expand f(x) = 5x2 − 4, −1 < x < 1, in a fourier series.

Answer:

49.7 mph

Step-by-step explanation:

divide the length value by 1.609

The specified nth term in the expansion of the binomial (x - 5), where n = 7, is \(-5^7x\). In the expansion of a binomial \((a + b)^n\), each term can be represented as \(C(n, r) * a^{(n-r)} * b^r\), where C(n, r) is the binomial coefficient, representing the number of ways to choose r items from a set of n distinct items.

In this case, the binomial is (x - 5), and n is 7. To find the specified nth term, we need to determine the values of r and (n - r) in the term \(C(n, r) * a^{(n-r)} * b^r\). In this case, a is x, b is -5, and n is 7. The specified nth term occurs when r = 7, which means (n - r) is 0.

Plugging in the values, we have \(C(7, 7) * x^{(7-7)} * (-5)^7. C(7, 7)\)is equal to 1, \(x^{(7-7)\) is equal to\(x^0\), which is 1, and \((-5)^7\) is equal to \(-5^7\).

Therefore, the specified nth term in the expansion of the binomial (x - 5), where n = 7, is \(-5^7*x\).

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Step-by-step explanation:

4m =16

divide both sides by 4

m = 4

he has 4 model trains

Answer:

Answer:

The door should be 1.6cm wide on the drawing.

Step-by-step explanation:

1 meter is 100 centimeters.

Elena's bedroom door is 80 centimeters wide.

To find how wide it should be on the drawing, divide by 50.

80/50 = 1.6cm

The door should be 1.6cm wide on the drawing.

The line with slope -2/3 that crosses the y -axis at the point (0,4) exists X = -2/3y + 4.

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

The values of the y-intercept and slope reveal details on the nature of the relationship between the two variables, x and y. According to a unit change in x, the slope shows how quickly y changes. When the x-value is 0, the y-intercept shows the value of the y-axis.

Vertical lines are described as having "unknown slope" because their slope seems to be an arbitrary, arbitrarily high amount. The four different slope types are represented in the graphs below.

Therefore, the correct answer is option d) X = -2/3y + 4.

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The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.

Using the properties of logarithm, we have,

logm 4/m = logm 4 - logm m

               =1.139 - logm m               .....................................(1)

Again, using the properties of logarithm, we know that:

logm 4 = logm (2 × 2)  

        = logm 2 + logm 2

         = 1.139 = 2logm 2                    ..................................(2)

Substituting equation (2) into (1) gives:

logm 4/m = 2logm 2 - logm

           m = 2logm (2/m)          ..................................................(3)

Using the property of logarithm once again, we know that:

loga b = logc b / logc a                     ............................................(4)

Substituting equation (4) into equation (3), we have:

logm 4/m = 2 logm 2 - logm

m= logm [(2/m)² / m]                       .............................................(5)

Now, we are to find logm 4/m by substituting the given values.

Using equation (2), we have:

logm 2 = (1.139)/2

     = 0.5695

Using equation (5), we get:

logm 4/m = logm [(2/m)² / m]

logm 4/m = logm [4/m²m]

 logm 4/m = logm 4 - logm

logm 4/m = 1.139 - 2 logm m

Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

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Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

Given that lines makes an angle α, β, γ with x - axis, y - axis and z - axis respectively.

So, By definition of direction cosines,

\(\rm :\longmapsto\:l = cos \alpha \)

\(\rm :\longmapsto\:m = cos \beta \)

\(\rm :\longmapsto\:n = cos \gamma \)

So,

\(\rm :\longmapsto\: {l}^{2} + {m}^{2} + {n}^{2} = 1\)

\(\rm :\longmapsto\: {cos}^{2} \alpha + {cos}^{2} \beta + {cos}^{2} \gamma = 1\)

On multiply by 2 on both sides we get

\(\rm :\longmapsto\: 2{cos}^{2} \alpha + 2{cos}^{2} \beta + 2 {cos}^{2} \gamma = 2\)

can be further rewritten as

\(\rm :\longmapsto\: 2{cos}^{2} \alpha - 1 + 1 + 2{cos}^{2} \beta - 1 + 1 + 2 {cos}^{2} \gamma - 1 + 1 = 2\)

\(\rm :\longmapsto\: (2{cos}^{2} \alpha - 1)+ (2{cos}^{2} \beta - 1)+ (2 {cos}^{2} \gamma - 1) + 3= 2\)

\(\rm :\longmapsto\:cos2 \alpha + cos2 \beta + cos2 \gamma + 3= 2\)

\( \red{ \bigg\{ \sf \: \because \: cos2x = {2cos}^{2}x - 1 \bigg\}}\)

\(\rm :\longmapsto\:cos2 \alpha + cos2 \beta + cos2 \gamma= 2 - 3\)

\(\rm :\longmapsto\:cos2 \alpha + cos2 \beta + cos2 \gamma= - 1\)

Hence,

\(\bf\implies \:\boxed{\tt{ \: cos2 \alpha + cos2 \beta + cos2 \gamma = - 1 \: }}\)

So, option (d) is correct.

