write a definite integral that yields the area of the region f(x)= 25-x^2

Answer:

We can use proportional reasoning to solve some questions directly, such as which size of laundry detergent is the cheapest per load, or what the dimensions of the model car should be. We can also use proportional reasoning to estimate answers and check answers to problems involving more complicated algebra techniques.

Step-by-step explanation:

The solution to the initial value problem is y(x) = 3x sin x + 2x cos x.

To solve the initial value problem, we can use an integrating factor method. First, we rewrite the given equation as dy/dx + y tan x = 2x sin x. By comparing this form with the standard form of a linear first-order differential equation, we can determine the integrating factor. The integrating factor is given by exp(integral(tan x dx)), which simplifies to cos x.

Multiplying the entire equation by cos x, we get cos x dy/dx + y sin x = 2x sin x cos x. The left-hand side of the equation is now the derivative of (y cos x) with respect to x. Integrating both sides, we have ∫(y cos x) dx = ∫(2x sin x cos x) dx.

Integrating the right-hand side and simplifying, we get y(x) cos x = x sin^2(x) + C, where C is the constant of integration. To find the value of C, we use the initial condition y(0) = 5. Plugging in x = 0 and y = 5 into the equation, we get 5 cos 0 = 0 + C. Simplifying, we find C = 5.

Substituting C back into the equation, we have y(x) cos x = x sin^2(x) + 5. Dividing both sides by cos x, we obtain the final solution y(x) = (x sin^2(x) + 5) / cos x. Simplifying further, we get y(x) = 3x sin x + 2x cos x, which is the solution to the initial value problem.

for such more questions on  solution

https://brainly.com/question/24644930

#SPJ8

Given the expression:

We will rewrite the expression to be as the form (x - a)² = b

So, we need to make a complete square

The coefficient of x = -2

Half the coefficient = -1

Square it will give 1

So, add (1) to both sides of the equation

Factor the left side of the equation, it is a complete square

Compare the result to the given form.

So, the answer will be:

Answer:

17

Step-by-step explanation:

Since we are evaluating g(x) for g(4), we would substitute x in the equation with 4.

x² + 1

(4)²+ 1

16 + 1

17

I hope this helps

Answer:

B

-10-10=20

10+10=20

20/20=0

The exponential function f(x) = 2^x is given by the blue graph on the given graph.

The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function in this problem is defined as follows:

y = 2^x.

Two relevant numeric values are given as follows:

Hence the function is represented by the blue graph.

The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.

More can be learned about exponential functions at https://brainly.com/question/2456547

#SPJ1

Sequence is take away 6 each time so the next three terms are....

7

1

-5

Answer:

7

Step-by-step explanation:

act

Pairwise comparison voting, also known as Condorcet voting, satisfies both majority rule and pairwise victory (the Condorcet criterion).

1. Pairwise comparison: In pairwise comparison voting, each candidate is compared to every other candidate in a head-to-head contest. Voters rank the candidates in order of preference, and the outcomes of these individual contests are used to determine the overall winner.

2. Majority rule: Majority rule is satisfied in pairwise comparison voting because, in each head-to-head contest, the candidate who receives more than 50% of the votes is considered the winner. This ensures that the candidate with the majority of votes in each comparison is acknowledged as the preferred choice.

3. Pairwise victory (Condorcet criterion): The Condorcet criterion states that if there is a candidate who can beat every other candidate in a one-on-one contest, that candidate should be the overall winner. Pairwise comparison voting satisfies the Condorcet criterion because it directly compares each candidate against all others, ensuring that any candidate who consistently wins these head-to-head contests is recognized as the overall winner.

In conclusion, pairwise comparison voting (Condorcet voting) satisfies both majority rule and pairwise victory (the Condorcet criterion) by comparing candidates in head-to-head contests, ensuring that the candidate with the majority of votes in each contest is acknowledged as the preferred choice, and recognizing any candidate who consistently wins these head-to-head contests as the overall winner.

Learn more about Condorcet voting here: brainly.com/question/15581499

#SPJ11

Answer:

-5m-3

Step-by-step explanation:

step 1 Collect like terms.

