Find the general solution of the given differential equation, and use it to determine how solutions behave as t \rightarrow [infinity] . y^{\prime}+\frac{y}{t}=7 cos (2 t), t>0 NOTE: Use c for

Answer:

Step-by-step explanation:

if the angles c and l were marked with the angle curve like angles j and a

Answer:

3.75

Step-by-step explanation:

If Alex borrowed 12.50 and paid him back only 8.75, that means he still owes him 3.75. 12.50 - 8.75 = 3.75

The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, The width and length of the  dimensions rectangle in terms of x are (80x/6) and (160x/6) respectively.

The dimensions of the rectangle in terms of x are as follows:

The perimeter of a rectangle is twice the sum of the length and the width. If the length and width of a rectangle are l and w, respectively, then the perimeter is 2(l + w).

According to the problem statement, the perimeter of a rectangle is 80x.

The width and length of a rectangle in terms of x are w and 2w, respectively. Because the base is two times the height.

Thus, we have the equation for the perimeter:

2 (l + w) = 80x Or,

substituting the value of l and w in terms of x, we have:

2 (2w + w) = 80x2(3w) = 80x6w = 80xw = 80x/6

The width of the rectangle, in terms of x is 80x/6. The length of the rectangle, in terms of x is 2(80x/6) or 160x/6.

Therefore, these are the dimensions of the rectangle.

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Each trip would have 1/56 ton to move.

Fractions are numbers which are of the form a/b where a and b are real numbers. Here, a is called the numerator and b is called the denominator.

Any number can be expressed as fractions.

Given that, a moving company had one-seventh of a ton of Wright to move across town.

Total amount of weight to move = 1/7 ton

This has to be tripped equally between 8 trips.

Amount of weight to move in each trip = (1/7) / 8

                                                                 = 1/56 ton

Hence the amount of weight that each trip would move is 1/56 ton.

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Step-by-step explanation:

angle e = 50 degree,,,,,,,

Answer:

The width of the compass is equal to DE.

Step-by-step explanation:

The true statement for this step C; The width of the compass is equal to DE.

The steps to construct the AG parallel line to PQ, passing through the point A outside of PQ are as follows;

Step 1 A line is drawn from point A to intersect PQ at point B.

Step 2 From the point B on PQ, an arc is drawn intersecting segment BQ of PQ at  D and segment BA at point E.

Step 3 In order to construct the angle equal to angle ∠DBE at point A, an arc is drawn from Point A with radius BD, that intersects the segment BA extended in point F.

The points A and G can be joined with a straight line and extended to form the line AG.

The correct option is C;

The width of the compass is adjusted to DE.

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The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Answer:

you too :)

Step-by-step explanation:

Answer:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Go to Khan Academy for more.

Step-by-step explanation:

Answer:

The way in which factors are grouped in a multiplication problem, does not change the product.

Step-by-step explanation:

my brain ;p

Step-by-step explanation:

0.45x, where x = number of bags sold

Hope this helped. Have a good day!

52 bags x $0.45 for each bag =$23.40 earned for sarah 's troop

Answer:

Solution given:

f(x) = x +1 and g(x) = x²,

now

(gºf)(x) =g(fx)=g(x+1)=(x+1)²

B) (gºf)(x) = (x + 1)^2

The solution of the given initial value problem is y(r) = (1/9) cos(3r) + (1/9) sin(3r) - (1/9) sin(3r) = (1/9) cos(3r)

We are given the initial value problem:

d^2y/dr^2 + 9y = sin(3r), y(0) = y'(0) = 0 ---------(1)

We can write the characteristic equation for the given differential equation as:

r^2 + 9 = 0

The roots of the characteristic equation are: r = 0 ± 3i

So, the general solution of the homogeneous differential equation d^2y/dr^2 + 9y = 0 is:

y_h(r) = c1 cos(3r) + c2 sin(3r) ------------(2)

Now, we will find the particular solution of the given differential equation. We use the method of undetermined coefficients and assume the particular solution to be of the form:

y_p(r) = A sin(3r) + B cos(3r)

Differentiating y_p(r) w.r.t r, we get:

y_p'(r) = 3A cos(3r) - 3B sin(3r)

