which of the following is the nth taylor polynomial tn(x) for f(x)=ln(1−x) based at b=0?

Observe that

\(x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1\)

so that

\(P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1\)

Then

\(P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}\)

Alternatively, we can avoid find \(P(x)\) altogether and instead first write \(x-1\) in terms of \(x+2\) :

\(x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3\)

Then

\(P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1\)

Answer: Depends on what radius you are giving. The Circumradius or the in radius.

If it was the inradius then your Area is 817.36 mm^2

If it was the circumradius then your Area is 534.969 mm^2

Step-by-step explanation:

Answer:

second worksheet :

7,673,495 : place value of 3 = 3,000 as the 3 in 7,673,495 is 3,000

7,673,495: place value of 6 = 600,000 as the 6 in 7,673,495 is 600,000

same applies for the rest of the questions

hope that helped

The overall shape of the distribution is normal.

If the overall shape of the combined distribution for both the class samples and the simulation samples was normal, then it suggests that the individual distributions of the samples were either normally distributed or approximately normally distributed.

A normal distribution, also known as a Gaussian distribution or a bell curve, is a probability distribution that is symmetric and bell-shaped. The normal distribution is commonly used in statistical analysis and modeling because it is often observed in real-world data and has some desirable properties.

When the individual distributions of the samples are combined, their values are added up or averaged, resulting in a larger sample size and a more representative estimate of the underlying distribution. If the individual distributions are normally distributed, then the central limit theorem states that the combined distribution will tend towards normality as the sample size increases. This can explain why the overall shape of the combined distribution for both the class samples and the simulation samples was normal.

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Virtual reality" is the appropriate answer.

The utilization of technological advances gives the impression of a 3D interactive environment wherein the things that have such a perception of space embodiment or involvement, are considered as Virtual reality.

Virtual reality implementations often include:

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The explicit formula for the nth term of the sequence 16, 19, 22 is:

\(a_n = 16 + 3(n-1)\)

What is an sequence ?

A sequence is an ordered list of numbers or other mathematical objects that follow a particular pattern. Each individual number or object in the sequence is called a term. The pattern that governs the sequence is usually defined by a rule or formula that determines how each term is related to the previous terms. Sequences can be finite or infinite, depending on whether there is a last term or not. They can also be arithmetic, geometric, or have more complicated patterns. The formula for the nth term of a sequence is typically derived from observing patterns or relationships among the given terms.

Finding the explicit formula for the given sequence :

To find the explicit formula for the given sequence 16, 19, 22, we can first observe that each term in the sequence is obtained by adding 3 to the previous term. That is, 19 = 16 + 3 and 22 = 19 + 3. This suggests that the sequence follows an arithmetic pattern, where each term is the sum of the first term and a multiple of a common difference d (in this case, d = 3) multiplied by the position of the term minus 1 (n-1).

Using this pattern, we can write the explicit formula as follows:

\(a_n = a_1 + d(n-1)\), where \(a_1\) is the first term and d is the common difference.

Plugging in the values for the first term and common difference in the given sequence, we get:

\(a_n = 16 + 3(n-1)\)

Therefore, the explicit formula for the nth term of the sequence 16, 19, 22 is:

\(a_n = 16 + 3(n-1)\)

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Answer:

Step-by-step explanation:

Note that the given height equation, which is a quadratic) has a graph that opens downward.  Borrowing the quadratic formula, we find the roots of this equation, that is, the t values at which h(t) = 0:

The coefficients of this equation are a = -16, b = 80 and c = 0.

We need to find the roots of this quadratic.  By the quadratic formula,

      -(80) ±√(80² - 4(-16)(0) )         -80 ± 0

t = ------------------------------------- = ----------------- = -5/2 and -5/2 (seconds).

                 2(-16)                               -32

The initial height is 0 at t = 0 seconds and the final height 0 at 5/2 seconds.

Answer:

the answer is the first one

Step-by-step explanation:

because

Answer

c                                                  hope it helps

Answer: It does make sense

Step-by-step explanation:

12*1/6= 12/6

12/6=2

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

(c) The equation, y = -3x + 100, represents the Model S tank.