3(5m+2)-20m+(-14+5)

step 2 Simplify.

3(5m+2)-20m-9

step 3 Expand by distributing terms.

15m+6-20m-9

step 4 Collect like terms.

(15m-20m)+(6-9)

step 5 Simplify.

-5m-3

Answer:-5m - 3

Step-by-step explanation:

1) Distribute

3(5m + 2) - 20m - 14 + 5

15m+6 - 20m - 14+5

2) Add the numbers

15m+6 - 20m- 14+5

15m-3 - 20m

3) Combine like terms

15m - 3-20m

Answer

-5m - 3

Hope this helps

Answer:

∠2 = 41°

Step-by-step explanation:

This is because, all three interior angles in a triangle will have a sum of 180 degrees.

So given that we have two angles, 90 degrees(right angle) and 49 degrees, we can replace angle 2 as our unknown value(a variable) and make it equal to 180 degrees then solve for x;

49 + 90 + x = 180

139 + x = 180

-139        -139

x = 41°, ∠2 = 41°

The volume generated by rotating the region bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3 is 79π/3 cubic units.

To use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3, we need to:

Express the curves in terms of x.

y = 10x - x^2 -> x^2 - 10x + y = 0 -> x = 5 ± sqrt(25 - y)

y = 21 -> this is a horizontal line

The region is bounded by the curves and the vertical lines x = 0 and x = 10. When we rotate the region about the line x = 3, we will create cylindrical shells with radius 3 and height Δy.

Therefore, the limits of integration will be from y = 0 to y = 21.

Express the volume V as an integral using the formula for the volume of cylindrical shell:

V = 2π∫(radius)(height)(thickness)dy

Since we are rotating about the line x = 3, the radius of each cylindrical shell is 3 - x. The height of each shell is given by the difference in the y-values of the curves at a given x-value, or y = 21 - (10x - x^2). The thickness of each shell is dy.

So we have:

V = 2π∫(3 - x)(21 - (10x - x^2))dy from y = 0 to y = 21

Evaluate the integral.

V = 2π∫(3 - x)(21 - (10x - x^2))dy from y = 0 to y = 21

= 2π∫(3 - x)(21 - 10x + x^2)dy from y = 0 to y = 21

= 2π∫(21(3 - x) - 10x(3 - x) + x^2(3 - x))dy from y = 0 to y = 21

= 2π∫(-x^3 + 13x^2 - 39x + 63)dy from y = 0 to y = 21

= 2π[-(1/4)x^4 + (13/3)x^3 - (39/2)x^2 + 63x] from x = 5 - sqrt(4) to x = 5 + sqrt(4)

= 2π[(79/12) + (79/12)] (after simplification)

= 79π/3

Therefore, the volume bounded by the curves y = 10x - x^2 and y = 21 about the line x = 3 is 79π/3 cubic units.

To know more about Volume:

https://brainly.com/question/25562559

#SPJ4

Answer:

John gets 24 dollars

Step-by-step explanation:

Divide 40 into 5 because 2+3 equals 5.

Each "section" equals 8. Now, multiply that by 3(John's section)

You get 24.

Answer:

for the 2 blank it is "22, 20.25"

Step-by-step explanation:

because each of them are subtracting by 1.75

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

A vertical line has an equation of the form ...

  x = constant

Here, the x-coordinate of every point on the line is 3, so the equation is ...

  x = 3

Answer:

x = 25

Step-by-step explanation:

The sum of the three interior angles of a triangle is always 180°.

4x + 2x + 30 = 180

6x + 30 = 180

6x = 150

x = 25

Answer:

sum of the interior angles of a triangle =180

2× + 4× + 30=180

6× + 30= 180

6× + 30 = 180

6× = 180-30

6× =150

6×/6=150/6

×= 25

Answer:

i. 2040  ii.1632

Step-by-step explanation:

I think i did this right..

Answer:

13

Step-by-step explanation:

Hello, we can write a two digit number 'ab' as 10 * a + b, where a and ba are two integer between 0 and 9.

