solve quadratic by square root

\(f(x) = x2ex − (2ex/x) + c1x + c2\)(required solution)

Hence, \(f(x) = x2ex − (2ex/x) + c1x + c2\)

(where c1 and c2 are constants)

The first step to solve the given question is to integrate

\(f ″(x) = 2x 5ex\)

two times using integration by parts.

The first integration of f ″(x) with respect to x would yield f ′(x) as given below:

\(f ″(x) = 2x 5ex\)

Integrate with respect to x on both sides:

\(f ″(x) dx = (d/dx)(f′(x))dx∫(2x 5ex) dx = ∫d/dx (f′(x)) dx\)

Here, we have;

\(∫(2x 5ex) dx = x2ex −∫2exdx∫(2x 5ex) dx = x2ex − 2ex + c1\)

(where c1 is the constant of the first antiderivative) So,

\(f′(x) = x2ex − 2ex + c1\)

After integrating f′(x), the next step is to integrate it again to get f(x).

Integrating f′(x) with respect to x would yield f(x) as given below:

\(f′(x) = x2ex − 2ex + c1∫f′(x) dx = ∫x2ex dx − ∫2ex dx + ∫c1 dx∫f′(x) dx = x2ex − (2ex/x) + c1x + c2\)

(where c2 is the constant of the second antiderivative)

Therefore, \(f(x) = x2ex − (2ex/x) + c1x + c2\) (required solution)

Hence, \(f(x) = x2ex − (2ex/x) + c1x + c2\) (where c1 and c2 are constants)

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Answer:

it would be B.

Step-by-step explanation:

Answer:

Substitute x = 4 into the equation.

f(4) = 2(4)² - 6

= 2(16) - 6

= 32 - 6

= 26

The probability that the sample mean is greater than 18 as calculated  is 0.8413.

Given data,

n = 36, sample size

μ = 17, population mean

σ = 6, population standard deviation

when x = 18

z = (18 - 17)/1 = 1

P(x <18) = 0.8413

Therefore , the probability = 0.8413

A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.

While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.

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Answer:

x = -10

Step-by-step explanation:

-2 (x + 6) = 8

-2x + -12 = 8

+12 +12

-2x = 20

÷ -2 ÷ -2

x = -10

Answer:

please ask some one else ...sorry

Answer:

6

Step-by-step explanation:

Answer:

$15

Hope this helps! Please mark Brainliest!

Answer:

a)13

b)64

c)26

Step-by-step explanation:

4x+12=6x-14

Divide by 2

2x+6=3x-7

2x-3x=-7-6

-x=-13

x=13

m<1

4x+12

4(13)+12

52+12

64

64+64+y+y=180

divide by 2

64+y=90

y=90-64

y=26

The value of the angle m∠EFA is:  127.5°

A parallelogram is defined as a quadrilateral that has its opposite sides parallel and equal to each other. It has its interior opposite angles equal. Also, the angles on the same side of the transversal sum up to 180 degrees or are supplementary to each other.

Since the figure is a parallelogram, it means that:

DC║AB

Thus:

m∠B = 75°

m∠DCB = 180° - 75°

m∠DCB = 105°

CF bisects ∠DCB
Thus:

m∠DCF = m∠FCB = ¹/₂ * 105° = 52.5°

Thus:

m∠EFA = 180° - 52.5°

m∠EFA = 127.5°

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Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

y=-3x+12

Step-by-step explanation:

y-y1=m(x-x1)

y-6=-3(x-2)

y-6=-3x+6

y=-3x+6+6

y=-3x+12

Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Answer: The triangles are not congruent.

Step-by-step explanation:

Because there is not enough information to tell us that these triangles are congruent (there would have to be at least 3 congruent things shared among the two triangles to even consider checking for congruency, and there are only two), the triangles are not congruent by any theorem or postulate.

I hope this helps!

These triangles are not congruent !

Answer:

x=7

Step-by-step explanation:

5(2x-5) = 10x-25

1) add 25 to both sides

10x+25=10x      6x+3+25=6x+28

10x=6x+28

2) subtract 6x from both sides

10x-6x=4x      6x+28-6x=28

4x=28

3) divide by 4 from both sides

4x/4=x      28/4=7

x=7

Hope this helps, have a great day!!

