Is X² and 2x like terms?

The required answers are:

a. The linear approximating polynomial at a = 1: P₁(x) = x - 2

b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²

c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.

Using Taylor polynomial series, the required approximating polynomials are calculated.

The Taylor polynomial series is

Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n

Where fⁿ(a) is the nth derivation of f(x) at a

The first order(linear) Taylor polynomial series is

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

The second order(quadratic) Taylor polynomial series is

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

The given function is f(x) = -1/x at a = 1

f(a) = f(1) = -1

f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1

f''(x) = -2/x³; f''(a) = f''(1) = -2

a. Linear approximating polynomial:

From the Taylor series, we have

P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹

On substituting,

P₁(x) = -1 + (1/1!)(x - 1)¹

       = -1 + (x - 1)

       = x - 2

b. Quadratic approximating polynomial:

From the Taylor series, we have

P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) +  [tex]\frac{f''(a)}{2!}[/tex](x - a)²

On substituting,

P₂(x) = f(1) + (1/1!)(x - 1) +  (-2/2!)(x - 1)²

        = -1 + (x - 1) - (x - 1)²

        = -1 + x - 1 - (x² - 2x + 1)

        = x - 2 - x² + 2x - 1

        = -3 + 3x - x²

c. Approximating the given quantity -1/1.06:

Substituting x = -1.06 in P₁(x) and P₂(x),

P₁(x) = x - 2

⇒ P₁(-1.06) = (-1.06) - 2 = -3.06

P₂(x) = -3 + 3x - x²

⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30

Therefore, the approximating polynomials are calculated by using Taylor polynomial series.

Disclaimer: The given question is incomplete. Here is the complete question.

Question:

a. Find the linear approximating polynomial for the following function centered at the given point a.

b. Find the quadratic approximating polynomial for the following function centered at the given point a.

c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.

f(x) = -1/x , a = 1; approximate -1/1.06

Learn more about approximating polynomials here:

https://brainly.com/question/15540322

#SPJ1

The domain and range of the graph of a logarithmic function are;

The basic equation of a logarithmic function can be presented in the form;

[tex]y = log_{b}(x) [/tex]

Where;

b > 0, and b ≠ 1, given that we have;

[tex]y = log_{1}(x)[/tex]

[tex] {1}^{y} = 1[/tex]

The inverse of the logarithmic function is the exponential function presented as follows;

[tex]x = {b}^{y} [/tex]

Given that b > 0, we have;

[tex] {b}^{y} = x > 0[/tex]

Therefore, the graph of a logarithmic function has only positive x-values

The graph of a logarithmic function is one with a domain and range defined as follows;

Domain; 0 < x < +∞

Range; -∞ < y < +∞, which is the set of real numbers.

The correct option therefore has a domain as x > 0 and range as the set of all real numbers.

Learn more about finding the graphs of logarithmic functions here:

https://brainly.com/question/13473114

#SPJ1

Answer:

3 or C

Step-by-step explanation:

The answer above is correct.

Answer:

Step-by-step explanation:96 in the fourth since they are adding the answer itself two times before you get the other like 12 bacteria and then 24 so that means 12 + 12 is 24 and the third one 48 so 24 +24 =48

fourth 48 + 48=96

 fifth 96+96=192

sixth  192+192=384

seventh 384+384=768

last but not least 768+768 = 1536

so your answer is 1,536

The number that is represented by the question mark in the sequence is 2

Sequence are set of numbers that follow a predefined and predetermined patterns guided by a rule

The sequence of numbers is given as:

111= 0, 3213=0,

7756= 1,  7662= 2,

6855= 3,   8096= 5,

6666=4  8193= 3,

9313= 1,   8639= 4,

1234=0,   2581 = 2,

7186= 3,  2(6)7(9)=

From the complete question, the values of the sequence are determined by the count of numbers that are circled or in brackets

In the 2(6)7(9), two numbers are circled.

The numbers are 6 and 9

This means that the value of 2679 is 2

i.e. 2(6)7(9)= 2

Hence, the number that is represented by the question mark in the sequence is 2

Read more about sequence at:

https://brainly.com/question/28150251

#SPJ1

When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.

In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.

In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.

Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.

By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.

Learn more about sampling here:

https://brainly.com/question/17831271

#SPJ1

Answer:

-2y= -23-15

-2y=-38

-y= -38/2

-y=19 proved

The transformation of the coordinate (-8, -3)  R 270° and T-2,-1 is (-5, -9)

Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.