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Direction cosines of a line segment is defined as the cosines of the angle which a line makes with the positive direction of respective axis.

The scalar components of unit vector always give direction cosines.

The scalar components of a vector gives direction ratios.

The Beck Depression Inventory (BDI) would be an example of a measurement instrument.

A measurement instrument is a tool or technique used to measure or assess a particular variable or construct, in this case, depression. The BDI is a standardized self-report questionnaire that is widely used to assess the severity of depressive symptoms. It consists of 21 questions or items that ask the respondent to rate the intensity of their depressive symptoms on a 4-point scale. The total score on the BDI can be used to classify the severity of depression and guide treatment decisions.

In contrast, a variable is a characteristic or attribute that can take on different values or levels, such as age, gender, or income. Data refers to the collection of measurements or observations obtained from a particular study or investigation. Internal validity is a concept that refers to the extent to which a study is designed and conducted in a way that minimizes the potential for bias or confounding variables.

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Answer:

1. Multiples

2. factors

3.multiples

4.factor

5.factor

Step-by-step explanation:

Answer:

see attachment

Step-by-step explanation:

The equation of the line that passes through the point (-4, 5) and has an undefined slope would be x = -4.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m is the slope and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept. The most important point, A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.

The given point is (-4, 5) and the slope is undefined means

m = ∞

Any vertical line has an undefined slope.

The equation of a vertical line will be of the form:  x = a number

By using the slope-point form of the line, we can write

   y - y1 = m(x - x1)

  y - 5 = ∞(x - (-4))

   ⇒ x + 4 = 0

   ⇒ x = -4.

Hence, the equation of the line that passes through the point (-4, 5) and has an undefined slope would be x = -4.

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The dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse \(4x^2+196y^2=196\) using Lagrange multipliers. The dimensions of the rectangle are length=4/7 and width=2.

We want to find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse \(4x^2+196y^2=196.\)

Let the length and width of the rectangle be 2x and 2y, respectively. Then the area of the rectangle is A = 4xy. We need to find the values of x and y that maximize A subject to the constraint \(4x^2+196y^2=196.\)

We can use the method of Lagrange multipliers to solve this problem. We consider the function \(L(x, y, \lambda) = 4xy + \lambda (4x^2+196y^2-196)\), where λ is the Lagrange multiplier. Taking the partial derivatives of L with respect to x, y, and λ, we get:

\(\partial L/ \partial x = 4y + 8\lambda x = 0\)

\(\partial L/\partial y = 4x + 392\lambda y = 0\)

\(\partial L/\partial \lambda = 4x^2+196y^2-196 = 0\)

Solving these equations simultaneously, we get:

x = 1/7, y = 1/2, λ = -1/98

Therefore, the dimensions of the rectangle of maximum area are 2x = 2/7 and 2y = 1, i.e., length is 4/7 and width is 2.

To summarize, we can use the method of Lagrange multipliers to find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse \(4x^2+196y^2=196\). The dimensions are length = 4/7 and width = 2.

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x = ㏑₂8 in the logarithmic function.

A logarithmic function is the inverse of an exponential function.

Given  function if f(x) = \(2^{x}\),

When strength is equal to 8 pascals, f(x) = 8

Therefore, 8 = \(2^{x}\)

Taking log on both sides:

                 ln8 = ln\(2^{x}\)

                 ln8 = xln2

       or         x  = ln8/ln2

                    x = ㏑₂8

Hence, the required function is x = ㏑₂8.

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The 10th percentile of the normal distribution with mean 43 and standard deviation 8 is approximately 32.16.

To find the 10th percentile of a normal distribution with mean mu and standard deviation sigma, we can use the inverse cumulative distribution function (CDF) of the standard normal distribution.

The 10th percentile is the value below which 10% of the observations fall. Therefore, we need to find the z-score such that the area under the standard normal curve to the left of z is 0.1.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 10th percentile is approximately -1.28.

Then, we can use the formula for transforming a standard normal distribution to a normal distribution with mean mu and standard deviation sigma:

z = (X - mu) / sigma

Rearranging the formula, we get:

X = mu + z * sigma

Substituting mu = 43, sigma = 8, and z = -1.28, we get:

X = 43 + (-1.28) * 8 = 32.16

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Answer:

6

Step-by-step explanation:

Apples are sold in bags of 6

Pears are sold in bags of 8

Jerry wants to buy the same number of each fruits

Therefore the least number apples and pears that Jerry needs to buy is 6

Question:

Solution:

Let the expression:

applying the distributive law, we obtain:

this is equivalent to:

then, we can conclude that the correct answer is:

The graph of the function is illustrated below and the domain of the function is [-2, 2].

