584 = 0.0479 miles/min

On day 2,

\(Speed_{2}\)= 10/175 = 0.0571 miles/min

Thus,the average speed is:

Average = \(Speed_{1} + Speed_{2}\) = 0.0479 + 0.0571= 0.105 miles/min

Hence,the average speed is 0.105 miles/min

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Answer:

Circle

Explanation:

I just took the test and got it right.

Answer:

\(28.07^{\circ}\)

Step-by-step explanation:

We can use basic trig. for a right triangle to solve this problem. In any right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse (longest side) of the triangle.

The right triangle we're looking at involves the two dotted lines and an edge of the prism.

The bottom dotted line is a diagonal of the rectangular base of the prism. We can use the Pythagorean Theorem to find its length.

The Pythagorean Theorem states that for any right triangle, \(a^2+b^2=c^2\), where \(a\) and \(b\) are the two legs of the triangle and \(c\) is the hypotenuse.

In this case, the two legs are 9 and 12 and we are solving for \(c\):

\(9^2+12^2=c^2,\\81+144=c^2,\\225=c^2,\\c=15\)

This is theta's adjacent side. Its opposite side is an edge of the prism labelled as 8 inches. Therefore, we have the following equation:

\(\tan \theta = \frac{8}{15}\)

Take the inverse tangent of both sides:

\(\arctan(\tan \theta)=\arctan(\frac{8}{15})\)

Simplify using \(\arctan(\tan\theta)=\theta, \theta \in (-90^{\circ}, 90^{\circ})\):

\(\theta=\arctan(\frac{8}{15}),\\\theta=28.07248694\approx \boxed{28.07^{\circ}}\)

Answer:

Step-by-step explanation:

Each point moves 3 times the distance from the center of dilation that it was.

You can compute the new coordinates by ...

 L = P - O . . . . . the length from O to P is P-O for some point P and origin O

Then 3 times that distance is

 3L = 3P -3O

We want to find the point P' that is 3L from O, so we add this distance to the coordinates of O. We get ...

 P' = 3L +O = 3P -3O +O

 P' = 3P -2O

So, for the lower left point A(-2, -7), the dilated image point A' is ...

 A' = 3(-2, -7) -2(2, -7) = (-6, -21) +(-4, 14) = (-10, -7)

That is, ...

 A' = 3A +(-4, 14)

The coordinates of the remaining points can be found similarly.

___

On a graph, it is usually fairly easy to count the grid squares in each direction between the point of interest and the center of dilation. The image point is 3 times the distance in each direction (horizontally, vertically).

Answer:

See the attached picture

Step-by-step explanation:

Verified correct with test results.

It will take Vincent 24 number of days to build the cubby house by himself.

Let's assume that Vincent can build the cubby house alone in h days.

From the given information, we know that Nadia takes 12 days to build the cubby house, and when Nadia and Vincent work together, they can finish it in 8 days.

We can use the concept of "work done" to solve this problem. The amount of work done is inversely proportional to the number of days taken.

Nadia's work rate is 1/12 of the cubby house per day, while the combined work rate of Nadia and Vincent is 1/8 of the cubby house per day.

When Nadia and Vincent work together, their combined work rate is the sum of their individual work rates:

1/8 = 1/12 + 1/h

To solve for h, we can rearrange the equation:

1/h = 1/8 - 1/12

1/h = (3 - 2) / 24

1/h = 1/24

Taking the reciprocal of both sides, we find:

h = 24

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Answer:

x=5 and y = 0 coordinate = (5,0)

Step-by-step explanation:

solve the simultaneous equation

hope this works :)

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Rule: opposite sides are equal/ angles are equal.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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On solving the provided question, Glenwood had 4676.85 mobile phone customers in 1990.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

As indicated by, the exponential rise function.

\(y = a(1 + r)^t\\\)

Where an is the starting value, r is the interest rate expressed in decimal form, and t is the passage of time.

as stated

In the little community of Glenwood, there were 285 mobile phone subscribers in 1985.

After 1985, the number of subscribers grew by 75% annually.

75% is shown in decimal form.

\(75/100\\= .75\\a = 285\\t = 5\\y = 285(1 + .75)^5\\y = 4676.85\)

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Answer:

2 days

Step-by-step explanation:

there is still 1/5 of his crops that need to be harvested. to see how many days that will take divide that amount and see how many 1/10 fit into it. 1/10+ 1/10 = 2/10 which is also 1/5 so it will take 2 days.

For the specified requirements, 97 sample size are required.

Given that,

Confidence Interval = 95

Margin of error (m) =0.099

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the  population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 95% confidence interval ,

Z* = 1.960 , m=0.099

Using equation we get

n = (1.96/0.099)²(0.5)( 1 - 0.5 )

By solving,

n = 97.02≅ 97

The necessary sample size is 97

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