a). Show that the following ODE is not exact. Find the integrating factor to make it exact and then find the general solution. (x + y) sin ydx + (x siny + cos y)dy = 0

Answer:

(x-1990)×25

Step-by-step explanation:

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The Equation is 25x-47500 as a function of the number of years since 1990.

To find equation for the number of students .

Statement that the values of two mathematical expressions are equal.

Given that:

The number of students in high school has been increasing linearly since 1990.

In 1997, 1125 students and in 2000, there were 1200 students.

Increase the number of students in 1997-2000

=1200-1125=75

In 3 years 75 student increased

In 1st years 25 student increased

number of students that will  increasing  in 1990=25

Equation=(x-1900)*25

Equation=25x-47500

where x is date/year

So, the Equation is 25x-47500 as a function of the number of years since 1990.

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The domain of this function p is (9,000 - x)/30, the marginal cost is 30 dollars per TV and revenue function is x(9,000 - x)/30. The marginal revenue is  (9,000 - 2x)/30 and  profit function in terms of x is R(x) -.

(A) To express the price p as a function of the demand x, we can solve the price-demand equation for p:

x = 9,000 - 30p

30p = 9,000 - x

p = (9,000 - x)/30

The domain of this function is the set of values of x for which the price is non-negative, since negative prices do not make sense in this context. Therefore, the domain is 0 ≤ x ≤ 9,000.

(B) The marginal cost is the derivative of the cost function with respect to x: C'(x) = 30

So the marginal cost is a constant value of 30 dollars per TV.

(C) The revenue function R(x) is the product of the demand x and the price p: R(x) = xp = x(9,000 - x)/30

The domain of this function is the same as the domain of the price function, which is 0 ≤ x ≤ 9,000.

(D) The marginal revenue is the derivative of the revenue function with respect to x: R'(x) = (9,000 - 2x)/30

(E) To find R'(3,000) and R'(6,000), we substitute x = 3,000 and x = 6,000 into the expression for R'(x):

R'(3,000) = (9,000 - 2(3,000))/30 = 100

R'(6,000) = (9,000 - 2(6,000))/30 = -100

Interpretation: R'(3,000) represents the extra money made from selling one more TV at a constant price when the demand is 3. When the demand is 6,000 TVs and the price remains the same, R'(6,000) represents the decrease in revenue from selling one fewer TV.

(F) To graph the cost function and the revenue function, we can plot the two functions on the same coordinate system, using the given domain of 0 ≤ x ≤ 9,000. The break-even points are the values of x for which the cost and revenue are equal, or C(x) = R(x).

C(x) = 150,000 + 30x

R(x) = x(9,000 - x)/30

Setting C(x) = R(x), we get:

150,000 + 30x = x(9,000 - x)/30

900,000 - 30x^2 = 30(150,000 + 30x)

900,000 - 30x^2 = 4,500,000 + 900x

30x^2 - 900x + 3,600,000 = 0

x^2 - 30x + 120,000 = 0

(x - 6,000)(x - 20) = 0

The break-even points are x = 6,000 and x = 20. These correspond to the intersections of the cost and revenue curves. The region to the left of x = 6,000 is a region of loss, since the revenue is less than the cost for x < 6,000. The region between x = 6,000 and x = 20 is a region of profit, since the revenue exceeds the cost for 6,000 < x < 20. The region to the right of x = 20 is again a region of loss, since the revenue is less than the cost for x > 20.

(G) The profit function is given by subtracting the cost function from the revenue function:

P(x) = R(x) -

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Answer:

$10

Step-by-step explanation:

6x-15=45

+15. +15

6x=60

/6. /6

x=10

Answer:

$7.5¢ or \(7\frac{1}{2}\)

Step-by-step explanation:

Do not use This solution:

Firstly, lets find how much the hats cost initially before the 15% coupon. To do that, divide, not multiply, divide $45 by 15% because 15% off means multiply 15% from the original price. But in this case we need to find the initial amount before the 15% coupon.

15% = \(\frac{15}{100}\)

Now, set it up;

\(\frac{15}{100}\) ×\(\frac{45}{1}\)

45 ÷ 6 = 7.5

Answer:

\(w\geq1\)

Step-by-step explanation:

\(4w\geq 3w+1\)

Take away \(3w\) from both sides

\(w\geq1\)

Answer:

4W ≥ 3W +1

4W-3W ≥ 1

W≥1

The answer is W ≥ 1

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.

Here,

The capacity of a cylinder and a cone that are the same height and radius are not the same.

The formula V = πr²h,

where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation

=> V = (1/3)r²h gives the volume of a cone.

To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,

False we must first know the cylinder's radius and height.

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To check the if a table represents a linear function we have to find the rate of change between the first two ordered pairs can be compared to the rate of change between the first and last ordered pairs to see if they are the same.

Well, a straight line is proportional to a linear function (on a graph). And the answers to the numbers can't be the same. If the X input is 5, for instance, and the Y output is 7, then Another non-linear X input of 5 and Y output of 8 follows.

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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The working of T critical value calculator is explained

What is t test?

t test is the test used  if the sample standard deviation is known and population standard deviation is unknown.

t test is used if the sample standard deviation is known and population standard deviation is unknown.

Here, t value is calculated by the formula

\(t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(\bar{x}\) = mean of the sample

\(\mu\) = mean of the population

s = standard deviation of sample

n = Number of samples

Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be \(t_{critical}\)

if the value of t lies between \(-t_{critical}\) and \(+t_{critical}\) then the null hypothesis is accepted, otherwise the null hypothesis is rejected.

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Answer: $75

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:

Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

According to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

The natural logarithm, often denoted as ln(x), is a mathematical function that represents the logarithm to the base e, where e is the mathematical constant approximately equal to 2.71828.

To find out how long it will take for 300 grams of Mercury 203 to decay, we can use the exponential decay model.

The general formula for exponential decay is given by:

A(t) = A₀ * e^(-rt),

where A(t) represents the amount of the substance at time t, A₀ is the initial amount, r is the decay rate, and e is the base of the natural logarithm.

In this case, we have the initial amount A₀ = 300 grams and the decay rate r = 0.01481 (1.481% written as a decimal).

We want to find the time t when the amount A(t) is equal to zero. Substituting these values into the formula, we have:

0 = 300 * e^(-0.01481t).

To solve for t, we can divide both sides of the equation by 300 and take the natural logarithm of both sides:

ln(0) = ln(e^(-0.01481t)),

0 = -0.01481t.

To isolate t, we divide both sides by -0.01481:

0 / -0.01481 = t,

t = 0.

Therefore, according to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

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640 solar panels were sold in the second month during the second month the sale was reduced by 20%.

During the second month, the sale was reduced by 20%, so the number of solar panels sold in the second month would be 800 - 20% of 800

= 800 - (20/100) * 800

= 800 - 160

= 640 solar panels.

An assembly of photovoltaic solar cells installed on a frame (often rectangular) is known as a solar cell panel, solar electric panel, photo-voltaic (PV) module, PV panel, or solar panel. A well-organized collection of PV panels is known as a photovoltaic system or solar array. Sunlight is used by solar panels to collect radiant energy, which is then transformed into direct current (DC) power. A photovoltaic system's arrays can be used to produce solar power that either directly powers electrical equipment or, through the use of an inverter system, is sent back into the alternating current (AC) grid.

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Answer:

x=0 and x=4/3

Step-by-step explanation:

The tangent line will be horizontal at the points where \(f'(x)=0\):

\(f(x)=x^3-2x^2\\f'(x)=3x^2-4x\\0=3x^2-4x\\0=x(3x-4)\\x=0,\frac{4}{3}\)

Thus, at x=0 and x=4/3, the tangent line will be horizontal at those points.

When we talk about the four Ps of marketing, "place" refers to the location where a product or service is sold or distributed. Therefore, any activity that involves the physical distribution of a product or service to a customer can be considered a "place" activity in marketing.

