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The antiderivative of f(x) = tan⁻¹(x) is x tan⁻¹(x) − ln(x²+1)/2 + C

The term antiderivative in math is referred as a function that reverses what the derivative does

Here we have given the expression f(x) = tan⁻¹(x).

Now, the antiderivative of the expression is calculated by doing the integral

=> ∫tan⁻¹(x)dx

By using the integration by parts ∫udv = uv−∫vdu

Here let us consider that u=tan⁻¹(x) and dv=dx

And the value of du is calculated as,

=> du =  ∫tan⁻¹(x)dx =  dx/(x² + 1)

And the value of v = x.

Then the expression is written as,

=>  ∫tan⁻¹(x)dx = x tan⁻¹(x) - ∫x/(x² + 1)dx

As per the concept of the constant of integration, it can be simplified as,

=> x tan⁻¹(x) − ln(x²+1)/2 + C

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Answer:

3rd one im pretty sure

Step-by-step explanation:

Answer: 3 months

Step-by-step explanation: if you had $30 + $19.50

you get 49.50 if you add 49.50+ 49.50 you get 99.00 add another 49.50 you get 148.50 add another 49.50 you get 198 and you cant keep going

49.50= the total for 1 month

Step-by-step explanation:

To find the cost of each bag of feed, we can use the equation:

24b = 720

where b represents the cost of one bag of feed in dollars.

To solve for b, we can isolate it on one side of the equation by dividing both sides by 24:

24b/24 = 720/24

Simplifying the calculation, we get:

b = 30

Therefore, each bag of feed costs $30.

Answer:

what ???

Step-by-step explanation:

No

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(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).

(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.

(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.

(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.

To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)

Substituting the given wavefunction, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)

Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.

To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).

(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.

(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).

To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).

If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:

\(\Delta x = \sigma\)

\(\Delta p = \frac{\hbar}{2\sigma}\)

By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.

Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.

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The conversion 336g to m³ is impossible because they measure different units

From the question, we have the following parameters that can be used in our computation:

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

Using the above as a guide, we have the following:

336g to m³  cannot be done because of the different quantities they represent

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Answer:

9the only correct answer is 9

Answer:

A

Step-by-step explanation:

p-2 ≥ 0

p ≥ 2

if p ≥ 2

p - 2 = 7

p = 9 (accettable)

if p < 2

-p+2 = 7

p = -5 (accettable)

Answer:

C. 24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

9 ÷ 3[12 - 4]

3[8] = 24

The answer is (d) 0.77, which is the closest rounded value to 0.7967.

We can use the formula for the normal distribution with the given mean and standard deviation to find the probability that the project is finished in 16 weeks or fewer.

First, we need to calculate the mean and standard deviation of the project completion time. From the table, we can see that the expected completion time for the project is 15 weeks and the variance is 1.44. Therefore, the standard deviation is the square root of the variance, which is 1.2.

Now, we can calculate the z-score for a project completion time of 16 weeks:

z = (16 - 15) / 1.2 = 0.83

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 0.83 is approximately 0.7967. This means that the probability of the project being finished in 16 weeks or fewer is about 0.7967 or 79.67%.

Therefore, the answer is (d) 0.77, which is the closest rounded value to 0.7967.

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Answer: −1−3k

Step-by-step explanation:

Distribute:

(−3+4k)−1(−2+7k)

(-3+4k)+{2-7k}

Eliminate redundant parentheses:

(−3+4k)+2−7k

-3+4k+2-7k

Add the numbers:

−3+4k+2−7k

−1+4k−7k

Add the same term to both sides of the equation:

−1+4k−7k

−1−3k

Answer:

1/4

Step-by-step explanation:

The Pythagorean theorem says the length of the hypotenuse squared is equal to the sum of both of the lengths of the legs squared. To put that visually, look at my attached image.

Based on the Pythagorean Theorem, we can put the known information, both legs' length is 7, into the equation.      

