Use the indicated table of integrals to evaluate this:
∫√(x-x^2)dx

Assuming that one snap cube represents one milliliter (ml) of paint, we can use five red snap cubes to represent 5 ml of red paint and three blue snap cubes to represent 3 ml of blue paint. We can arrange these snap cubes in a row to represent the recipe:

RRRRR BBB

This indicates that we mix 5 ml of red paint with 3 ml of blue paint to create the maroon paint.

To draw a sketch of the snap-cube representation of the maroon paint, we can combine the red and blue snap cubes into a single row:

RRRRR BBB

This gives us a row of eight snap cubes, which represents the maroon paint. Visually, the maroon paint will appear as a blend of red and blue, with a darker, richer hue than either color alone.

Each snap cube represents one milliliter (ml) of paint. Therefore, in this representation, each snap cube represents a fixed amount of paint, regardless of the color. In other words, each cube represents a unit of volume, rather than a unit of color or pigment.

Probability of Janie winning game = (2⁴⁷ - 1)/2⁴⁷  or approximately 0.999999999999978, using binomial distribution with given information.

We can solve this probability by using the binomial distribution. Let X be the random variable representing the number of heads in the remaining tosses until one of the players wins the game. Since Luka has 24 points, Janie needs to win X heads before Luka wins one more.

We want to find the probability that Janie wins the game, which is the probability that X is greater than or equal to Luka's remaining points needed to win(25 - 24 = 1).

Let p be the probability of the coin landing heads up, and q be the probability of the coin landing tails up, so that p + q = 1. Since the coin is fair, p = q = 1/2.

Using the binomial distribution, the probability that Janie wins the game is:

P(X >= 1) = 1 - P(X = 0)

where

P(X = k) = [tex](47 - 24 choose k) (1/2)^k (1/2)^(47 - 24 - k)[/tex]

= (23 + k choose k) (1/2)⁴⁷

where k = 0, 1, 2, ..., 23.

Therefore,

P(X = 0) = (23 choose 0) (1/2)⁴⁷ = 1/2⁴⁷

P(X >= 1) = 1 - P(X = 0) = 1 - 1/2⁴⁷

Simplifying,

P(X >= 1) = (2⁴⁷ - 1)/2⁴⁷

Therefore, the probability that Janie wins the game is (2⁴⁷ - 1)/2⁴⁷ or approximately 0.999999999999978.

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Therefore, it will take Sam 8 minutes to cut another identical plank into only 3 pieces, working at the same pace.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equals sign (=). The LHS and RHS can be made up of variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the relationship between the LHS and the RHS. Equations are fundamental to many areas of mathematics, science, engineering, and everyday life.

Here,

If Sam cuts a plank of wood into 4 pieces, then he needs to make 3 cuts. Since each cut takes equally as long, he spends 12/3 = 4 minutes per cut.

To cut another identical plank of wood into 3 pieces, he needs to make 2 cuts. Since he spends 4 minutes per cut, it will take him 2 * 4 = 8 minutes to complete this task.

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The correct sequence of steps for copying Line Segment DE using dynamic geometry software is in the order of 2,1,4,3. So, correct option is C.

The correct sequence of steps for copying Line Segment DE using dynamic geometry software is:

1.) Draw Line Segment DE with endpoint H on the circle.

2.) Draw a point and label it G.

3.) Construct a circle centered at the point G with radius Line Segment DE.

4.) Line Segment DE ≅ Line Segment GH

Therefore, option c.) 2,1,4,3 is the correct sequence of steps. The first step is to draw the original line segment DE with endpoint H on the circle.

The second step is to draw a point and label it G. The third step is to construct a circle centered at G with the same radius as Line Segment DE. Finally, in the fourth step, the line segment GH is drawn such that it is congruent to Line Segment DE, completing the copy of Line Segment DE.

So, correct option is C.

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The correct symbol to compare the expressions is < (less than).

7 × (2/10) is equivalent to 1.4, which is less than 7. Therefore, 7 is greater than 1.4, and we can write 7 × (2/10) < 7 as the comparison between the expressions.