The value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

According to the given question

We have an equation in one variable

⇒  -5(2x - 5) = 6x + 3

For finding the value of x solve the above equation by adding and subtracting the like terms.

So, -5(2x - 5) = 6x + 3

⇒ -5 x 2x + 5 x 5 = 6x + 3

⇒ -10x + 25 = 6x + 3

⇒  25 - 3 = 6x + 10x

⇒  22 = 16x

⇒ x = 22/16

Hence, the value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

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The length of the radius is 5 cm.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Substituting A = 78.93cm^2, we get:

78.93 = πr²

Solving for r, we get:

r² = 78.93/π

r = √(25)

r = 5 cm (rounded to 2 decimal places)

Therefore, the length of the radius is 5 cm.

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Answer:

The answer is 30 ROWS.

Step-by-step explanation:

Please give brainlyest

The probability that in an hour there will be at least 10 requests for parts is P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9) . The probability that the 10th request in the morning requires at least 2 hours of waiting time is P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) .

i) Poisson Distribution: The Poisson distribution can be used to model the number of requests for parts in a given time period, assuming that the average rate of requests is constant. The Poisson distribution with parameter λ is given by the following formula:

P(k requests in a time period) = (e^-λ * λ^k) / k! , where k is the number of requests, e is the mathematical constant approximately equal to 2.71828, and λ is the average rate of requests.

a) Using Poisson distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9)

b) To find the probability that the 10th request in the morning requires at least 2 hours of waiting time, we need to find the distribution of the time between requests. Since the requests are modeled as a Poisson process, the time between requests is modeled as an exponential distribution with parameter λ.

ii) Gamma Distribution: The gamma distribution is a continuous probability distribution that can be used to model the sum of k independent and identically distributed exponential random variables. In this case, the distribution of the time between requests is exponential, and the sum of 10 independent exponential random variables gives us the distribution of the time until the 10th request.

a) To find the probability that in an hour there will be at least 10 requests for parts using the gamma distribution, we need to first find the distribution of the number of requests in an hour.The sum of 10 independent exponential random variables with rate λ follows a gamma distribution with shape parameter k = 10 and scale parameter 1/λ.

Using the cumulative distribution function of the gamma distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(number of requests ≥ 10) = 1 - P(number of requests < 10)

b) Using Gamma distribution, the probability that the 10th request in the morning requires at least 2 hours of waiting time is given by:

P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) , where the cumulative distribution function of the gamma distribution can be used to calculate the probability.

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The function of Car A is an exponential function.

The function that describes the value is g(x) = \(18,000(0.94^{x})\).

The value of f(x) in 9 years is $10,313.91.

The function of Car B is a linear function.

The function that describes the value is  g(x) = 18,500 -750x.

The value of f(x) in 9 years is $11,750.

The value of the car declines with the passage of time. Thus, the value of the car depreciates with the passage of time.

A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value.  

The general form of a linear function is f(x) = a + bx

Where:

Rate of change = value of the car B in year 2 - value of the car B in year 1

17,000 - 17,750 = - 750

g(x) = 18,500 -750x

Value of g(x) when x is 9:

g(x) = 18,500 -750(9)

g(x) = 18,500 - 6,750

g(x) = $11,750

An exponential function can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential function is f(x) = \(e^{x}\)

Where:

• x = the variable

• e = constant

Constant = (Value of the car in year 2 / value of the car in year 1) - 1

Constant = (16,346.60 / 17,390) - 1 = -0.06 = -6%

g(x) = \(18,000(0.94^{x})\)

Value of the car in 9 years =  \(18,000(0.94^{9})\) = $10,313.91

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The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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Answer:

The area is 528.7031796 or 528.7

Step-by-step explanation:

If the hub cap were smaller, the circumference wouldn't be 81.51 cm, so that's why the area would change. Both the circumference and the area would be smaller.

the determinant of matrix b using the cofactor formula is 14.