For instance, 54= 50 + 4 = 5 *10 + 4, a = 5 b = 4, right?

The sum of a two digit number is 4.

a + b = 4

If the order of the digits are reversed, the result is a number that exceeds the original number by 18.

10b + a = 10a + b + 18

9b = 9a + 18

b = a + 2

We can replace in the first equation,

a + a + 2 = 4

2a = 2

a = 1

and then, b = 3

So the number is 13.

thank you

Answer:

x=7

Step-by-step explanation:

The price of the book at the furniture store is $150

Given the parameters:

The price of book in the furniture store would be :

Hence, we have :

125 + (0.2 * 125)

125 + 25

= 150

Therefore, the price at the furniture store is $150

Learn more on percentages: https://brainly.com/question/19994681

#SPJ1

A combination of numbers, symbols, or other values that produce a result when evaluated is called an expression.

Expressions can be simple or complex, and they can include operations such as addition, subtraction, multiplication, and division, as well as functions, variables, and constants.

Expressions are an essential part of mathematics and are used in a wide range of applications, including algebra, calculus, and statistics.

They are often used to represent real-world situations and to solve problems in various fields such as engineering, physics, economics, and finance.

Evaluating expressions involves performing the indicated operations in the correct order, according to the rules of arithmetic, algebra, or calculus, and simplifying the result as much as possible.

To know more about expression refer to-

https://brainly.com/question/14083225

#SPJ11

Answer:

x=2

Step-by-step explanation:

Answer:

\( \huge \boxed{ \boxed{ \tt x = 2}}\)

Step-by-step explanation:

The function f can be implemented using a single 4-to-1 multiplexer and two inverters.

A 4-to-1 multiplexer is a digital logic component that selects one of four input signals based on the select lines. It has four data inputs (D0, D1, D2, D3), two select lines (S0, S1), and one output (Y). By properly connecting the inputs and select lines, we can realize the desired function f.

To implement the function f using a single 4-to-1 multiplexer and two inverters, we need to carefully assign the input signals and select lines to achieve the desired behavior. The truth table of the function f will guide us in determining the appropriate connections.

First, we can use the inverters to complement the required inputs if needed. Then, we can connect the complemented and uncomplemented inputs to the select lines of the multiplexer. The output of the multiplexer will be the result of the function f.

By carefully selecting the input assignments and connections, we can effectively implement the function f using a single 4-to-1 multiplexer and two inverters. This approach offers a compact and efficient solution for realizing the desired logic function.

Learn more about lines here: https://brainly.com/question/31454782

#SPJ11

It is important to consider the scale of measurement and the specific characteristics of the variables when selecting an appropriate statistical test.The tests can be classified as follows:

1. A researcher measures the proportion of schizophrenic patients born in each season.

This test is nonparametric. The scale of measurement is categorical, as the seasons (spring, summer, fall, winter) represent distinct categories rather than continuous numerical values. Therefore, parametric assumptions, such as normality and equal variances, do not apply to this measurement.

2. A researcher measures the average age that schizophrenia is diagnosed among male and female patients.

This test is parametric. The scale of measurement is continuous and numerical (age in years). Parametric tests, such as t-tests or ANOVA, can be applied when working with continuous data, assuming the data meet the required assumptions (e.g., normality, independence, and equal variances).

3. A researcher tests whether frequency of Internet use and social interaction are independent.

This test can be both parametric or nonparametric, depending on the measurement scale and the specific statistical test used. If the variables are measured on a nominal or ordinal scale, nonparametric tests, such as the chi-square test, would be appropriate. If the variables are measured on a continuous scale, parametric tests, such as logistic regression, could be employed.