For example, a marketer might consider the following activities to be "place" activities:
1. Setting up a retail store or outlet in a specific location.
2. Delivering products to customers via a courier or postal service.
3. Distributing products to wholesalers or retailers through a supply chain.
4. Creating an online store or marketplace for customers to purchase products from anywhere.
5. Partnering with other businesses to sell products or services in their locations.
The "place" aspect of marketing is crucial as it ensures that products are available and accessible to customers where and when they need them. Therefore, a marketer must carefully consider the right channels of distribution to ensure that the product reaches the target audience efficiently and effectively. In conclusion, the "place" element in the four Ps of marketing involves all activities that facilitate the physical distribution of a product or service to customers.

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Answer:

-4/5

Step-by-step explanation:

y2-y1/x2-x1 is the formula for slope

Having different confidence intervals can give more precise information on the accuracy of an agent's decision-making and is useful in measuring the trustworthiness of agents. However, it can also create discrepancies between agents that are otherwise performing the same task and it can lead to unequal confidence in the decisions being made.

The advantages of having different confidence intervals for the agents would be that it allows for more precise estimates of the true population mean. This can be useful when there is a lot of variability in the data or when the sample size is small. Additionally, different confidence intervals can also be useful when comparing different groups or populations.

On the other hand, the disadvantages of having different confidence intervals for the agents would be that it can be confusing and difficult to interpret. It can also be more difficult to make comparisons between different groups or populations when there are different confidence intervals.

Overall, the decision to use different confidence intervals for the agents should be based on the specific goals and objectives of the study. It is important to carefully consider the advantages and disadvantages of different confidence intervals in order to make the best decision for your study.

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Answer:

Step-by-step explanation:

The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.

For the integral from [0, 2], the equation of the line is -3x + 6;

For the integral from [2, 3], the equation of the line is 3x - 6.

We integrate then:

\(\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx\)    and

\(-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right. +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.\)  sorry for the odd representation; that's as good as it gets here!

Using the First Fundamental Theorem of Calculus, we get:

(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5

The value of the integral   \(\int\limits^3_0 {|3x-6|} \, dx\)  is -9/2.

The given integral is \(\int\limits^3_0 {|3x-6|} \, dx\)

We have to find the value of this integral.

We know that ∫xⁿ dx= xⁿ⁺¹/n+1

So,  \(\int\limits^3_0 {|3x-6|} \, dx\) = 3x²/2 -6x (from 0 to 3)

Apply the limits.

=3(3)²/2-6(3)

=27/2-18

=27-36/2

=-9/2.

Hence, the value of the integral   \(\int\limits^3_0 {|3x-6|} \, dx\)  is -9/2.

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Event A: Probability = 1/24. Event A can be considered. Event B: Probability = 1/8. Event B can be considered.Event C: Probability = 5/24. Event C can be considered.Event D: Probability = 19/24. Event D can be considered.

To find the probability of each event and determine if it can be considered, we can use a tree diagram.

Event A: rolling a 5 and the spinner landing on blue.

The tree diagram for Event A would have two branches:

Rolling a 5: Probability = 1/6

Spinner landing on blue: Probability = 1/4

To find the probability of Event A, we multiply the probabilities along the branches: (1/6) * (1/4) = 1/24.

Event A can be considered.

Event B: rolling an odd number and the spinner landing on green.

The tree diagram for Event B would have three branches:

Rolling an odd number: Probability = 3/6 = 1/2

Spinner landing on green: Probability = 1/4

To find the probability of Event B, we multiply the probabilities along the branches: (1/2) * (1/4) = 1/8.

Event B can be considered.

Event C: rolling a number less than 6 and the spinner landing on yellow.

The tree diagram for Event C would have five branches:

Rolling a number less than 6: Probability = 5/6

Spinner landing on yellow: Probability = 1/4

To find the probability of Event C, we multiply the probabilities along the branches: (5/6) * (1/4) = 5/24.

Event C can be considered.

Event D: not rolling a number less than 6 and the spinner landing on yellow.

To determine the probability of Event D, we need to find the complement of Event C (rolling a number less than 6 and the spinner landing on yellow). The complement of an event A is denoted as A'.

The probability of Event D is equal to 1 - Probability of Event C:

1 - 5/24 = 19/24.

Event D can be considered.

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Answer:

2

Step-by-step explanation:

The scale factor between the two shapes is 2 because when you look at the number between the two triangles, 6/3 is 2 and 20/10 is also 2.

The value of the variable is equal to 12.

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):

y/6 = 8/4

By cross-multiplying, we have the following:

4y = 6 × 8

4y = 48

By dividing both sides of the equation by 4, we have the following:

y = 48/4

y = 12

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The specifics of Mark's policy and the insurance company he is using are not known, it is not possible to estimate the total annual premium.

A company is a legal entity made up of individuals, usually called shareholders, who have come together to carry out a specific business or economic activity. The company is a separate legal entity from its shareholders, meaning that it has its own rights and obligations.

The total annual premium will depend on the specifics of Mark's policy and the insurance company he is using. Liability insurance typically covers bodily injury and property damage. Collision and comprehensive insurance covers damage to the insured's car.
Liability insurance usually costs less than collision and comprehensive coverage. The premium for liability insurance will depend on the amount of coverage, driving record, and the age and type of car being insured.
Collision and comprehensive insurance premiums are usually higher, and are based on the age, type and value of the car, the driver's driving record, and the type and amount of coverage purchased.
Since the specifics of Mark's policy and the insurance company he is using are not known, it is not possible to estimate the total annual premium.

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To stop a 1200 kg car moving at 99 km/h in a straight path,

the work that must be done in Joules is 453750.

Step-by-step Given,

Mass of car, m = 1200 kg

Initial velocity, u = 99 km/h = 27.5 m/s

Final velocity, v = 0 m/s (as the car is brought to rest)

Initial kinetic energy, K.E1 = 1/2 m u²

Final kinetic energy, K.E2 = 1/2 m v²

Work done to bring the car to rest,

W = K.E1 - K.E2W

= 1/2 m u² - 1/2 m v²W

= 1/2 × 1200 × (27.5)² - 1/2 × 1200 × (0)²W

= 1/2 × 1200 × (27.5)²W

= 453750 J

Therefore, the work that must be done in Joules to stop the car is 453750.

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Answer:

Step-by-step explanation:

The value of a simple interest account is

A=P(1+rt), A=present amount, P=principle, r=rate, t=time

A=20000(1+0.02(8))

A=20000(1.16)

A=$23200.00

Answer:

A book was 53 pages shorter than you expected

Jennifer sold 53 apples.

Andrew spent $53.

Step-by-step explanation:

The question proposed that we should determine which situation can be said to be the opposite of 53. From the listed option, we will realize that the following:

A book was 53 pages shorter than you expected

Jennifer sold 53 apples.

Andrew spent $53.

The above options are the opposite of 53. This is because a book that was shorter than expected will need to be refilled.

Suppose Jennifer has x apples, and She sold 53 apples out of it. It means x = -53, which is the opposite of 53.

Andrew spent $53; let say Andrew had y+$53. After spending $53, he has y = - $53, which is the opposite of 53.

But the temperature, which was 53°F, will still be at that position on the thermometer provided it is not being affected by external conditions.

The first approximation of 537 can be written as a = 536 and b = 1, where the greatest common divisor of a and b is 1.

In number theory, the greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. In this case, since a = 536 and b = 1, the GCD of a and b is 1. This means that 536 and 1 have no common factors other than 1.

The first approximation of 537 can be expressed as a product of these two numbers, a and b, where a represents the larger part of the approximation and b represents the smaller part. In this case, a is equal to 536, and b is equal to 1. Since the GCD of a and b is 1, it indicates that 536 and 1 have no common factors other than 1. This approximation may not be the most accurate, but it satisfies the condition of having a GCD of 1.

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Answer:

hola

Step-by-step explanation:

como estas?

Answer:

4.) 2 7/8 ÷ 2 3/5 =

1. Greater than 1

2. Greater than 1

3. Less than 1

4. Greater than 1

Step-by-step explanation:

I took the quiz