To find the determinant of matrix b using the cofactor formula, we need to follow these steps:
Step 1: Find the cofactors of each element in the matrix b. The cofactor of an element is the determinant of the submatrix obtained by deleting the row and column containing that element, multiplied by (-1)^(i+j), where i and j are the row and column indices of the element.
Step 2: Use the cofactors to calculate the determinant of matrix b using the formula:
det(b) = a11×C11 + a12×C12 + a13×C13
where aij is the element in the ith row and jth column of matrix b, and Cij is the cofactor of that element.
For example, let's say matrix b is:
b = [ 1 2 3
     0 4 5
     1 0 6 ]
Step 1: Finding the cofactors
C11 = det([ 4 5
           0 6 ]) = 24
C12 = -det([ 0 5
            1 6 ]) = -5
C13 = det([ 0 4
           1 0 ]) = 0
C21 = -det([ 2 3
            0 6 ]) = -36
C22 = det([ 1 3
          1 6 ]) = 3
C23 = -det([ 1 2
            1 0 ]) = -2
C31 = det([ 2 3
           4 5 ]) = -2
C32 = -det([ 1 3
            0 5 ]) = 5
C33 = det([ 1 2
          0 4 ]) = 4
Step 2: Calculating the determinant
det(b) = a11×C11 + a12×C12 + a13×C13
      = 1×24 + 2×(-5) + 3×0
      = 14

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The inner product of f(x)=-2cos(2x) and g(x)=-sin(2x) is 0.

To find the inner product of f(x) and g(x), we use the formula:

⟨f,g⟩= ∫[a,b] f(x)g(x)dx

where [a,b] is the interval of integration.

Substituting the given functions, we get:

⟨f,g⟩= ∫[0,π] -2cos(2x)(-sin(2x))dx

= 2 ∫[0,π] sin(2x)cos(2x)dx

Using the identity sin(2θ)cos(2θ) = sin(4θ)/2, we get:

⟨f,g⟩= ∫[0,π] sin(4x)/2 dx

= [-cos(4x)/8]π0

= (-1/8)[cos(4π)-cos(0)]

= (-1/8)[1-1]

= 0

Therefore, the inner product of f(x) and g(x) is 0.

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Answer:

Step-by-step explanation:

4 boxes should do

Answer:

\( length = 12 ft \)

\( width = 8 ft \)

Step-by-step explanation:

Earl's garden:

\( length = (x + 6) ft \)

\( width = (x + 2) ft \)

\( perimeter = 2(length) + 2(width) \)

\( perimeter = 2(x + 6) + 2(x + 2) \)

\( perimeter = 2x + 12 + 2x + 4 = (4x + 16) ft \)

Dylan's garden:

\( length = (2x - 2) ft \)

\( width = (x + 4) ft \)

\( perimeter = 2(length) + 2(width) \)

\( perimeter = 2(2x - 2) + 2(x + 4) \)

\( perimeter = 4x - 4 + 2x + 8 = (6x + 4) ft \)

Generate an equation to solve for the value of x.

Since the perimeters of both gardens are the same, therefore:

\( 6x + 4 = 4x + 16 \)

Collect like terms

\( 6x - 4x = - 4 + 16 \)

\( 2x = 12 \)

Divide both sides by 2

\( x = 6 \)

Earl's garden:

\( length = (x + 6) ft \)

Plug in the value of x

\( length = 6 + 6 = 12 ft \)

\( width = (x + 2) ft = 6 + 2 = 8 ft \)

Answer:

l: 12ft

w: 8ft

Step-by-step explanation:

Answer:

2.12482717E22

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

   Step-by-step explanation:)

The derivative of the function g(y) = (y^2 / (y+2))^4 is g'(y) = 8y^7 / (y+2)^5 - 16y^6 / (y+2)^4.

To find the derivative of the function g(y) = (y^2 / (y+2))^4, we can use the chain rule and the power rule of derivatives.

First, using the quotient rule, we can simplify the function as follows:

g(y) = (y^2 / (y+2))^4

g(y) = y^8 / (y+2)^4

Now, applying the chain rule and the power rule, we get:

g'(y) = 4 * y^7 * (y+2)^-4 * (2y - 4)

g'(y) = 8y^7 / (y+2)^5 - 16y^6 / (y+2)^4

Therefore, the derivative of the function g(y) = (y^2 / (y+2))^4 is:

g'(y) = 8y^7 / (y+2)^5 - 16y^6 / (y+2)^4

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.