Analysis:

When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)

so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)

When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9

Therefore the transformed coordinate becomes (-5, -9)

Learn more about transformation: brainly.com/question/4289712

#SPJ1

The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

Functions and values

Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;

1/2(x-120)=10

where x is the amount spent on food.

In order to determine the least and greatest amounts that the two friends could spend on food,

For the least amount

-(x-120) = 20

-x+120 = 20

x = 100

For the greatest amount

(x-120) = 20

x = 140

Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively

learn more on functions and values here: https://brainly.com/question/2284360

#SPJ1

The required probability is 0.171.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We can find required Probability as shown:

From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials

[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]

[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]

[tex]=\frac{120+45+10+1}{2^{10}}[/tex]

[tex]=\frac{176}{1024}[/tex]

=0.171

Hence, the required probability is 0.171.

Learn more about Probability here:

https://brainly.com/question/6649771

#SPJ4

Given question is incomplete. This is complete question:

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?

The percent of the time Nicholas earned is the percent of the time 25%

The 5 values of the given box plot are;

The minimum fee = 20

In the first quartile, the 25th percentile point, Q₁ = 25

In the median or second quartile, the fiftieth percentile factor, Q₂ = 30

The 1/3 quartile, the 75th percentile point, Q₃ = 40

The maximum value = 55

The range = The most value - The minimal fee

The range = 55 - 20 = 35

We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.

Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.

In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.

A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.

Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).

Learn more about the percentage here https://brainly.com/question/809966

#SPJ4

c. the least squares method.

Regression equation:

In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).

Least squares method:

The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.

Learn more about Regression Equation on:

https://brainly.com/question/16438646

#SPJ4

Answer:

p ≈ 7.3 m

Step-by-step explanation:

using the Sine Rule in the triangle

[tex]\frac{p}{sinP}[/tex] = [tex]\frac{r}{sinR}[/tex] ( substitute values )

[tex]\frac{p}{sin40}[/tex] = [tex]\frac{10}{sin62}[/tex] ( cross- multiply )

p × sin62° = 10 × sin40° ( divide both sides by sin62° )

p = [tex]\frac{10sin40}{sin62}[/tex] ≈ 7.3 m ( to the nearest tenth )

Answer:

[tex]\fbox {p = 7.3 m}[/tex]

Step-by-step explanation:

Applying the Law of Sines :

[tex]\boxed {\frac{sin R}{PS} = \frac{sin P}{RS}}[/tex]

Substitute the values :

Considering the definition of the absolute value function, the expression is written as -7m + 56.

The absolute value function is defined as follows:

That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.

In this problem, the expression is:

|7m - 56|

For m < 8, we have that one example is m = 0:

7(0) - 56 = -56.

The expression is negative, hence the signal is changed, that is:

|7m - 56| = -(7m - 56) = -7m + 56.

More can be learned about the absolute value function at https://brainly.com/question/24734454

#SPJ1

The complete sentence for the unit circle is:

When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.

In this problem we have sentence to be completed by direct observation to the variables seen in a unit circle, a form used to teach trigonometric functions in a graphic manner. Now we proceed to present the complete sentence below:

When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.

To learn more on trigonometric functions: https://brainly.com/question/6904750

#SPJ1

Each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

The angle of an octagon can be found as follows;

An octagon is a polygon that has 8 sides.

The sum of angles in an octagon is 1080 degrees.

Therefore,

x + x + x + x + x + x + x + 2x = 1080

Hence,

9x = 1080

divide both sides by 9

x = 1080 / 9

x = 120

Therefore, each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

learn more on octagon here:https://brainly.com/question/8517157

#SPJ1

Answer: 0=-4.9t²+19.6t+24.5

Step-by-step explanation:

[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]

(a) The value of the unknown length, a, is 18 cm
(b) The value of the unknown angle measurement, θ, is 39°

From the question, we are to determine the unknown length and angle measurement

(a)

A + B + C = 180° (Sum of angles in a triangle)

A = 180° - (B + C)

A = 180° -(68° + 59°)

A = 53°

Using the law of sines

[tex]\frac{a}{sin A}=\frac{c}{sin C}[/tex]

[tex]\frac{a}{sin 53^\circ}=\frac{19.5}{sin 59^\circ}[/tex]
[tex]a=\frac{19.5 \times sin 53^\circ}{sin 59^\circ}[/tex]

[tex]a= 18.168[/tex]

[tex]a \approx 18 cm[/tex]

(b)

[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]

[tex]\frac{sin \theta}{15}=\frac{sin 57^\circ}{20}[/tex]

[tex]sin \theta=\frac{15 \times sin 57^\circ}{20}[/tex]

[tex]sin \theta=0.6290[/tex]

[tex]\theta=sin ^{-1} (0.6290)[/tex]

[tex]\theta=38.976 ^\circ[/tex]

[tex]\theta \approx 39^\circ[/tex]

Hence, the value of the unknown length, a, is 18 cm
The value of the unknown angle measurement, θ, is 39°

Learn more on Law of sines here: https://brainly.com/question/17021875

#SPJ1

The minimum sample size required to estimate the mean usage of water = 2225.07

What is Standard deviation?

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

We can find the minimum sample size required to estimate the mean usage of water as shown below:

Standard deviation [tex]\sigma =3.61[/tex]

Margin of error E=0.15

Critical value for 95% confidence interval = 1.96

Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]

[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]

=2225.07

Hence, the minimum sample size required to estimate the mean usage of water = 2225.07

Learn more about Standard deviation here:

https://brainly.com/question/22920224

#SPJ4

Answer:

B.

Step-by-step explanation:

If the measures of angles 3 and 4 add to 90, then lines r and p meet at right angles making them perpendicular.

Answer: B.

Answer:

Step-by-step explanation:

Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For the first ticket, since 5 out of 26 letters are vogal, the probability is:

5/26.

For the second ticket, since there is no replacement, the probability is:

4/25.

The probability of both tickets is:

[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]

0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The equation of the unique function exists g(x) = -4(x-3)².

The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.

Given: F(x) = x²

The vertical stretch by a factor of 4 exists can be satisfied by (b)

if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.

Multiply 4 by f(x) which provides 4x².

As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².

Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.

Hence, the unique graph would be g(x) = -4(x-3)²

Therefore, the correct answer is option B. g(x) = -4(x-3)².

To learn more about  equations refer to:

https://brainly.com/question/2273184

#SPJ9

You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.

The Volume that can take up by single blanket is 557 cubic inches.

The dimension of the moving box = 14 × 14 × 14

Hence, the volume of the moving box = 2744 cubic inches

The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5

Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.

Learn more about Volume of box on

https://brainly.com/question/1972490

#SPJ1

19 books can fit into a bookshelf that has a width of 19/4 feet

An equation is an expression that shows the relationship between two or more number and variables.

The bookshelf is 4 3/4 feet wide = 19/4 feet

1 ft = 12 in, hence:

19/4 feet = 19/4 feet * 12 in per feet = 57 inches

Number of books = 57 inches / 3 in = 19

19 books can fit into a bookshelf that has a width of 19/4 feet

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).

A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.

According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.

Learn more about methodical in: https://brainly.com/question/14560322

#SPJ1

$6.12

A percentage is some portion of a whole number. Multiple methods can be used to find percentages.

Multiplication to Find Percentages

One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.

For example,

To convert a percentage to a decimal, just move the decimal point 2 places to the left.

Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.

19% of $32.20

Now, to solve we can just multiply.

The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.

1 tablet weekly reduction in his consumption of tablets.

Algebraic expression is a set of variable, constant and algebraic operations like addition, subtraction, multiplication and division. for example 3x^2+2x+3=0

Tablet after 10 week of doctor visit = 40 tablet

Tablet after 20 week of doctor visit= 30

In 10 week there is a difference of (40-30) 10 tablets.

in 10 week there is reduction of 10 tablets its mean there is reduction of 1 tablet per week

so, the weekly reduction of 1 tablet per week.

To learn more, please refer: https://brainly.com/question/4344214

#SPJ9

The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

According to the statement

Number of blue suit = 1

Number of black suit = 2

Number of brown suit = 1

Number of blue ties = 2

Number of red ties = 3

Number of pink ties = 3

Now we find the probability by its formula

Probability that picked suit is blue = blue suits/ total number of suits

Probability = 1/4

Now,

Probability that picked tie is pink = Pink tie / total number of ties

Probability = 3/8

So, The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

Learn more about PROBABILITY here https://brainly.com/question/7965468

#SPJ4

Answer:

Step-by-step explanation:

1/2 57 * 19.5 =

28.5 * 19.5 =

555.75m²

The value of the expression if x = -1/2 is 15

Given the expression below shown;

f(x) = -6(x - 2)

If the value of x is -1/2, hence;

f(-1/2) = -6(-1/2 - 2)

Simplify

f(-1/2) = -6(-5/2)

f(-1/2) = 6 * 5/2

f(-1/2) = 3 * 5 = 15

Hence the value of the expression if x = -1/2 is 15

Learn more on function and values here: https://brainly.com/question/10439235

#SPj1