Differentiating y_p'(r) w.r.t r, we get:

y_p''(r) = -9A sin(3r) - 9B cos(3r)

Substituting these values in the differential equation (1), we get:

-9A sin(3r) - 9B cos(3r) + 9(A sin(3r) + B cos(3r)) = sin(3r)

Simplifying the above equation, we get:

-9A sin(3r) + 9B cos(3r) = sin(3r)

Comparing the coefficients of sin(3r) and cos(3r) on both sides, we get:

-9A = 1 and 9B = 0

Solving the above equations, we get:

A = -(1/9) and B = 0

So, the particular solution of the given differential equation is:

y_p(r) = -(1/9) sin(3r)

Therefore, the general solution of the given differential equation is:

y(r) = y_h(r) + y_p(r) = c1 cos(3r) + c2 sin(3r) - (1/9) sin(3r) ------------(3)

Now, we will apply the initial conditions to find the values of c1 and c2.

Given that y(0) = 0. Substituting r = 0 in equation (3), we get:

c1 - (1/9) = 0

So, c1 = 1/9

Differentiating equation (3) w.r.t r, we get:

y'(r) = -3c1 sin(3r) + 3c2 cos(3r) - (1/3) cos(3r)

Given that y'(0) = 0. Substituting r = 0 in the above equation, we get:

3c2 = (1/3)

So, c2 = (1/9)

Therefore, the solution of the given initial value problem is:

y(r) = (1/9) cos(3r) + (1/9) sin(3r) - (1/9) sin(3r) = (1/9) cos(3r)

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Answer:

(.25)(.30) = .075 probability that both children will get the flu

The probability that both a youngster in New York and a kid in Los Angeles will get this season's virus can be determined by duplicating the singular probabilities. Consequently, the likelihood that both will get influenza is 0.075.

To find the probability of the two occasions happening, we duplicate the probabilities of every occasion. Considering that the probability of a kid in New York getting this season's virus is 0.25 (or 25%) and the probability of a youngster in Los Angeles getting influenza is 0.30 (or 30%), we multiply these probabilities: 0.25 * 0.30 = 0.075. This implies there is a 0.075 probability, or 7.5%, that both a youngster in New York and a kid in Los Angeles will get influenza.

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Answer:

(2,4)

Step-by-step explanation:

It's the one that the line intersects.

Answer:

-18+20=2 so (2,4) is a solution

Step-by-step explanation:

to be able to figure out if the ordered pair is a part of solution, only need to input the x value and see if you can get the output which is y

-9x+5y=2     for (4,2)

-9(4)+5(2) does not equal 2

for :(3,4)

-9(3)+5(4)=2

-27+20 does not equal 2

for (4,3)

-9(4)+5(3)=

-36+15 no solution

for : (2,4)

-9(2)+5(4)=

-18+20=2 so (2,4) is a solution

Answer:

a

Step-by-step explanation:

It says m=50 minus the three that fell out. That's m=50-3

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

f(x) = max{0,x} then f(x)=0 if x<0 and f(x)=x if x≥0.

f(x)=7x-2xlnx

When x tends to -∞, f is the constant function zero, therefore limit n tends to infinity f(x) = 0.

When x tends to ∞, f(x)=x and x grows indefinitely. Thus limit n tends to infinity f(x) = infinity.

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x) = x and if x<0, f'(0)=0 (the derivative of the constant zero).

In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

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Answer:

Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution.

Step-by-step explanation:

We are looking at two lines.

4(x + 3) + 2x = 6(x +2)

4x + 12 + 2x = 6x + 12

6x + 12 = 6x + 12

These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).

5 + 2(3 + 2x) = x + 3(x + 1)

5 + 6 + 4x = x + 3x + 3

4x + 11 = 4x + 3

Both lines have the same gradient but have a different incline with the y axis. By definition, they are parallel to each other and there fore have zero solutions. Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution, which is the answer we are looking for.

5(x + 3) + x = 4(x +3) + 3

5x + 15 + x = 4x + 12 + 3

6x + 15 = 4x + 15

These are two different lines with exactly one solution.

4 + 6(2 + x) = 2(3x + 8)

4 + 12 + 6x = 6x + 16

6x + 16 = 6x + 16

These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).