To compare the two expressions, we can analyze their values without actually multiplying them. The expressions are:

1. 7 × (2/10)
2. 7

Now let's simplify the first expression without multiplying:

7 × (2/10) = 7 × (1/5) (since 2 and 10 have a common factor of 2)

Now let's compare:

7 × (1/5) ? 7

Since we're multiplying 7 by a fraction that is less than 1 (1/5), the result will be smaller than 7. Therefore, the correct comparison symbol is "<":

7 × (1/5) < 7

The correct expression so formed is 7 × (2/10) < 7.

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The style that will be least expensive for the project, based on the product of the fractions representing the dimensions is the Style D that will yield a total cost of $25.92

A fraction is a representation of a part of a whole. It is a quantity which forms part of a whole number.

The area Qiang wants to tile = 3 ft × 3 ft

The price list and area of each tile, based on the product of the fractions of the tile dimensions are;

A; (5/6) × (1 1/12) = 65/72 cost 3.25

B; (5/6) × (2 1/12) = 125/72 cost 6.20

C; (5/6) × (5/6) = 5/16 cost  2.75

D; (5/12) × (3/4) = 5/16 cost 0.90

E; (5/12) × (5/12) = 25/144 cost 0.65

The areas of the tiles are;

The number of tiles required,  are;

Cost of tiles style A = 9/(65/72) × 3.25 = 32.4

Cost of tiles style B = 9/(125/72) × 6.20 = 32.14

Cost of tiles style C = 9/(5/16) × 2.75 = 79.2

Cost of tiles style D = 9/(5/16) × 0.90 = 25.92

Cost of tiles style E = 9/(25/144) × 0.65 = 33.696

The least expensive style for the project is style D

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Answer:

Sure. Here is the equation for the cost, C, after h hours of babysitting:

```

C = 3 + 5h

```

This equation can be found by combining the flat fee of $3 with the hourly rate of $5. For example, if Nicole babysits for 2 hours, she will make $3 + (2 * $5) = $13.

To find how much Nicole will make after babysitting for 8 hours, we can simply substitute h = 8 into the equation. This gives us:

```

C = 3 + 5(8) = 3 + 40 = $43

```

Therefore, Nicole will make $43 after babysitting for 8 hours.

Answer:c= 3 + 5(8)

Step-by-step explanation:

3 is flat fee, and then plus $5 and hour. you know she's going for 8 hours, so you multiply hourly rate by the number of hours plus flat fee and you get your answer

Rachel's beginning balance one year ago if she has made no other deposits during the year is $800.00. Therefore, the correct option is 2.

To find Rachel's beginning balance one year ago, given that she currently has $836 in a savings account with a 4.5% annual compound interest rate, we'll use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount ($836)

P = the principal (beginning balance) - this is what we're trying to find

r = the annual interest rate (0.045 or 4.5%)

n = the number of times interest is compounded per year (assuming it's compounded annually, n = 1)

t = the number of years (1 year)

First, rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Now, plug in the values:

P = 836 / (1 + 0.045/1)^(1*1)

Simplify the equation:

P = 836 / (1.045)^1

Calculate the result:

P ≈ 800.00

So, Rachel's beginning balance one year ago was approximately $800.00 which corresponds to option 2.

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The equation y=0.96x represents the cost in dollars and cents, y, for x bottles of apple juice at store A. This means that if Landon wants to buy x bottles of apple juice from store A, he would pay 0.96x dollars and cents. However, we do not know the value of x from the given information.

On the other hand, we know that Landon can buy 14 bottles of apple juice from store B for $34.16. This means that the cost of one bottle of apple juice at store B is $2.44 (34.16 ÷ 14). We do not know the cost of one bottle of apple juice at store A, but we can use the equation y=0.96x to find out.

Let's assume that Landon wants to buy 14 bottles of apple juice from store A as well. We can substitute x=14 in the equation to find the total cost:

y = 0.96(14) = 13.44

This means that Landon would pay $13.44 for 14 bottles of apple juice at store A. However, we can see that buying 14 bottles of apple juice from store B is cheaper than buying the same amount from store A, as Landon would pay $34.16 at store B and $13.44 at store A. Therefore, it is more cost-effective for Landon to buy apple juice from store B in this case.

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Answer:

4

Step-by-step explanation:

2/3 / 1/6

= 2/3 * 6/1

= 12/3

= 4.

The general solution to the differential equation dy/dt - 5y = A is y = Ce^(5t) + A/5, where C is a constant of integration. The general solution is y = (A/5) + Ce^(5t). so, the correct answer is D).

The general solution to the differential equation dy/dt - 5y = A, where A is a constant, is

y = Ce^(5t) + A/5

where C is an arbitrary constant determined by any initial or boundary conditions given.

The general solution is a combination of the homogeneous solution y_h = Ce^(5t) (which satisfies the differential equation without the constant term A) and the particular solution y_p = A/5 (which satisfies the differential equation with A but without any initial or boundary conditions).

so, the correct option is D).

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--The given question is incomplete, the complete question is given

" Answer quickly please

Given that A is a constant, the general solution to the differential equation dy/dt -5y = A is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y = Ce^(5t) +A/5 The solution to the exact differential equation"--

To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.

What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where     P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.

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The maximum value of f(x, y) = x^y on the unit circle can be found using the constraint x^2 + y^2 = 1, which defines the unit circle. To solve this, we can use the method of Lagrange multipliers.

Let g(x, y) = x^2 + y^2 - 1. Then, the gradient of f(x, y) and the gradient of g(x, y) should be proportional:
∇f(x, y) = λ∇g(x, y)

Calculating the gradients:
∇f(x, y) = (yx^(y-1), x^y * ln(x))
∇g(x, y) = (2x, 2y)

Equating the components and dividing the equations, we get:
y * x^(y-1) / 2x = x^y * ln(x) / 2y

Simplifying, we obtain:
ln(x) = y

Now, using the constraint x^2 + y^2 = 1, we can substitute y with ln(x) and solve for x:
x^2 + (ln(x))^2 = 1

Numerically solving this equation, we get x ≈ 0.90097 and y ≈ ln(0.90097) ≈ -0.10536. Since we are only interested in positive values of x and y, this is the only solution in our domain. Now, we can find the maximum value of f(x, y):
f_max = f(0.90097, -0.10536) ≈ 0.79307

So the maximum value of f(x, y) on the unit circle is approximately 0.79307.

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The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.

To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:

A(shaded) = A(large circle) - A(small circle)

= πR² - πr²

We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:

A(shaded) = πR² - π(R/2)²

= πR² - πR²/4

= 3πR²/4

Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.

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The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.

To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:

A(shaded) = A(large circle) - A(small circle)

= πR² - πr²

We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:

A(shaded) = πR² - π(R/2)²

= πR² - πR²/4

= 3πR²/4

Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.

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The solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a)

For the polynomial; k²x³ - 6kx + 9 divided by x - 1, we shall evaluate for f(1) to solve k as follows:

k²(1)³ - 6k(1) + 9 = 1

k² - 6k + 9 - 1 = 0

k² - 6k + 8 = 0

by factorization;

(k - 4)(k - 2) = 0

k = 4 or k = 2

Therefore, solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .

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Step-by-step explanation:

the

answer

of

this

question

is

9 \sqrt{2}

Do you like this (^__^) ??

Answer:

The integers are 129 and 130.

Step-by-step explanation:

[tex] {(x + 1)}^{2} - {x}^{2} = 259[/tex]

[tex] {x}^{2} + 2x + 1 - {x}^{2} = 259[/tex]

[tex]2x + 1 = 259[/tex]

[tex]2x = 258[/tex]

[tex]x = 129[/tex]

[tex]x + 1 = 130[/tex]

The two consecutive integers whose squares have a difference of 259 are 8 and 9.

Let x be the first of the two consecutive integers, then the next integer would be x+1. We are given that the squares of these two integers have a difference of 259, so we can write an equation as (x+1)^2 - x^2 = 259. Expanding the equation gives x^2 + 2x + 1 - x^2 = 259.

Simplifying the equation gives 2x + 1 = 259. Subtracting 1 from both sides gives 2x = 258, which means x = 129. Therefore, the two consecutive integers are 129 and 130. However, we need to check if their squares have a difference of 259. We find that 130^2 - 129^2 = 169 + 260 = 429, which is not equal to 259.

Therefore, the assumption that x is 129 is incorrect. Instead, we try x = 8. Then, the next integer is 9, and their squares are 64 and 81 respectively. The difference between their squares is 81 - 64 = 17, which is not equal to 259. However, if we reverse the order, we get 81 - 64 = 259. Therefore, the answer is 8 and 9.

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part a.

the percentage of eggs between 42 and 45mm is 48.48%

part b.

The median width is approximately (42+45)/2 = 43.5mm.

The median length is approximately (56+59)/2 = 57.5mm.

part c.

The width of grade A chicken eggs has a range of about 24mm.

part d.

I think its impossible to determine because we don't have the value for the standard deviation.

The second option should be correct.

A histogram is described as an approximate representation of the distribution of numerical data.

part a.

From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have  a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.

part b.

we have an  estimation  that the median of the width is 48mm and the median of the length is around 60mm.

part c.

Also from the histogram, we notice  that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.

In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.

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The only possible value of W is:

W ≈ 71.6° to the nearest 10th of a degree.

We can use the Law of Cosines to find the angle W opposite to the side w:

cos(W) = (v^2 + w^2 - u^2) / (2vw)

cos(W) = (3.6^2 + 5.3^2 - u^2) / (2 * 3.6 * 5.3)

We can solve for u by using the Law of Cosines for the angle V:

cos(V) = (u^2 + v^2 - w^2) / (2uv)

cos(32°) = (u^2 + 3.6^2 - 5.3^2) / (2 * u * 3.6)

Simplifying the equation and solving for u, we get:

u = sqrt(3.6^2 + 5.3^2 - 2 * 3.6 * 5.3 * cos(32°)) ≈ 3.8 inches

Now we can substitute this value of u into the equation for cos(W) and solve for cos(W):

cos(W) = (3.6^2 + 5.3^2 - 3.8^2) / (2 * 3.6 * 5.3) ≈ 0.315

Taking the inverse cosine, we get:

W ≈ 71.6° or W ≈ 288.4°

Note that since the angle W is in a triangle, it must be between 0° and 180°. Therefore, the only possible value of W is:

W ≈ 71.6° to the nearest 10th of a degree.

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We can start by using the formula for the volume of a cylinder, which is:

V = πr^2h

where V is the volume, r is the radius (half of the diameter), and h is the height.

In this problem, we are given the height and volume of the can, but we need to find the diameter (which is twice the radius). We can rearrange the formula above to solve for the radius:

r = √(V/πh)

Substituting the given values, we get:

r = √(144/π x 11.4) ≈ 1.5 cm

Finally, we can find the diameter by doubling the radius:

d = 2r ≈ 3 cm

Therefore, the can's diameter is approximately 3 centimeters.

To determine if we can conclude that more than 60% of the sampled population have completed the Hepatitis B vaccine series, we need to perform a hypothesis test.

Our null hypothesis (H0) is that the proportion of infants who completed the vaccine series is equal to or less than 60%, while our alternative hypothesis (Ha) is that the proportion is greater than 60%.

We can use a one-sample proportion test to test this hypothesis. The test statistic is calculated as follows:

z = (p - P) / sqrt(P(1-P)/n)

where p is the sample proportion (0.66), P is the hypothesized proportion under the null hypothesis (0.6), and n is the sample size (14).

Plugging in the values, we get:

z = (0.66 - 0.6) / sqrt(0.6(1-0.6)/14) = 0.67

Using a significance level of α = 0.01, our critical value for a one-tailed test is 2.33 (from a z-table). Since our test statistic (0.67) is less than the critical value (2.33), we fail to reject the null hypothesis.

Therefore, we cannot conclude that more than 60% of the sampled population have completed the hepatitis b vaccine series based on these data.

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Let's simplify the expression step by step:

25xy * sqrt(81/625 * x^2 * y^2)

= 25xy * (sqrt(81)/sqrt(625) * sqrt(x^2) / sqrt(y^2))

= 25xy * (9/25 * x/y)

= 9xy * 5/5

= 9xy

Therefore, the simplified form of the expression 25xy * sqrt(81/625 x^2y ^2) is option C, 9xy|xy|.

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To conduct a hypothesis test comparing the mean voltages of the two types of batteries (K and Q), you'll need to state the null and alternative hypotheses. The null hypothesis (H₀) is that there is no difference between the mean voltages, while the alternative hypothesis (H₁) is that there is a difference between the mean voltages. In this case:

Step 1 of 5: State the null and alternative hypotheses for the test.

H₀: μ1 - μ2 = 0 (The true mean voltage for type K batteries is equal to the true mean voltage for type Q batteries.)