(f) The Model T tank drains the fastest at 3.5 gallons per minute.

Step-by-step explanation:

Given

See attachment for models S and T

First, we calculate the equation of both models

Model S

\((x_1,y_1) = (0,100)\\\\(x_2,y_2) = (6,82)\)

Calculate drainage rate (m)

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{82-100}{6-0}\)

\(m = \frac{-18}{6}\)

\(m = -3\) -- This implies that model S drains at 3 gallons per minutes

The equation is:

\(y = m(x - x_1) + y_1\)

\(y = -3(x - 0)+100\)

\(y = -3(x)+100\)

\(y = -3x+100\)

Model T

\((x_1,y_1) = (0,100)\\\\(x_2,y_2) = (4,86)\)

Calculate drainage rate (m)

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{86-100}{4-0}\)

\(m = \frac{-14}{4}\)

\(m = -3.5\) -- This implies that model T drains at 3.5 gallons per minutes

The equation is:

\(y = m(x - x_1) + y_1\)

\(y = -3.5(x - 0)+100\)

\(y = -3.5(x)+100\)

\(y = -3.5x+100\)

From the calculations above, the following options are true:

(c) and (f)

It is required to find which statements are true.

The statements that are true are

The equation, y = -3x + 100, represents the Model S tank.

The Model T tank drains the fastest at 3.5 gallons per minute.

Equation of a line is

\(y=mx+c\)

where,

\(y=\text{Gallons of water left}\)

\(x=\text{Minutes passed}\)

\(m=\text{Slope}=\dfrac{\Delta y}{\Delta x}\)

\(c=\text{Y intercept}\)

The equation of the line for model S is

\(y-100=\dfrac{82-100}{6-0}(x-0)\\\Rightarrow y-100=-3x\\\Rightarrow y=-3x+100\)

The option C is true.

The equation of the line for model T is

\(y-100=\dfrac{86-100}{4-0}(x-0)\\\Rightarrow y-100=-3.5x\\\Rightarrow y=-3.5x+100\)

The slope or rate of drain is 3.5 gallons per minute.

So, option F is true.

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Answer:

y=2x is it I think because the y intercept is the origin

The options that can be used as indices for the array are option A (i) and option E ((int)(Math.random() * 100)).

To determine which expressions can be used as an index for the array double[] t = new double[100], let's evaluate each option :

A. i: Since i is an integer variable with a value of 5, it can be used as an index because it falls within the valid index range of the array (0 to 99).

B. I + 6.5: This expression adds 6.5 to the variable i. Since array indices must be integers, this expression would result in a double value and cannot be used as an index.

C. 1 + 10: This expression evaluates to 11, which is an integer value and can be used as an index.

D. Math.random() * 100: The Math.random() function returns a double value between 0.0 (inclusive) and 1.0 (exclusive). Multiplying this value by 100 would still result in a double value, which cannot be used as an index.

E. (int)(Math.random() * 100): By multiplying Math.random() by 100 and casting the result to an integer, we obtain a random integer between 0 and 99, which falls within the valid index range and can be used as an index.

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The equivalent expression of 2^8 x 2^4 is 2^4

The expression is given as

expression 2 exponent 8 x 2 exponent 4

Rewrite the expression as

2^8 x 2^4

The base of the factors in the above expression are the same

i.e. Base = 2

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

2^8 x 2^4 = 2^(8 + -4)

Evaluate the sum in the above equation

So, we have

2^8 x 2^4 = 2^(8 - 4)

Evaluate the difference in the above equation

So, we have

2^8 x 2^4 = 2^4

Hence, the simplified expression of the expression given as 2^8 x 2^4 is 2^4

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Answer: 0.35

Step-by-step explanation:

3.325 divided by 9.5 = 0.35

Answer:

y = -4x - 17

Step-by-step explanation:

y + 1 = -4 (x + 4)

First, distribute the -4

y + 1 = -4x - 16

Then subtract 1 from both sides to make the equation y=

y = -4x - 17

This makes the equation standard form

the linear approximation for 3√126 is approximately 5.06667, rounded to five decimal places.