The question pertains to a population of a town, which is divided into three age classes: people less than or equal to 20 years old, people between 20 and 40 years old, and people over 40 years old.

After each period of 20 years, there are 80% people of the first age class still alive, 73% people of the second age class still alive, and 54% people of the third age still alive. The average birth rate of people in the first age class during this period is 1.45; for the second age class is 1.46, and for the third age class is 0.59.

At present, the town has 10,932, 11,087, and 14,878 people in the three age classes, respectively.  Let's start by calculating the number of people in each age class, after the next 20 years.For the first age class: the population will increase by 1.45 × 0.80 = 1.16 times. Therefore, there will be 1.16 × 10,932 = 12,676 people.For the second age class: the population will increase by 1.46 × 0.73 = 1.0658 times. Therefore, there will be 1.0658 × 11,087 = 11,824 people.For the third age class: the population will increase by 0.59 × 0.54 = 0.3186 times. Therefore, there will be 0.3186 × 14,878 = 4,742 people.After 40 years, we have to repeat this process, but now we have to start with the populations that we have just calculated. This is summarized in the following table:Age class Initial population in 2020 Population in 2040 Population in 2060 Population in 2080 Less than or equal to 20 years old 10,932 12,676 14,684 17,019 Between 20 and 40 years old 11,087 11,824 12,609 13,453 Greater than 40 years old 14,878 4,742 1,509 480We know that the number of people in each age class in 2080 is equal to the sum of people in the same age class in 2040 (that we just calculated) and the number of people that survived from the previous 20 years. Therefore, we can complete the table as follows:Age class Population in 2080 Number of people alive after 20 years alive after 40 years alive after 60 years Less than or equal to 20 years old 17,019 12,676 9,348 6,886 Between 20 and 40 years old 13,453 11,824 10,510 9,341 Greater than 40 years old 480 1,509 790 428Now, we can easily calculate the population in the town after each 20 years. In particular, after 20 years, we will have:10,932 + 1.16 × 10,932 + 1.0658 × 11,087 + 0.3186 × 14,878 = 10,932 + 12,540.72 + 11,822.24 + 4,740.59 = 39,036After 40 years, we will have:17,019 + 12,676 + 10,510 + 790 = 41,995After 60 years, we will have:6,886 + 9,341 + 428 = 16,655Therefore, the town's population will increase from 10,932 to 39,036 in the next 20 years, then to 41,995 in the following 20 years, and then to 16,655 in the final 20 years.

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Answer:

step by step solution:

(r/p)(9) = (9+1)²/(9-4) = 100/5 = 20

(q.s)(3) = (-2(3)+7).(3(3)² - 5(3)) = 1×12 = 12

(q/r)(-1) = (-2(-1) + 7)/(-1+1)² = 9/0 = Undefined

(t + s)(4) = -(4)² + 4(4) + 9 + 3(4)² -5(4) = -16 + 16 +9 + 48 - 20= 37

(s o p)(8) = s(p(8)) = s(8-4) = s(4) = 3(4)² -5(4) = 48 - 20 = 28

(q o t)(7) = q(t(7)) = q(-(7)² + 4(7) + 9) = q(-12) = -2(-12) + 7= 24+7 = 31

(r o u)(1) = r(u(1)) = r(1+6) = r(7) = (7+1)² = 64

(t o s)(0) = t(s(0)) = t(0) = 9

(u-p)(-3) = (-3)³ + 6(-3) - (-3) + 4 = -27 -18 + 3 + 4 = -38

(u o r)(-2) = u(r(-2)) = u((-2+1)²) = u(1) = 1 + 6 = 7

(q o q)(6) = q(q(6)) =q (-2(6) + 7) = q(-5) = -2(-5) + 7 = 17

END

The  constant of proportionality 'k' is 247.

Since y = k/x

x= 13 y= 19

19=k/13

k=19*13

k=247

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a distinct meaning in mathematics than it does in everyday language (see variable (mathematics)); these two ideas use the same name due to a shared etymology.

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The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

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\(f(x) = \sqrt{2} + \frac{1}{\sqrt{2} } ( x -1) - \frac{1}{4\sqrt{2} } ( x -1)^{2}\) series about the point x0 for the given function and value of x0.

What is the definition of series in math?

