find the taylor series for f(x) centered at the given value of a. (assume that f has a power series expansion. do not show that rn(x) 0.) f(x) = x3, a = -1

Answer:

hope this helpss

Step-by-step explanation:

Answer:

Step-by-step explanation:

if you have to simplify it then distribute -2

x²-2(x+5)=x²-2x-10

if problem is as mentioned by other answerer,then

\(\frac{d}{dx} (x^2-2(x+5))=-2\\x^2-2x-10= \int (-2dx)+c\\x^2-2x-10=-2x+c\\x^2=c+10\\x=\pm \sqrt{c+10}\)

According to the described way the volume of solid S is 156.25π.

Since the cross sections perpendicular to the x-axis and the base are semicircles, we know that the radius of each cross section is given by:

r = y = √(25 -\(x^{2}\) )  

where x is the distance from the center of the circle to the cross section, which lies along the x-axis.

The circle  \(x^{2}\)+ \(y^{2}\) = 25 has a radius of 5, and its center is at the origin (0,0). Thus, the farthest a cross section can be from the center of the circle is at x = 5 or x = -5.

To find the volume of the solid S, we need to integrate the area of each cross section over the range from x = -5 to x = 5. The area of each cross section is given by:

A = (1/2)πr^2

Substituting the expression for r above, we get:

A = (1/2)π(25 - x^2)

Integrating this expression over the range from x = -5 to x = 5 gives us:

V = ∫(-5)^5 (1/2)π(25 - x^2) dx

Using integration rules, we can evaluate this integral to get:

V = (1/2)π ∫(-5)^5 (25x - x^3) dx

V = (1/2)π [ (25/2)x^2 - (1/4)x^4 ]|_-5^5

V = (1/2)π [ (25/2)(5^2) - (1/4)(5^4) - (25/2)(-5^2) + (1/4)(-5^4) ]

V = (1/2)π [ 625/2 - 625/4 + 625/2 - 625/4 ]

V = (1/2)π (625/2)

V = (312.5/2)π

V = 156.25π

Therefore, the volume of solid S is 156.25π.

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Answer:

\(10 \times 3.5 = 22x\)

Step-by-step explanation:

It is given that:

Parker wishes to construct a \(\text{playhouse}\) for his sister. The width and the height of the house is not scaled to the yard space.

So the width of the play house = 22 centimeters

The height of the play house = 10 centimeters

Bu the space in the \(\text{yard is large}\) enough that a play house can be constructed so that it have a width of \(3.5\) meters.

So the cross multiplication of the proportion that parker uses to find the height of the playhouse is given by : \(10 \times 3.5 = 22x\)

Answer:

The answer is C, (10) (3.5) = 22 x

Hope this helped!

P. S. : Can I get brainliest please?

The number 8.49 × 10⁻⁷ in decimal form is 0.000000849.

When a number is expressed in scientific notation, such as 8.49 × 10⁻⁷, it means that we need to multiply the first part (8.49) by the power of 10 raised to the exponent (-7). In this case, the exponent is negative, indicating that the decimal point needs to be shifted to the left.

To convert the number into decimal form, we move the decimal point 7 places to the left since the exponent is -7. This gives us the decimal representation of 0.000000849.

So, the correct answer is 0.000000849.

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The transfοrmatiοn frοm the parent graph \(f(x) = 3^x\)tο \(g(x) = -2(3)^x+5\) can be described as a reflectiοn abοut the x-axis, fοllοwed by a vertical cοmpressiοn by a factοr οf 2, and finally, a vertical shift upward by 5 units.

The functiοn g(x) is οbtained by transfοrming the parent graph οf \(f(x) = 3^x\)in the fοllοwing way:

Therefοre, the transfοrmatiοn frοm the parent graph \(f(x) = 3^x\) tο\(g(x) = -2(3)^x+5\) can be described as a reflectiοn abοut the x-axis, fοllοwed by a vertical cοmpressiοn by a factοr οf 2, and finally, a vertical shift upward by 5 units.

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Answer:

m is the slope and b is the y intercept

Answer:

can you translate to English

Step-by-step explanation:

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

After answering the given query, we can state that The property was sold  equation for R 2,8 million, so the estate agency will receive a commission of R 196,000.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

We must multiply the selling price by the royalty rate in decimal form to determine the estate agent's fee on a property sold for R 2,8 million:

Selling Price x Commission Rate equals Commission

Commission: R2,800,000 multiplied by 0.07

R 196,000 is the commission.

The property was sold for R 2,8 million, so the estate agency will receive a commission of R 196,000.

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The company spends $649 on advertising

The sales function after advertising is given as:

\(S(x) = 5 + 7\ln(x + 1)\)

When the total sales is $19,100, we have S(x) = 19100

So, the sales function becomes

\(5 + 7\ln(x + 1) = 19.1\)

Subtract 5 from both sides

\(7\ln(x + 1) = 14.1\)

Divide both sides by 7

\(\ln(x + 1) = 2.014\)

Take exponents of both sides

\(x + 1 = e^{2.014\)

\(x + 1 = 7.49\)

Subtract 1 from both sides

\(x= 6.49\)

Hence, the company spends $649 on advertising

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If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Thus, the velocity of money in would be 3.5 .

The velocity of money is a measure of the rate at which money changes hands in an economy. It is calculated by dividing the nominal GDP by the money supply.

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Therefore, Verne can line up his books in 4,920 more orders than Jenny can line up hers.

To calculate the difference in the number of possible orders for lining up the books, we need to find the factorial of the number of books for each person.

The number of ways Verne can line up his 7 math books is 7 factorial (7!), which is calculated as:

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

= 5,040

The number of ways Jenny can line up her 5 English books is 5 factorial (5!), which is calculated as:

5! = 5 × 4 × 3 × 2 × 1

= 120

To find the difference in the number of possible orders, we subtract the number of ways Jenny can line up her books from the number of ways Verne can line up his books:

7! - 5! = 5,040 - 120

= 4,920

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Answer:

Answer: A

Step-by-step explanation:

The cos(theta) = adjacent / hypotenuse

The cos(theta) = 4/5

cos(theta) = 0.8

theta = cos^-1 (0.8)

theta = 36.9

theta = A

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit. If Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. Then the original investment is $1500.

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

Percent to decimal 4%=4/100=0.04

A=P(1+rt)

where A is the final amount

P is initial principle balance, t is time and r rate of interest.

1560=P(1+0.04)

1560=1.04P

P=1560/1.04

P=1500

Therefore $1500 is originally invested.

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The scale factor would be 9/4 (last option) as 4*(9/4) is equal to 9.

Answer:  Choice B

We are 90% confident that the mean weight of all newborn babies is between 6.5 and 8.5 pounds.

Explanatiion:

The idea is that if we generate say 100 confidence intervals, then about 90 of them should capture the true population mean (mu) somewhere in them. Choice A is close to being true, but replace "sample" with "population" to make the statement fully correct.

We don't need a confidence interval to estimate a sample statistic. A confidence interval is used to estimate a population parameter. Choice C is a trick answer and a common misconception about confidence intervals. Choice D is a slight variation of choice A. These facts allow us to rule out choices A, C and D.

a)1 unit or less away from the x-plane. b) 1 unit or less away from the y-plane. c)1 unit or less away from the z-plane.

d)1 unit or less away from the w-plane.

a. The region on or the parabola in the ​x-plane and all points which are 1 unit or less away from the ​x-plane.
To find the region on or the parabola in the x-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the x-plane.

b. The region on or the parabola in the ​y-plane and all points which are 1 unit or less away from the ​y-plane.
To find the region on or the parabola in the y-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the y-plane.

c. The region on or the parabola in the z-plane and all points which are 1 unit or less away from the z-plane.
To find the region on or the parabola in the z-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the z-plane.

d. The region on or the parabola in the w-plane and all points which are 1 unit or less away from the w-plane.
To find the region on or the parabola in the w-plane, we need to graph the equation of the parabola and determine the points that are 1 unit or less away from the w-plane.

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To find the Taylor polynomial t3(x) for the function f(x) = xe^(-4x) centered at a = 0, we need to find the first four derivatives of f(x) at x = 0, evaluate them at x = 0, and use them to construct the polynomial.

The first four derivatives of f(x) are:

f'(x) = e^(-4x) - 4xe^(-4x)

f''(x) = 16xe^(-4x) - 8e^(-4x)

f'''(x) = -64xe^(-4x) + 48e^(-4x)

f''''(x) = 256xe^(-4x) - 256e^(-4x)

Evaluating these derivatives at x = 0, we get:

f(0) = 0

f'(0) = 1

f''(0) = -8

f'''(0) = 48

f''''(0) = -256

Using these values, we can construct the third-degree Taylor polynomial t3(x) for f(x) centered at x = 0:

t3(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3!

t3(x) = 0 + 1x - 8x^2/2 + 48x^3/3!

t3(x) = x - 4x^2 + 16x^3/3

Therefore, the third-degree Taylor polynomial for the function f(x) = xe^(-4x) centered at a = 0 is t3(x) = x - 4x^2 + 16x^3/3.

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The experimental probability of the coin landing heads up is calculated by dividing the number of times the coin landed heads up (16) by the total number of flips (40). So the experimental probability of the coin landing heads up is:

P(heads up) = 16/40

Simplifying the fraction by dividing both the numerator and denominator by 8, we get:

P(heads up) = 2/5 or 0.4

Therefore, based on the results, the experimental probability of the coin landing heads up is 0.4 or 2/5.

To find the experimental probability of the coin landing heads up, you'll need to use the following formula:

Experimental probability = (Number of successful outcomes) / (Total number of trials)

In this case, the successful outcome is the coin landing heads up, which occurred 16 times. The total number of trials is 40 flips. So, the experimental probability would be:

Experimental probability (heads up) = (16 successful outcomes) / (40 total flips)

Now, divide 16 by 40 to get the probability:

Experimental probability (heads up) = 16/40 = 0.4 or 40%

So, based on the results, the experimental probability of the coin landing heads up is 40%.

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Answer:

107

Step-by-step explanation:

Probability = numbers that add up to 10 / total of numbers

There are 120 positive integers between 1 - 2020 that add up to 10.

120 / 2020

convert to its simplest form by dividing by 20

6 / 101

m + N = 101 + 6 = 107

Answer:

15x^2 - 48x + 36

Step-by-step explanation:

You have done the first part correctly. Now, we add all the terms inside the box and add them all together.

15x^2 - 18x - 30x +36

Simplify by adding like terms

15x^2 - 48x +36

Answer: 15x2−48x+36 as simplified!!

Step-by-step explanation: maybe

Answer:

6+3i

Step-by-step explanation:

4+2=6

-3i+6i=3i

6+3i

Answer:

6+3i

Step-by-step explanation:

just got it right besties

Answer:

Angle CAB

Step-by-step explanation:

Find the points that correspond to angle 2 and name them in order.

Step-by-step explanation:

female workers:2250

% female workers:?

First, find the percentage of workers who aren't men since we are told the number of workers who aren't men

100-55=45

Therefore 45% of workers aren't men

Let the total number of workers =x

Now form an equation for the problem

\(x \times \frac{45}{100} = 2250\)

\(x = 2250 \div \frac{45}{100} \)

\(x = 5000\)

Therefore, there are 5000 workers in total

If Argyle says that she has collected data that only tell her whether the cases are the same or different, one can accurately say that she has collected data on the nominal level.

The nominal level of measurement is the least strict type of data measurement in which the measurements or observations are grouped into distinct categories without a specific order or value structure. At this stage of measurement, variables are defined as categorical because the groups and categories can only be counted, which is usually done using frequencies and proportions.

The nominal level of measurement can take the form of either binary or multichotomous. Binary variables have only two groups, while multichotomous variables have more than two groups. Variables that are frequently used in this level of measurement include gender, race, or political affiliations.

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Answer:

Step-by-step explanation:

30  30 x 3 = 90

x 3

90  

first  multiply 4 x 5 = 20 bring down 0 then multiply 4 x 2 = 8 then add+2= 10

25 x 4 = 100

12 x 15 = 180

Answer:

d

Step-by-step explanation:

Answer:

D. infrared

Step-by-step explanation:

edge 2021