The term domain in math is referred as the set of all inputs of the function

Here we have to find and sketch the domain of the function f(x, y, z) = ln(64 − 4x² − 16y² − z²)

In order to sketch the function, we have to use the graphing calculator, and following the listed steps to sketch the graph.

The first step is to label the graph with appropriate axis like x, y, and z.

Now we have to input the function f(x, y, z) = ln(64 − 4x² − 16y² − z²) on the input field and then click on generate.

Now, we get the graph for the function.

After that we have to adjust the limit for the given graph.

Then we finally get the resulting graph as follows.

As per the definition of domain, and with the help of the given graph, we have identified the value of the domain is [-2, 2].

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Answer: 25

Step-by-step explanation:

2^3=8

3^2=9

8+9=17

17-10=7

Answer:

7

Step-by-step explanation:

2 to the 3rd power is equal to 8 and 3 to the 2nd power equals 9. You add 8 and 9 to get 17 and then subtract 10 to get your answer which is 7

The theoretical domain is all real numbers greater than or equal to one and less than or equal to two. Then the correct option is C.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

Kellen runs for at least 1 hour but for no more than 2 hours. He runs at an average rate of 6.6 kilometers per hour. The equation that models the distance he runs for t hours is d = 6.6t

Then the domain of the function d will be a real number.

But in the problem, the value of t is more than or equal to one but less than or equal to two.

1 ≤ t ≤ 2

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Answer:

(-9,-3)

Step-by-step explanation:

When you are talking about in relation you do what I do.

The given statement "2 6e6x 3e3x еx e3x" is false because the correct particular solution is \(\(y_p(x) = 6e^{6x}\tan(9x)e^{3x} + 3e^{3x}xe^{3x}\)\).

To find a particular solution of the nonhomogeneous differential equation (DE) 2y'' - 18y' + 36y = tan(9x) using the variation of parameters method, we assume a particular solution of the form \(\(y_p(x) = u_1(x)y_1(x) + u_2(x)y_2(x)\)\), where \(\(y_1(x)\)\) and \(\(y_2(x)\)\) are the solutions of the associated homogeneous DE, and \(\(u_1(x)\)\) and \(\(u_2(x)\)\) are functions to be determined.

The solutions of the associated homogeneous DE 2y'' - 18y' + 36y = 0 can be found by solving the characteristic equation:

\(\(2r^2 - 18r + 36 = 0\)\),

which gives us the repeated root r = 3.

Hence, the homogeneous solutions are \(\(y_1(x) = e^{3x}\)\) and \(\(y_2(x) = xe^{3x}\)\).

To find \(\(u_1(x)\)\) and \(\(u_2(x)\)\), we use the formulas:

\(\(u_1(x) = -\frac{{y_2(x) \int y_1(x)f(x)dx}}{{W(y_1, y_2)}}\)\)

and

\(\(u_2(x) = \frac{{y_1(x) \int y_2(x)f(x)dx}}{{W(y_1, y_2)}}\)\),

where \(\(W(y_1, y_2)\)\) is the Wronskian of \(\(y_1(x)\)\) and \(\(y_2(x)\)\).

Evaluating the integrals and simplifying the expressions, we obtain:

\(\(u_1(x) = 6e^{6x} \tan(9x)\) and \(u_2(x) = 3e^{3x}\)\).

Therefore, the particular solution of the nonhomogeneous DE is:

\(\(y_p(x) = u_1(x)y_1(x) + u_2(x)y_2(x) = 6e^{6x}\tan(9x)e^{3x} + 3e^{3x}xe^{3x}\)\).

So, the given statement is false.

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The correct interpretation of the 95% confidence interval is: "We estimate with 95% confidence that the true population proportion of people who own a tablet computer is between 0.62 and 0.78."

This means that if we were to repeat the survey many times and construct a confidence interval for each sample, 95% of those intervals would contain the true proportion of people in the population who own a tablet computer. The interval (0.62, 0.78) is the range of values that is likely to contain the true population proportion with 95% confidence, based on the sample data.

Hence, the correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population proportion of people who own a tablet computer is between 0.62 and 0.78."

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Answer:

100

Step-by-step explanation:

\(4\times(2+3)^{2}\)

This can be turned into:

\(4\times5^{2}\)  (if we add the numbers inside the brackets)

Following PEDMAS, this becomes:

\(4\times25\) which equals \(100\)

∴  \(4\times(2+3)^{2}=100\)

Answer:

Post the question along with this

Answer:

I don't know ask your parents

Step-by-step explanation: