Find the exact length of the curve. y = 1/4 x^2 − 1/2 ln(x), 1 ≤ x ≤ 2

Answer: 5%

Step-by-step explanation:

Answer:

its B guys

Step-by-step explanation:

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

Concept: Mathematical Representation

Answer:

length=50m

width=25m

Step-by-step explanation:

perimeter is the distance all round,hence

2(l+w)=2(2x+x)=

4x+2x=6x=150

6x=150x

x=25

l=50m

w=25m

(a)  The cumulative distribution function F(t) = 0 for t<0, F(t) = t/a for 0<=t<=a, and F(t) = 1 for t>a.

(b)  The reliability function R(t) = 1 for t<0, R(t) = 1-t/a for 0<=t<=a, and R(t) = 0 for t>a.

(c) The hazard rate h(t) = 1/t for 0<t<=a, and the failure rate is decreasing.

(d)  The mean time to failure MTTF = a/2 and tmedian = a/2.

(e) p(T > a) = 0 and the uniform distribution does not have the memoryless property.

(a) The cumulative distribution function (CDF) for a uniform distribution over (0,a] is given by:

F(t) = P(T ≤ t) =

{ 0 if t < 0,

{ t/a if 0 ≤ t ≤ a,

{ 1 if t > a.

(b) The reliability function is defined as R(t) = 1 - F(t).

Therefore, for the uniform distribution over (0,a], we have:

R(t) =

{ 1 if t < 0,

{ 1 - t/a if 0 ≤ t ≤ a,

{ 0 if t > a.

(c) The hazard rate h(t) is defined as the instantaneous rate of failure at time t, given that the system has survived up to time t.

It is given by:

h(t) = f(t) / R(t),

where f(t) is the probability density function (PDF) of the distribution.

For the uniform distribution over (0,a], the PDF is constant over the interval (0,a], and zero elsewhere:

f(t) =

{ 1/a if 0 < t ≤ a,

{ 0 otherwise.

Therefore, we have:

h(t) =

{ 1/t if 0 < t ≤ a,

{ undefined if t ≤ 0 or t > a.

Since the hazard rate is decreasing with time, the failure rate is also decreasing.

This means that the system is more likely to fail early on than later on.

(d) The mean time to failure (MTTF) is given by:

MTTF = ∫₀ᵃ t f(t) dt = ∫₀ᵃ t/a dt = a/2.

The median time to failure (tmedian) is the time t such that F(t) = 0.5. Since F(t) is a linear function over the interval (0,a], we have:

tmedian = a/2.

(e) The probability that T > a is zero, since the uniform distribution is defined over the interval (0,a]. Therefore, p(T > a) = 0.

The uniform distribution does not have the memoryless property, which states that the probability of failure in the next time interval depends only on the length of the interval and not on how long the system has already been operating.

The uniform distribution is not memoryless because as time passes, the probability of failure increases, unlike in a memoryless distribution where the probability of failure remains constant over time.

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Answer:

think its this not sure : Alternate interior angles theorem

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a right triangle.

Pythagorean Theorem can be used to find the sides.

IF the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.  The right angle is opposite the longest side.

72² + 8.5² = 72.5²

5184 + 72.25 = 5256.25

5256.25 = 5256.25

The goal of a confidence interval is to provide a range of values that are reasonable for the parameter of interest. So the correct option is (A).

The goal of a confidence interval is to provide a range of values that is reasonable for the parameter of interest. The confidence interval is based on the sample data and the level of confidence. The level of confidence is the probability that the confidence interval contains the true value of the parameter.

The confidence interval is calculated using the sample mean, the sample standard deviation, and the level of confidence. The confidence interval is calculated by adding and subtracting the margin of error from the sample mean. The margin of error is the product of the critical value and the standard error. The critical value is based on the level of confidence. The standard error is the standard deviation of the sampling distribution.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

Step-by-step explanation:

10*4*6

10*24

240

Answer:

2043; 60,900 students

Step-by-step explanation:

Let the number of years since 2004 be x.

\(14100+1200x=37500+600x \\ \\ 23400=600x \\ \\ x=39\)

This will be in 2043, and the enrollment will be 60,900 students

The value of the range of function is found as f(5) = -21.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The given function:

f(x) = {3x-5;x<5

        {-x^2 +4;x>= 5

f(5) = -x^2 +4

Put x = 5

f(5) = -(5)^2 +4

f(5) = -25 +4

f(5) = -21

Thus, the value of the range of the function is found as f(5) = -21.

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Answer:

Step-by-step explanation:

Area of the sector B:

A = πr²*70/360 =

     π*10²*7/36 =

     175π/9 in²

Correct choice is C

Answer:

given;

inscribed angle =35°

central angle=35×2=70°

radius [r]=10in

area of shaded region=70°/360×πr²

=70°/360×π×10²=159π/9 or 61.08in²

Answer: 1/7

Step-by-step explanation:

7x=1

x=1/7

Answer: \(6\dfrac13\text{ inches.}\)

Step-by-step explanation:

Given: Length in drawing = \(8\dfrac49\ \text{inches}\)

\(=\dfrac{9\times8+4}{9}\text{ inches}\\\\=\dfrac{72+4}{9}\text{ inches}\\\\=\dfrac{76}{9}\text{ inches}\)

Also, half inch on drawing = \(\dfrac38\ foot\) actual length.

1 inch on drawing = \(2\times\dfrac38 =\dfrac34\ foot\)

\(\dfrac{76}{9}\text{ inches}=\dfrac{76}{9}\times\dfrac{3}{4}\ foot\\\\=\dfrac{19}{3}\text{ inches}\\\\=6\dfrac13\text{ inches}\)

The actual length of the surfboard = \(6\dfrac13\text{ inches.}\)

Answer:

x=75

Step-by-step explanation:

Sum of the interior angles of a trapezoid = 360°

That being said we can calculate the measure of the missing angle (x) by subtracting the given angles (131, 107 and 47) from 360

so x = 360 - 131 - 107 - 47

360 - 131 = 229

229 - 107 = 122

122 - 47 = 75

so x = 75

Step-by-step explanation:

As I do not have the work shown to calculate the number of ways to choose the passengers, I cannot identify the specific error made. However, I can provide some insight on how to approach this type of problem correctly.

When choosing 2 people from a group of 10, we can use combinations, which are denoted as "n choose k" and represented by the formula:

n choose k = n! / (k! * (n-k)!)

where n is the total number of items in the group and k is the number of items to be chosen.

In this case, we want to choose one passenger for first class and one passenger for coach. Therefore, we can separate the group of 10 into two subgroups: one subgroup with 1 person (for first class) and another subgroup with 9 people (for coach).

Using combinations, we can calculate the number of ways to choose 1 person from the subgroup of 1 and 1 person from the subgroup of 9:

(1 choose 1) * (9 choose 1) = 1 * 9 = 9

Therefore, there are 9 ways to choose the passengers to fill the seats.

The statement "There are 68% data values within μ and μ+σ" is true. (option b).

The empirical rule states that approximately 68% of data values in a normal distribution lie within one standard deviation (σ) of the mean (μ). This means that if we consider the interval from μ to μ+σ, it will contain roughly 68% of the data values.

In summary, among the given statements, only statement b) is true. The empirical rule helps us understand the distribution of data values based on their distance from the mean (μ) in a normal distribution. It is important to remember that the rule provides approximate percentages and does not provide precise values for specific intervals.

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Complete Question:

Which of the following statement(s) is/are TRUE about the number of data values that lie over an interval for normal distribution by using the empirical rule?

a) There are 71.5% data values within μ-σ and μ+20.

b) There are 68% data values within μ and μ+σ.

c) There are 50% data values within μ and ∞.

d) There are 50% data values within µ - 30 and μ.

e) There are 100% data values within μ-30 and μ+30.

Answer:

D) x+y=12, x=2y

Step-by-step explanation:

We know that x+y=12 and x=2y given the word problem, so D is correct.

Answer:

the answer is d

Step-by-step explanation:

i just did the test

Given

Mass, Volume, and Density

Procedure

Mass, volume and density are three of an object's most basic properties. Mass is how heavy something is, volume tells you how big it is, and density is mass divided by volume. Although mass and volume are properties you deal with every day, the idea of density is a little less obvious and takes careful thought.

The answer is (B) 1/e.

To find the absolute maximum value of f(x) = ln(x)/x, we need to find the critical points and endpoints of the function and then evaluate f(x) at these points to determine the maximum value.

First, we find the derivative of f(x):

f'(x) = (1/\(x^2\)) * (xln(x) - 1)

Setting f'(x) = 0, we get:

xln(x) - 1 = 0

Solving for x, we get:

x = 1/e

Since f(x) is only defined for x > 0, the only critical point is x = 1/e.

Next, we evaluate f(x) at the critical point and at the endpoints of the domain of the function:

f(1/e) = ln(1/e)/(1/e) = -1/e

f(0+) = lim(x→0+) ln(x)/x = lim(x→0+) (1/x) / 1 = ∞

f(∞) = lim(x→∞) ln(x)/x = lim(x→∞) (1/x) / (1/x) = 1

Since f(x) approaches infinity as x approaches 0+, and f(x) approaches 1 as x approaches infinity, the absolute maximum value of f(x) occurs at x = 1/e, and the maximum value is f(1/e) = -1/e.

Therefore, the answer is (B) 1/e.

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Given:

y varies directly with x,

It is given that y = 7 when x = -9.

To find:

The value of y when x = 27 for the direct variation.

Solution:

It is given that y varies directly with x, so

\(y\propto x\)

\(y=kx\)             ...(i)

Where, k is the constant of proportionality.

It is given that y = 7 when x = -9. Putting these values in (i), we get

\(7=k(-9)\)

\(-\dfrac{7}{9}=k\)

Putting \(k=-\dfrac{7}{9}\) in (i), we get

\(y=-\dfrac{7}{9}x\)

Putting \(x=27\),  we get

\(y=-\dfrac{7}{9}(27)\)

\(y=-21\)

Therefore, the required value is \(y=-21\).

Answer:

4 pairs of socks.

Step-by-step explanation:

$44 dollars and divide that by 9

44 / 9 = 5

As the fraction is 2/9 and not 1/9, then the 5 would be 10, so

$10

$10 / $2.50 = 4

You take the $10 and divide that by each pair of socks to get the total amout of pairs.

Hope this helped.

Answer:

0.91

30.4

850

Step-by-step explanation:

Answer:

The width of the window is 176 cm

Step-by-step explanation:

The perimeter is the outside of a shape. If the perimeter is 242 cm and we know the length is 66 cm, we use what we have. We take 242 and subtract it by 66 and get 176 cm

Work Shown:

A = pi*r^2

A = 3.14 * 10^2

A = 3.14 * 100

A = 314 square inches

This value is approximate since pi = 3.14 is approximate.

The area of the circle is :

Work:

To calculate the circle's area, I will use the formula

\(\sf{C=\pi r^2}\)

Diagram:

\(\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 10\ inches}\end{picture}\)

Plug in the values :

      \(\begin{gathered}\sf{A=3.14\times10^2}\\\\\sf{A=3.14\times100}\\\\\boxed{\boxed{\bf{A=314\:in^2}}}\end{gathered}\)