H₁: μ1 - μ2 ≠ 0 (The true mean voltage for type K batteries is not equal to the true mean voltage for type Q batteries.)

In the next steps, you would calculate the test statistic, determine the critical value, make a decision to reject or fail to reject the null hypothesis, and finally interpret the results based on the 0.02 level of significance.

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Nine ears of sweetcorn will cost $2.25 at this store.

To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:

1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.

2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.

So, nine ears of sweetcorn will cost $2.25 at this store.

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If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy.

If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy. This could happen due to various reasons such as work done against a force, energy transferred to another object, or energy lost as heat. Here's a step-by-step explanation:

1. Identify the initial energy of the object.
2. Subtract 50 joules from the initial energy to find the final energy: Final energy = Initial energy - 50 J.
3. Analyze the situation to determine the reason for the energy loss, such as work done, energy transfer, or heat loss.
4. If necessary, calculate the amount of work done, energy transferred, or heat lost using appropriate equations and given data.

By following these steps, you can determine the final energy of the object after it has lost 50 joules and understand the reason for the energy loss.

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The farmer sold 3.16 kilograms of apples at the farmers market.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Let's start by finding out the weight of pears the farmer sold.

Weight of pears = 3/5 x 7.9 kg = 4.74 kg

To find the weight of apples, we can subtract the weight of pears from the total weight:

Weight of apples = Total weight - Weight of pears

Weight of apples = 7.9 kg - 4.74 kg

Weight of apples = 3.16 kg

Therefore, the farmer sold 3.16 kilograms of apples at the farmers market.

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The derivative of f(x) is: f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

The Fundamental Theorem of Calculus is a pair of theorems that link the concept of differentiation and integration. It states that if a function f(x) is continuous on an interval [a, b] and F(x) is the antiderivative of f(x) on the same interval, then:

Part I: The derivative of the integral of f(x) from a to x is equal to f(x):

d/dx ∫a to x[tex]f(t) dt = f(x)[/tex]

Part II: The integral of the derivative of a function f(x) on an interval [a, b] is equal to the difference between the values of the function at the endpoints of the interval:

∫a to b [tex]f'(x) dx = f(b) - f(a)[/tex]

Using Part I of the Fundamental Theorem of Calculus, we have:

f(x) = x∫4 1/(1+4t⁴) dt

Then, by the Chain Rule, we have:

f'(x) = d/dx [x∫4 1/(1+4t⁴) dt] = ∫4 d/dx [x(1/(1+4t⁴))] dt

= ∫4 (1/(1+4t⁴)) dt

= [tan⁻¹(2t)/2]₄¹

= [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

Therefore, the derivative of f(x) is:

f'(x) = [tan⁻¹(2)/2] - [tan⁻¹(1/2)/2]

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The length of the diagonal of the square is 22 meters.

A square is a four-sided two-dimensional geometric shape in which all sides are equal in length and all angles are right angles (90 degrees).It is a unique instance of a rectangle with equal sides. The opposite sides of a square are parallel to each other and the diagonals bisect each other at right angles.

A square is divided into two 45-45-90 triangles by its diagonal.

In a 45-45-90 triangle, the hypotenuse (the side opposite the right angle) is √2 times as long as each leg.

Therefore, in this square, the length of the diagonal (d) can be found by multiplying the length of one side (s) by √2:

d = s√2

In this case, the side length of the square is 11√2 meters, so:

d = 11√2 × √2 = 11 × 2 = 22 meters

Therefore, the length of the diagonal of the square is 22 meters.

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Answer:

10.24 gallons

$276.48

Step-by-step explanation:

The area of the wall can be calculated by multiplying the length and height of the wall:

Area of wall = length x height = 32 x 16 = 512 square feet

To calculate the number of gallons of paint needed, we need to divide the area of the wall by the coverage of one gallon of paint:

Number of gallons of paint = Area of wall / Coverage of one gallon of paint

Number of gallons of paint = 512 / 50

Number of gallons of paint = 10.24

Therefore, it will take approximately 10.24 gallons of paint to paint the wall.

To calculate the cost of the paint, we need to multiply the number of gallons of paint by the cost per gallon:

Cost of paint = Number of gallons of paint x Cost per gallon

Cost of paint = 10.24 x $27

Cost of paint = $276.48

Therefore, it will cost $276.48 to paint the wall.