Taylor series of a function f(x)at a point \(x_{0}\) will be defined as -

\(f(x) = f(x_{0} )+ \frac{f'(x_{0}) }{1 !}( x - x_{0}) + \frac{f''(x_{0}) }{2!} ( x - x_{0} )^{2} + \frac{f'''(x_{0}) }{3!} ( x - x_{0} )^{3} + .....................\)

The function we have is -

\(f(x) = \sqrt{2x} and x_{0} = 1\)

Since we need only the first three terms of the taylor series we need to find

\(f(x) = \sqrt{2x}\)

\(f'(x) = \sqrt{2} * \frac{1}{2\sqrt{x} } = \frac{1}{\sqrt2{x} }\)

\(f''(x) = \frac{1}{\sqrt{2} } * \frac{-1}{2x\sqrt{2x} } = - \frac{1}{2\sqrt{2} x\sqrt{x} }\)

putting the value of x = x0 in the above equations we get

   f (1) = \(\sqrt{2}\)

    f''(1) = \(\frac{1}{\sqrt{2} }\)

     f'''(1) = \(\frac{-1}{2\sqrt{2} }\)

putting the values

\(f(x) = f(1) + \frac{f'(1)}{1!}(x -1) + \frac{f''(1)}{2!}(x-1)^{2}\)

\(f(x) = \sqrt{2} + \frac{\frac{1}{\sqrt{2} } }{1} (x- 1) + \frac{\frac{-1}{2\sqrt{2} } }{2} (x - 1 )^{2}\)

\(f(x) = \sqrt{2} + \frac{1}{\sqrt{2} } ( x -1) - \frac{1}{4\sqrt{2} } ( x -1)^{2}\)

The first three terms of taylor series for the given function is given above

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The series Σ (5)/(x^(1/5)), n=1 to infinity is divergent.

Step:1. Write the given series: Σ (5)/(x^(1/5)), n=1 to infinity
Step:2. Set up the corresponding integral: ∫ (5)/(x^(1/5)) dx, from 1 to infinity
Step:3. Evaluate the integral
Step:4. Analyze the result to determine if the series converges or diverges
Let's evaluate the integral: ∫ (5)/(x^(1/5)) dx, from 1 to infinity
First, rewrite the integrand with a negative exponent: ∫ 5x^(-1/5) dx, from 1 to infinity
Now, integrate with respect to x: 5 * (x^(1 - 1/5) / (1 - 1/5)) evaluated from 1 to infinity
= 5 * (x^(4/5) / (4/5)) evaluated from 1 to infinity
Now, evaluate the integral at the limits: (5/4) * (x^(4/5)) evaluated from 1 to infinity
= (5/4) * [(∞^(4/5)) - (1^(4/5))]
= (5/4) * [∞ - 1]
Since the integral evaluates to infinity, it means that the integral diverges. According to the Integral Test, if the integral diverges, the original series also diverges.
Therefore, the series Σ (5)/(x^(1/5)), n=1 to infinity is divergent.

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Answer:

Yes

Step-by-step explanation:

Remember that a rational number is any integer (any whole numbers negative or positive) that can be written as a fraction which also means that any fraction no matter is numerator or denominator is a rational number, because it what was integers that were written as a fraction. Therefore your answer is "Yes, 1/2 is a rational number."

Hope this helps.

Answer:

large box = 3 feet, small box = 1 foot

Step-by-step explanation:

large box = l

small box = s

3l + 2s = 11

2l + 1s = 7

This is simultaneous equations

so you make the one of the boxes equal

I am going to make the small boxes equal each other

4l + 2s = 14

3l + 2s = 11

Take them both away from each other

1l = 3

put that back into the equation

so s = 1

Answer:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

Step-by-step explanation:

The positions of the letters in naming the triangles in the statement of congruent tells you which sides are congruent.

△ABC≅△EFG

Sides AB and EF are congruent

△ABC≅△EFG

Sides BC and FG are congruent

△ABC≅△EFG

Sides AC and EG are congruent

Look at the choices:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

Answer:

x = -60

Step-by-step explanation:

1/3x=−20

X is 1/3

X times 3 = a full X

Fill it in

X times -20 = -60

Hope this helps :)

The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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