the answer to the question obviously

Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

To use Taylor polynomial approximation to avoid loss-of-significance error in the formula x^3 * x - sin(x) when x is near 0, we can first find the Taylor polynomial of degree 6 for the function.

P(x) = f(a) + f'(a)(x-a) + (f''(a)(x-a)^2)/2! + (f'''(a)(x-a)^3)/3! + ... + (f^(n)(a)(x-a)^n)/n!

where f(a) represents the function value at the point a, and f^(n)(a) represents the nth derivative of the function evaluated at a.

For the given function, we have:
f(x) = x^3 * x - sin(x)

Taking the derivatives of f(x), we have:
f'(x) = 4x^3 - cos(x)
f''(x) = 12x^2 + sin(x)
f'''(x) = 24x - cos(x)

To find the Taylor polynomial of degree 6, we need the function values and derivatives evaluated at x = 0:
f(0) = 0
f'(0) = 0
f''(0) = 0
f'''(0) = 0

Using these values in the Taylor polynomial formula, we get:
P(x) = 0 + 0(x-0) + 0(x-0)^2/2! + 0(x-0)^3/3! + 0(x-0)^4/4! + 0(x-0)^5/5! + 0(x-0)^6/6!

Simplifying the polynomial, we have:
P(x) = 0
To know more about avoid visit :

https://brainly.com/question/30637335

#SPJ11

There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.

What is permutation?

In mathematics, it is the number of ways in which given number of items can be arranged in different orders.

Here, we need to select 5 iteams from the given 14 iteams.

\(P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240\)

Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.

Learn more about permutation from the following link:

https://brainly.com/question/12468032

#SPJ4

The sytem of liner equation are that satisfies the given conditon are:

L1 : 2x-y=5

L2 : 3x - y = 10

Given that one of the line of the sytem of equations passes through (2,-1) and also given that solution of system of equations is (5,5) so it justifies that  the 1st line passes through (2.-1) and (5,5) so the equation of 1st line is given by:

To find the equation of a line that passes through the points (2, -1) and (5, 5), we can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two given points and the formula for the slope into the point-slope form, we get:

y - (-1) = ((5 +1) / (5 - 2))(x - 2)

= (6 / 3)(x - 2)

= 2(x - 2)

= 2x - 4

=> 2x- y =5

so the equation of line 1 is 2x-y=5

And as mentioned that equation of line that passes through (5,5) but as given it won't pass through (2,-1)

so let m be the slope of 2nd line and passes through (5,5)

so the equation of line is given by:

y-5 = m (x-5)

and if this  line won't pass through (2,-1) then

-1 - 5 ≠ m (2 -5)

m  ≠ 2

so the equation of 2nd line is given by:

y - 5 = 3(x-5)

=> 3x - y = 10

So the equation of sytem of liner equation are

L1 : 2x-y=5

L2 : 3x - y = 10

To know more about linear equation click on below link:

https://brainly.com/question/11897796#

#SPJ4

The amount of the annual withdrawals will be $16,574.24.The amount is the sum of the principal and the simple interest gain.

The complete repayment of money at the end of the time period for which it was borrowed is referred to as the amount.

The given data in the problem is;

P ia the annual payment

PV is the present value = $150,261

r is the rate of intreast = 9.1% = 0.091

n is the time period= 20

The formula for the annual payment is found as;

\(\rm P= \frac{r \times PV}{1-(1+r)^{-n}} \\\\ \rm P= \frac{0.091 \times 150261}{1-(1+0.091)^{-20}} \\\\ \rm P=16,754.2437\)

Hence the amount of the annual withdrawals will be $16,574.24.

To learn more about the amount refer to the link;

https://brainly.com/question/12184047

Answer:

7 ( x + 3 )

Step-by-step explanation:

Use order of operations to multiply first.

3+2x2 +7 x + 14

3+4 +7 x + 14

Now group like terms.

3+ 7x + 4 + 14

Add like terms

7x + 21

Find the two multiples of 21.

7x + 7 x 3

Now factor out the 7.

7( x + 3 )

Using linear approximation, the estimated distance the boat will coast is approximately 266 feet. (Rounded to the nearest whole number.)

To estimate the distance the boat will coast using a linear approximation, we can consider the average velocity over the given time interval.

The initial velocity is 39 ft/s, and 9 seconds later, the velocity decreases to 20 ft/s. Thus, the average velocity can be approximated as:

Average velocity = (39 ft/s + 20 ft/s) / 2 = 29.5 ft/s

To estimate the distance traveled, we can multiply the average velocity by the time interval of 9 seconds:

Distance ≈ Average velocity * Time interval = 29.5 ft/s * 9 s ≈ 265.5 ft

Using linear approximation, we estimate that the boat will coast approximately 266 feet.

To learn more about number, click here:

brainly.com/question/3589540

#SPJ1

Answer:

sorry. I need points.

Step-by-step explanation:

.......................

As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .

The initial price of the car is set at P = 18300 (units)

The price after lowering drom P becomes A= 16000 (units)

Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.

The formula for calculating percentage change is given as follows,

Change in percentage = [(Change in value)/ ( Initial value) ]*100

⇒Change in percentage = (C/ P)*100

⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)

To know more about change iin percentage here

https://brainly.com/question/14801224

#SPJ4

The equation of motion we will use is

Where

v is the final velocity

u is the initial velocity

a is the acceleration

t is the time

From the problem, we can figure out that the starting velocity, u, is 20. The time, t, is 40. The final velocity, v, will be 0.

Substituting, let's figure out acceleration, a :

The acceleration is negative because it is deceleration.

Answer:

There is no solution (since none has side length of 4 units)

Step-by-step explanation:

If V (-1,1) is one of vertex of a square, then the next vertex to V distance must be the known value of 4

VA: V to (-3,3)   = √(-1 - -3)² + (1 - 3)² = √8 = 2.8

VB: to (-5,-3)     = √(-1 - -5)² + (1 - -3)² = √32 = 5.7

VC: o (3,3)        = √(-1 -3)² + (1 - 3)² = √20 = 4.47

VD: to (-5,3)      = √(-1 - -5)² + (1 - 3)² = √20 = 4.47

VE: to (4,5)        = √(-1 - 4)² + (1 - 5)² = √41 = 6.4

ANSWER:

Shift 3 units left and 4 units down

STEP-BY-STEP EXPLANATION:

The function g(x) is located in the third quadrant, that is, in the quadrant that is down and to the left.

We can carefully observe that the translation was 3 units to the left and 4 units down.

Answer:

The length of side x in a 30-60-90 triangle is 2√3.

Step-by-step explanation:

The numbers 30-60-90 are angles, so we need to find the side x of a right triangle with the following information:

θ: is one angle of the right triangle = 30°

α: is the other angle of the right triangle = 60°

a: is one side of the right triangle = √3

b: is the other side of the right triangle =?

x: is the hypotenuse of the right triangle =?

The length of the hypotenuse can be found by Pitagoras:

\( x^{2} = a^{2} + b^{2} \)    (1)

So, we need to find the side "b". We can calculate it with the given angles.

From the side "a" we have:

\( cos(\alpha) = \frac{a}{x} \)

\( cos(60) = \frac{\sqrt{3}}{x} \)    (2)

From the side "b":

\( sin(\alpha) = \frac{b}{x} \)

\( sin(60) = \frac{b}{x} \)   (3)

Now, we can calculate "b" by dividing equation (3) by equation (2).

\( tan(60) = \frac{\frac{b}{x}}{\frac{\sqrt{3}}{x}} \)

\( b = tan(60)*\sqrt{3} = 3 \)

Finally, we can find the length of the hypotenuse with equation (1):

\( x = \sqrt{a^{2} + b^{2}} = \sqrt{(\sqrt{3})^{2} + (3)^{2}} = 2\sqrt{3} \)

Therefore, the length of side x in a 30-60-90 triangle is 2√3.

I hope it helps you!

Hey there!

The answer is D

We solve this by multiplying the exponents, and we get 15:

3 x 5 = 15

So, the answer is 2^15

Hope it helps and have a great day!

Answer:

Step-by-step explanation:

The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe

is 5.75 inches

Determine the volume of metal used to build the pipe.

Answer:

225.1°

155mph

Answer:

True- She needs $3 more. She will not have enough money to buy everything. The cost is $28.

False- She has $3 left over.

Step-by-step explanation:

2 pounds of burgers for $3 each is $6

1 bag o bun equals $2

5 bags of chips for $4 each is $20

$20 + $6 +$2 = $28

She only had $25 to spent, so she doesn't have enough money and needs to 3 more dollars.

Answer:

y = 5 x + 3  

Step-by-step explanation:

I took the quiz

We can use the fact that 1 pound is equal to 0.45359237 kg and then convert it to kg first and then divide it by 0.45359237 kg/lb. So, 500 kg / 0.45359237 kg/lb = 1102.31 lbs

To convert a weight from kilograms (kg) to pounds (lbs), you need to know the conversion factor between the two units.

The conversion factor between kilograms and pounds is 1 kilogram = 2.20462 pounds. To convert a weight in kilograms to pounds, you simply multiply the weight in kilograms by the conversion factor.

To convert 500 kg to lbs, we can use the following calculation:

500 kg * 2.20462 lbs/kg = 1102.31 lbs

For more such questions on Conversion.

https://brainly.com/question/24545553#

#SPJ11

technical feasibility is concerned with evaluating the technological aspects of a proposed project, assessing available resources, and determining if the project can be successfully implemented within the given constraints. It does not directly address user acceptance or incorporation into ongoing business operations, which fall under other aspects such as operational feasibility or organizational feasibility.

Technical feasibility is the evaluation of whether a proposed solution is capable of being developed with available technology and within budgetary and schedule constraints. It assesses the technical resources available in the business and the extent to which the proposed project may be developed from a technical standpoint.

A technical feasibility study focuses on the cost, time, and complexity of the project. It aims to identify and examine the factors that would help or hinder the implementation of the proposed system. This study determines whether the proposed system is achievable within the constraints of available technology, budget, and resources.

To achieve technical feasibility, the project should be analyzed from various angles, such as software, hardware, manpower, and location. It answers the question of whether the project is feasible in terms of the available technology. If the required technology is available, the project can be implemented; otherwise, it will not be feasible.

In summary, technical feasibility is concerned with evaluating the technological aspects of a proposed project, assessing available resources, and determining if the project can be successfully implemented within the given constraints. It does not directly address user acceptance or incorporation into ongoing business operations, which fall under other aspects such as operational feasibility or organizational feasibility.

To know more about technical feasibility

https://brainly.com/question/14009581

#SPJ11

Answer:

X= 5.44  y= 17.85

Step-by-step explanation:

Given that your B angle is 60 degress you can use 17tan(60) to get X which is 5.44.

Then you a²+b²=c² to find y.

y=√17²+5.44²

y= 17.85

Answer: X= 5.44  y= 17.85

Hope this helps

The value of a and b is 1.

The probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is ab, where a and b are integers.

To find the value of a and b, we need to determine the total number of ways Nate can place the disk (the denominator of the probability fraction) and the number of ways he can place the disk so that it touches an equal number of shaded and unshaded squares (the numerator of the probability fraction).

Since the center of the circle must be at the meeting point of four squares, the only possible places for the center are the points where four squares meet. Since the grid is made of 2 cm x 2 cm squares, there are 4 shaded squares and 4 unshaded squares. So, there are 4 centers that could be placed on a shaded square and 4 centers that could be placed on an unshaded square.

So the denominator of the probability fraction is 8.

Now, to calculate the numerator, we need to determine the number of ways Nate can place the disk so that it touches an equal number of shaded and unshaded squares.

As the center of the circle is at the meeting point of four squares, the center of the circle is placed at the intersection of 2 shaded and 2 unshaded squares.

So, the numerator of the probability fraction is 8.

Therefore, the probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is 8 ÷ 8 =1.

So the value of a and b is 1.

Learn more about Probability here:

https://brainly.com/question/11234923

#SPJ4

Answer:

Option 1 = 10pi

Step-by-step explanation:

Formula-2•radius•pi

2•5•pi

10 pi

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

Learn more about probability here;

https://brainly.com/question/6598268

#SPJ4

Answer:

1/6

Step-by-step explanation:

Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = \(2^{4}\), where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

To learn more about Exponential form please visit:

https://brainly.com/question/23275698

#SPJ4

Therefore, the area of the pentagon is 928 square units.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Find the area.

Pentagon

apothem = 16 side = 23.2

Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth

For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.

For the second question, the formula to find the area of a regular pentagon is:

Area = (perimeter x apothem)/2

Since we are given the apothem and the side, we can find the perimeter of the pentagon as:

perimeter = 5 x side = 5 x 23.2 = 116

Substituting the values in the formula, we get:

Area = (116 x 16)/2 = 928

Therefore, the area of the pentagon is 928 square units.

To know more about perimeter visit:

https://brainly.com/question/9369181

#SPJ1

(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

To know more about standard deviation, visit;
https://brainly.com/question/31516010
#SPJ11