  \((length-of-hypotenuse)^2=(length-of-leg-1)^2+(length-of-leg-2)^2\\ (length-of-hypotenuse)^2 = 7^2 + 7^2\\ (length-of-hypotenuse)^2 = 98\\length-of-hypotenuse=\sqrt{98} \\length-of-hypotenus=9.899\)

Thus the unknown side length is about 9.899.

Hope that helped!

The expression is simplified to 2/3x²y⁻³

Index forms are described as mathematical forms of writing numbers that are too large or small in more convenient forms.

Other names for index forms are scientific notation and standard forms.

The rules of index forms are;

From the information given, we have that;

8x⁵y/12x³y⁴

Divide the values

2/3 x⁵⁻³y¹⁻⁴

Subtract the exponents

2/3x²y⁻³

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Answer:

You can multiply them in any order to get the same different result. The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.

Step-by-step explanation:

You can multiply them in any order to get the same different result. The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.

Answer:

1 /

Step-by-step explanation:

2 x

3 /

4 x

5 /

Basta Yan answer mrron akong anwer key

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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This is an example of a sample survey or a sampling method.

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

In the given scenario, you are conducting a sample survey to determine the proportion of each color of Peanut Butter M&Ms. A sample survey is a method used to collect data from a subset of a larger population in order to make inferences about the entire population.

Instead of counting every single Peanut Butter M&M in existence, which would be impractical and time-consuming, you decide to take a smaller representative sample. You purchase 10 packages of Peanut Butter M&Ms, each weighing 1.69 ounces, and count the number of M&Ms of each color in those packages.

By analyzing the data collected from this sample, you can estimate the proportion of each color of Peanut Butter M&Ms in the larger population. This approach is more feasible and provides a reasonable approximation of the overall distribution of colors without having to examine every individual item.

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Answer:

x^2 + 2x + 1

Step-by-step explanation:

Divide the original equation by 3x-1

The big three similarity theorems are AA rule, SAS rule, or SSS rule.

There are three rules for checking similar triangles: AA rule, SAS rule, or SSS rule.

Angle-Angle (AA) Similarity Theorem: With the AA rule, two triangles are said to be similar if two angles in one particular triangle are equal to two angles of another triangle.

The SAS Similarity Theorem: If an angle of one triangle is congruent to an angle of a second triangle and the including sides of that angle are proportional, then the triangles are similar.

The SSS Similarity Theorem: If three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

Euclidean geometry may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional. If the three angles (AAA) are congruent between two triangles, that does NOT mean that the triangles have to be congruent. They are the same shape (and can be called similar), but we don’t know anything about their size.

Thus, the big three similarity theorems are AA rule, SAS rule, or SSS rule.

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(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

Could you explain the problem a bit more?

Step-by-step explanation:

Answer:

d 180 miles

Step-by-step explanation:

4.5×40= 180 miles

The actual distance to college Lisa and Susan going together is 180 miles.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The map scale is 1 in. = 40 mi.

Lisa and Susan are driving to college together, On the map, Lisa measures the distance to be 4.5 inches.

Therefore,

The actual distance to college is,

= (4.5×40) miles.

= 180 miles.

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The Justification for each step in solving the system of equations is listed below.

A system of equations is a set of two or more equations with the same variables, used to describe a problem with multiple relationships between the variables. Solving a system of equations means finding the values of the variables that satisfy all the equations in the system simultaneously.

3x-2y=1

2x+2y=4

5x = 5    (Addition Property of Equality)

x = 5/5  

x = 1       (Division Property of Equality)

3x-2y=1

3(1) - 2y = 1 (Substitution Property of Equality)

3 - 2y = 1

-2y = 1 - 3

-2y = -2  (Subtraction Property of Equality)

y = -2/(-2)

y = 1       (Division Property of Equality)

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The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

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Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

Answer & Step-by-step explanation:

In the problem, we are asked to find the quotient. The quotient is the number that we get once we divide two numbers.

We are asked to find the quotient of 9⁵ ÷ 9⁵.

When a number is divided by itself, then the answer is always going to be 1.

So, the quotient of 9⁵ ÷ 9⁵ is going to be 1.

Answer:

a

Step-by-step explanation:

Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

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