4. A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes.

This test is parametric. The scale of measurement is continuous (time in seconds), and parametric tests, such as t-tests or ANOVA, can be utilized to compare means or variances, assuming the required assumptions are met.

know more about researcher :brainly.com/question/24174276

#SPJ11

Answer:

10: -11n^5

12: 6k^2 -6k+7

Step-by-step explanation:

Ok so what your gonna do is add or subtract the ones with the same exponent.

so -15+4= -11 since they are both n^5 you can add them so your answer is:

-11n^2

now you have 8k^2-k-5k+7-2k. so you are gonna rearrange them so the same exponents are together.(keep the sign in front in front, if no sign it is positive)

8k^2-2k^2-5k-k+7

add like exponents

6k^2-6k+7

Answer:

the missing section is 49%

Step-by-step explanation:

11 + 18 + 15 + 7= 51

51 + 49 = 100

add the percentages together and you get 100%

The value of the test statistic for testing H0: rho = 0 vs. H1: rho ≠ 0, given a correlation coefficient of 0.47 for a sample of 17 students, is approximately 2.06.

To find the value of the test statistic for testing H0: rho = 0 vs. H1: rho ≠ 0, given a correlation coefficient of 0.47 for a sample of 17 students, you can follow these steps:

Step 1: Calculate the degrees of freedom.
Degrees of freedom (df) = n - 2, where n is the sample size.
df = 17 - 2 = 15

Step 2: Use the formula for the test statistic, t:
t = (r * sqrt(df)) / sqrt(1 - r^2), where r is the correlation coefficient.
t = (0.47 * sqrt(15)) / sqrt(1 - 0.47^2)

Step 3: Calculate the value of the test statistic:
t = (0.47 * sqrt(15)) / sqrt(1 - 0.2209)
t = (0.47 * 3.87298) / sqrt(0.7791)
t = 1.8202046 / 0.88270386

t ≈ 2.06

Thus, The value of the test statistic is approximately 2.06.

To learn more about test statistic visit : https://brainly.com/question/15110538

#SPJ11

Answer:

$3,745

Step-by-step explanation:

First, you have to calculate the price after the discount is applied:

Price of the car: $25,000

Discount: 18%

$25,000*18%= $4,500

$25,000-$4,500= $20,500

Second, you have to calculate the total amount she has to pay including the 7% tax:

$25,000*7%= $1,750

$25,000+$1,750= $26,750

Third, as the statement indicates that Ms. Eve had to put  14% of what she had to pay as down payment, you have to calculate the 14% of $26,750:

$26,750*14%= $3,745

According to this, Ms. Eve has to pay $3,745 for the down payment.

Answer:

------------------------

We know that:

Substitute and evaluate the given expression:

It's important to note that while these methods may be used for inferences on two population proportions, the choice of method depends on the specific research question, data, and assumptions.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent approaches, while the P-value method is a distinct approach. Let's discuss each of these methods in more detail.

Confidence Interval Method:

The confidence interval method involves constructing a confidence interval around the sample estimate of the difference between two population proportions. The confidence interval provides a range of plausible values for the true difference in proportions, along with a specified level of confidence. The confidence interval is calculated using the sample proportions, sample sizes, and the appropriate critical value based on the desired level of confidence. If the confidence interval does not contain zero, it suggests that there is a statistically significant difference between the two population proportions.

P-Value Method:

The P-value method involves calculating the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. In the context of comparing two population proportions, the null hypothesis typically assumes that the two proportions are equal. The P-value is then compared to the significance level (commonly denoted as alpha) to determine whether the null hypothesis is rejected or not. If the P-value is less than the significance level, the null hypothesis is rejected, suggesting a statistically significant difference between the proportions.

Critical Value Method:

The critical value method involves comparing the test statistic (such as the z-statistic or chi-square statistic) to the appropriate critical value determined based on the desired level of significance. The critical value corresponds to the cutoff point beyond which the null hypothesis is rejected. If the test statistic exceeds the critical value, the null hypothesis is rejected, indicating a statistically significant difference between the proportions.

So, to summarize:

The confidence interval method and the critical value method are equivalent because they both provide a range of plausible values for the difference in proportions and use critical values based on the desired level of confidence or significance.

The P-value method is distinct as it calculates the probability of obtaining the observed test statistic under the assumption of the null hypothesis and compares it to the significance level.

It's recommended to consider the context and consult statistical guidelines or a statistical expert when conducting hypothesis testing or constructing confidence intervals for two population proportions.

Learn more about Confidence Interval at: brainly.com/question/32546207

#SPJ11