To estimate the given number 3√126 using a linear approximation (or differentials), follow these steps:

Choose a nearby value that is easy to work with: For 3√126, we can choose 3√125 since 125 is a perfect cube (5^3). So, let our base point be x=125, and we want to estimate at x=126.

Compute the actual value at the chosen point: We know that 3√125 = 5, since 5^3 = 125.

Find the derivative of the function: Our function is f(x) = 3√x, so its derivative f'(x) = (1/3)x^(-2/3).

Compute the derivative at the chosen point: Plug x=125 into f'(x) to get f'(125) = (1/3)(125^(-2/3)) = (1/3)(5^(-2)) = 1/15.

Calculate the linear approximation: Use the formula L(x) = f(a) + f'(a)(x-a), where a is our chosen point (125) and x is the point we want to estimate (126). In this case, L(126) = 5 + (1/15)(126-125) = 5 + (1/15)(1) = 5 + 1/15.

Simplify the linear approximation: L(126) = 5 + 1/15 ≈ 5.06667.

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Step-by-step explanation:

the answer is 10x +100 = 250

The answer is D. R2, also known as the coefficient of determination, shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable.

Of the four answer choices provided, only one is true of R2. Answer D is the correct statement regarding R2. It indicates that R2 shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable. This statement is commonly used to evaluate the strength of a linear relationship between two variables. It is important to note that a high R2 value does not necessarily mean that the explanatory variable causes the dependent variable, but it does suggest a strong correlation between the two. This answer is provided in one paragraph consisting of three sentences.

In other words, R2 measures the proportion of the variance in the dependent variable that can be predicted from the independent variable(s). A higher R2 value indicates a better fit of the data, while a lower value suggests that the model may not explain much of the variation in the dependent variable.

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Answer:

(1, - 5 ) and (5, - 1 )

Step-by-step explanation:

Given the 2 equations

x² + y² = 26 → (1)

x - y = 6 → (2)

Rearrange (2) making x the subject by adding y to both sides

x = 6 + y → (3)

Substitute x = 6 + y into (1)

(6 +y )² + y² = 26 ← expand (6 + y)² and simplify left side

36 + 12y + y² + y² = 26

2y² + 12y + 36 = 26 ( subtract 26 from both sides )

2y² + 12y + 10 = 0 ( divide through by 2 )

y² + 6y + 5 = 0 ← in standard form

(y + 5)(y + 1) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 5 = 0 ⇒ y = - 5

y + 1 = 0 ⇒ y = - 1

Substitute these values into (3) for corresponding values of x

x = - 5 : x = 6 - 5 = 1 ⇒ (1, - 5 )

x = - 1 : x = 6 - 1 = 5 ⇒ (5, - 1 )

The area of the courtyard with a rectangle shape is the expression (4x² + 30x)m²

In calculating for the area of rectangle, the breadth is multiplied by the length of the rectangle

The courtyard has a shape of rectangle with the dimensions 6m by 9m, hence given that the width of the walkway around the courtyard is x.

one of the walkway breadth has area = (6 + 2x) × x

total area of the two walkway breadth = 2 × (6 + 2x) × x

total area of the two walkway breadth = 12x + 4x²

one of the walkway length has area = 9 × x

total area of the walkway length = 2 × 9 × x

total area of the walkway length = 18x

Therefore, the total area of the rectangular walkway = 12x + 4x² + 18x which is 4x² + 30x by simplification.

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Ans

Add 15 to 6  so w= 21

Step-by-step explanation:

Answer:

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Step-by-step explanation:

Let's solve for x.

3x2+y2=9

Step 1: Add -y^2 to both sides.

3x2+y2+−y2=9+−y2

3x2=−y2+9

Step 2: Divide both sides by 3.

3x^2/3= -y^2+9/3

x^2=-1/3 y^2 +3

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Hope it helped!

Answer:

A

Step-by-step explanation:

First you will get 4dz

The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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Answer: 25.00 discount

Step-by-step explanation: the original price of the book was 250 but the man paid 225 which means that he saved 25.