Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Enter your answers as a comma-separated list.) f(x)=x2,[0,2]

Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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Answer: 47.12

Step-by-step explanation: 15 x pi. Or 15 x 3.14159.

The Fourier Cosine Transform of the given function f(x) = (ae^(-mx) + be^(-nx))^3, where x > 0, can be evaluated as follows:

1. Begin by expressing the function in terms of cosines using Euler's formula:

  f(x) = (ae^(-mx) + be^(-nx))^3

  f(x) = (a(cos(mx) - i*sin(mx)) + b(cos(nx) - i*sin(nx)))^3

2. Expand the cube of the expression using the binomial theorem:

  f(x) = (a^3(cos(mx))^3 - 3a^2(cos(mx))^2i*sin(mx) + 3a(cos(mx))i^2sin^2(mx) - i^3*sin^3(mx))

         + 3a^2b(cos(mx))^2(cos(nx) - i*sin(nx)) - 3ab^2(cos(mx))(cos(nx) - i*sin(nx))^2

         + a^3(cos(nx) - i*sin(nx))^3 + 3ab^2(cos(mx) - i*sin(mx))^2(cos(nx)) - 3a^2b(cos(mx) - i*sin(mx))(cos(nx) - i*sin(nx))^2

         + 3ab^2(cos(nx))^2(cos(mx) - i*sin(mx)) - 3ab^2(cos(nx) - i*sin(nx))(cos(mx) - i*sin(mx))^2

         + b^3(cos(nx))^3 - 3ab^2(cos(nx))^2i*sin(nx) + 3ab(cos(nx))i^2sin^2(nx) - i^3*sin^3(nx)

3. Since we are interested in the Fourier Cosine Transform, we only need the even terms in the expansion (those containing cosines).

4. Taking only the even terms from the expansion, we have:

  f(x) = a^3(cos(mx))^3 + 3a^2b(cos(mx))^2(cos(nx)) + 3ab^2(cos(nx))^2(cos(mx)) + b^3(cos(nx))^3

5. Apply the trigonometric identity: cos^3(theta) = (3cos(theta) + cos(3theta))/4, to simplify the terms:

  f(x) = (3a^3 + 3ab^2)(cos(mx) + cos(nx)) + (a^3 + 3a^2b + 3ab^2 + b^3)(cos(3mx) + cos(3nx))

6. The Fourier Cosine Transform of f(x) can be obtained by evaluating the coefficients of the cosine terms, as follows:

  F(w) = ∫[0 to ∞] f(x) * cos(wx) dx

       = (3a^3 + 3ab^2)∫[0 to ∞] (cos(mx) + cos(nx)) * cos(wx) dx

         + (a^3 + 3a^2b + 3ab^2 + b^3)∫[0 to ∞] (cos(3mx) + cos(3nx)) * cos(wx) dx

7. Evaluate each integral using trigonometric identities:

  ∫ cos(mx) * cos(wx) dx = (m^2cos(wx) - w^2) / (m^2 - w^2)

  ∫ cos(nx) * cos(wx) dx = (n^2cos(wx) - w^2) / (n^2 - w^2)

  ∫ cos(3mx) * cos(wx) dx = (9m^2

cos(wx) - w^2) / (9m^2 - w^2)

  ∫ cos(3nx) * cos(wx) dx = (9n^2cos(wx) - w^2) / (9n^2 - w^2)

8. Substitute the values of a, b, m, n into the above expressions and simplify.

Now, to evaluate the transform F(w) when w = 17.9, we substitute w = 17.9 into the expression obtained in step 8 and round off the final answer to five decimal places. However, since the calculations involved are extensive, I would recommend using appropriate mathematical software or a symbolic calculator to obtain the accurate result.

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Answer:   jnes

Step-by-step explanation:

sed

ws

wed

Answer:

the answer is 10

Step-by-step explanation:

I just puted value and calculated it's simple

Answer:

C

Step-by-step explanation:

C It makes the line become steeper. When the coefficient in front of x is increased, the slope of the line becomes larger, so the line becomes steeper. The other responses are not correct.

Answer:

m (slope) = 664

Step-by-step explanation:

Formula:

m (slope) = y1-y2/x1-x2

m = 16570 - 21226 / 1982 - 1986

= -4,656 / -4

= 664

Valid solutions for a positive demand are in the interval (3, 17).

Let's discuss it further below.

The given function is C(t) = t² + 48 - 12t + 3. To find the valid solutions for a positive demand, we need to determine when C(t) > 0.

Step 1: Simplify the given function.
C(t) = t² - 12t + 51

Step 2: Find the critical points by setting C(t) equal to 0 and solve for t.
t² - 12t + 51 = 0

Using the quadratic formula, we find two solutions for t: t ≈ 3 and t ≈ 17. These are the critical points where the demand changes from positive to negative or vice versa.

Step 3: Determine the intervals of positive demand.
Since the coefficient of t^2 is positive, the parabola opens upward. Therefore, the function is positive between the two critical points.

Hence, the valid solutions for a positive demand are in the interval (3, 17). Out of the given options, the solution (6, 3) falls within this interval, making it the correct answer.

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The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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Answer:

-19

Step-by-step explanation:

so you are just going to substitute in -5 for a and 7 for b.

-2(7)+ (-5)

Answer:

Step-by-step explanation:

4 1/7 = 29/7

6 = 42/7

What you need to add to 4 1/7 is:

6 - 4 1/7

42/7 - 29/7

13/7.

In mixed fractions, it's 1 6/7.

Answer:

a

Step-by-step explanation:

for she was going faster then amy

Answer:

1. y=-2x+5

2. y=1/2x-7.5

Step-by-step explanation:

you plug in the cordinates for the y intercept and you already have the slope.

y=mx+b

m= slope which is -2

Yes, women save more money than men. The value of the test statistic for this hypothesis test is 1.93.

The hypothesis test used in this case is a two-sample t-test. This test is used to compare two independent means from two different groups. The null hypothesis states that there is no difference between the means of the two groups, while the alternative hypothesis states that there is a difference.  

To begin, the value of the test statistic must be calculated. The test statistic is calculated by subtracting the two means and dividing by the standard error. The standard error is calculated by taking the standard deviation of each group and dividing it by the square root of the sample size. So, for this hypothesis test, the test statistic is calculated as follows: (54 - 50) / (10/√25 + 5/√30) = 4 / (2.06) = 1.93.

To determine if women save more money than men, the test statistic must be compared to the critical value associated with the significance level. As the significance level is 0.01, the corresponding critical value is -2.575 and 2.575. Since the test statistic (1.93) is greater than the critical value (2.575), the null hypothesis can be rejected. This indicates that there is sufficient evidence to suggest that women save more money than men.

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Answer:

yes.

Step-by-step explanation:

Answer:

n<2

Step-by-step explanation:

-2n+5>1

-2n>1-5

(-2n>-4)divide by -2

Answer:

n<2

Step-by-step explanation:

Solve the Inequality for n

Isolate the variable by dividing each side by factors that don't contain the variable.

-2n+5>1

-2n>1-5

(-2n>-4)divide by -2

Interval Notation: (−∞,2)

Answer:

5

Step-by-step explanation:

I honestly just need the points

Answer:

31.4

Step-by-step explanation:

3.14 x 2 x 5 = 31.4

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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The answer is all real numbers for x

because simplifying, you get both sides are equal

With 70% off the regular price, a dishwasher, regularly priced at $519.89, will be $155.97 only. The answer is C.

Discount is the deduction in the price of a good or service. When this reduced price is expressed in percentage then we call it a discount rate.

If the discount is given in percent, then the amount of discount can be found by using the formula:

Amount of Discount = Regular Price × Rate of Discount

If the regular price of a dishwasher is $519.89, and the discount rate is 70%, using the formula, solve for the discount value.

Amount of Discount = $519.89 x 70%

Amount of Discount = $519.89 × 0.70

Amount of Discount = $363.92

To get the final price of the dishwasher, subtract the discount value from the original or regular price.

price = $519.89 - $363.92

price = $155.97

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Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).

(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then

|2x + 3| + |x - 2| = 6x

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

-2x - 3 - x + 2 = 6x

-3x - 1 = 6x

9x = -1

x = -1/9

But -1/9 is not smaller than -3/2, so this case provides no valid solution.

(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,

|2x + 3| + |x - 2| = 6x

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

2x + 3 - x + 2 = 6x

x + 5 = 6x

5x = 5

x = 1

This solution is valid because it does fall in the interval -3/2 ≤ x < 2.

(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So

|2x + 3| + |x - 2| = 6x

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

-2x - 3 + x - 2 = 6x

-x - 5 = 6x

7x = -5

x = -5/7

This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.

(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.

|2x + 3| + |x - 2| = 6x

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

2x + 3 + x - 2 = 6x

3x + 1 = 6x

3x = 1

x = 1/3

This is yet another invalid solution since 1/3 is smaller than 2.

So there is one solution at x = 1.

Answer:

y=-17

Step-by-step explanation:

4(-5)= -20

then -20+3= -17

Answer:

y= -17

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Formula to find slope: y - y1 / x - x1

0 - 4 ÷ 1 - 2

-4 ÷ -1

Slope = 4

Answer:

slope = 4

Step-by-step explanation:

y2-y1/x2-x1

0-4/1-2 = 4

Suppose that {Sn} and {Tn} are sequences of positive numbers, then we can conclude that we can choose a number larger for the denominator to make the fraction small.

In arithmetic, a sequence is a collection of items (usually integers) in which the order of the components is important. The components in this case follow a precise pattern. In real life, we encounter sequences in a variety of contexts. For example, the home numbers in a row, pay in successive years (by a predetermined amount or a by a defined percentage), page numbers of a book, etc depict sequences.

If {Sn} is bounded and positive, then we can say 0< Sn < M for some real number M. Then Sn/Tn < M/Tn . If this approaches infinity, the Tn could not be bounded "below" by any positive number, no matter how small. Otherwise the Sn/Tn would be finite. Thus . {Tn} → 0

For part b Sn/Tn → 0  . Since the denominator is unbounded, we can always choose a number larger for the denominator to make the fraction as small as we like.

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Answer:

x²+x-30

x=5

Step-by-step explanation:

The equation is

(x+3+x-1)/2 × x=30

x²+x-30 (it's the quadratic equation)

x²+6x-5x-30=0

x(x+6)-5(x+6)=0

(x+6)(x-5)=0

x=-6

x=5

It's impossible for Length to be negative

So x=5

The value of x in the trapezium is equal to 6

The area of a trapezium can be calculated using the lengths of two of its parallel sides and the distance (height) between them. The formula to calculate the area (A) of a trapezium using base and height is given as, A = ½ (a + b) h

Given here: The area of the trapezium as 30 cm² and the dimensions are

x-1 , x, x+3

Now the area of the trapezium is given by A=(a+b)×h/2

Thus we have 30=(x-1+x+3)x/2

                       60=2x²-2x

                x²-x-30=0

               x²-6x+5x-30=0

              x(x-6)+5(x-6)=0

               (x+5) (x-6)=0

                 x=-5,6

But length cannot be negative thus x=6 is the right answer.

Hence, The value of x in the trapezium is equal to 6

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Answer:

2000 g/L

Step-by-step explanation:

(10.0 g) / (0.005 L) = 2000 g/L

Answer:

About 7

Step-by-step explanation: