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Answer:

6

Step-by-step explanation:

The Taylor series expansion for the function f(x) = 1/x centered at c = 7 is given by the infinite sum:

f(x) = 1/7 - 1/49(x-7) + 1/343(x-7)² - 1/2401(x-7)³ + ...

And the interval of convergence for this series is (7 - R, 7 + R),

To find the Taylor series for a function, we start by calculating the derivatives of the function at the center point (c) and evaluating them at c. In this case, we have f(x) = 1/x, so let's begin by finding the derivatives:

f(x) = 1/x f'(x) = -1/x² (derivative of 1/x)

f''(x) = 2/x³ (derivative of -1/x²)

f'''(x) = -6/x^4 (derivative of 2/x³)

f''''(x) = 24/x⁵ (derivative of -6/x⁴) ...

We can observe a pattern in the derivatives of f(x). The nth derivative of f(x) can be written as (-1)ⁿ⁺¹ * n! / xⁿ⁺¹, where n! represents the factorial of n.

Now, we can use these derivatives to construct the Taylor series expansion. The general form of the Taylor series for a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)²/2! + f'''(c)(x-c)³/3! + ...

In our case, the center point is c = 7. Let's substitute the values into the series:

f(x) = f(7) + f'(7)(x-7) + f''(7)(x-7)²/2! + f'''(7)(x-7)³/3! + ...

To find the coefficients, we need to evaluate the derivatives at c = 7:

f(7) = 1/7 f'(7) = -1/49 f''(7) = 2/343 f'''(7) = -6/2401 ...

Plugging these values into the series, we get:

f(x) = 1/7 - 1/49(x-7) + 2/343(x-7)²/2! - 6/2401(x-7)³/3! + ...

Simplifying further:

f(x) = 1/7 - 1/49(x-7) + 1/343(x-7)² - 1/2401(x-7)³ + ...

Now, let's talk about the interval of convergence for this Taylor series. The interval of convergence refers to the range of values of x for which the Taylor series accurately represents the original function. In this case, the function f(x) = 1/x is not defined at x = 0.

Therefore, the interval of convergence for this Taylor series is (7 - R, 7 + R), where R is the distance from the center point to the nearest singularity (in this case, x = 0).

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Recall that the general form of a straight line is

where A,B and C are real numbers.

To find this equation, we will first find the slope intercept form of the line and then apply mathematical operations so we get the form we are looking form. Recall that the slope-intercept form of a line is of the form

where m is the slope and b is the y intercept. We will first find the slope.

Recall that the slope of a line that passes through the points (a,b) and (c,d) is given by the formula

so in our case we have a=5,b=2, c=-1 and d=4. So we get

So far, our line equation would look like this

Note that as we want this line to pass through the point (5,2), this means that if we replace x=5 in this expression we should get y=2. So we have

so if we add 5/3 on both sides, we get

so our equation becomes

Now, from this equation we can look for the general form. First, we will multiply both sides by 3, so we get

now, we add x on both sides, so we get

Finally, we subtract 11 on both sides, so we get

which is the general form of the line

Answer:

  maximum: 3

Step-by-step explanation:

You want to know if the quadratic f(x) = -3(x -5)(x -3) has a minimum or a maximum, and what that extreme value is.

In this factored form the leading coefficient is the constant factor outside parentheses: -3. The fact that it is negative means the graph opens downward, so has an extreme value that is a maximum.

The other factors are zero for x=5 and for x=3. The x-value of the maximum is the average of these zeros: (5+3)/2 = 4.

The value of the function at x=4 is ...

  f(4) = -3(4 -5)(4 -3) = (-3)(-1)(1) = 3

The maximum value is 3.

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A cubic close-packed (ccp) unit cell has a coordination number of 12.

A cubic close-packed (ccp) unit cell has an arrangement of atoms where each atom is surrounded by 12 other atoms, resulting in a coordination number of 12.

A cubic close-packed (ccp) unit cell is a type of unit cell that has an arrangement of atoms where each atom is surrounded by 12 other atoms. This arrangement forms a structure with a coordination number of 12, meaning that each atom has 12 other atoms in contact with it. This type of arrangement is very common in many materials, and is often used to describe the structure of metals and other crystalline materials. The atoms in a ccp unit cell are arranged in a regular pattern, with three atoms in each of the eight corners and four atoms in the center of each face of the unit cell.

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Answer:

Step-by-step explanation:

A. m<1 + m<2 + m<3 + m<4 = 360

B. The sum of the measures of angles of a triangle is 180°

C. The measure of all right is 90°

D. Because <1 and <2 are each supplementary to <3, they are therefore congruent

Step-by-step explanation:

f(x) = 4x-5

g(x) = 2x

(f + g)(x)=f(x) +g(x)=4x-5+2x=6x-5

Answer:

105

Step-by-step explanation:

7x15=105

Answer: 35

Step-by-step explanation:

If you multiply 5X7 it gives you 35 if 3lbs cost 15 that means every lb cost 5 , or you can add 5 +5 till you get 35

Answer:

14/27

Step-by-step explanation:

7/3 ÷ 9/2

7/3 x 2/9 = 14/27

Answer:

Step-by-step explanation:

Answer

254.34

Step-by-step explanation:

A = pi * r^2

A = 3.14 * 9^2

A = 3.14 * 81

A = _____ square feet

each base angle would be 56 degrees

Answer:

b

Step-by-step explanation:

0.223 rounds to 0.2 and 0.54 rounds to 0.5 so 0.5-0.2

Answer:

5 problems an hour

Step-by-step explanation:

7 days x 5 hours = 35 total hours

150 problems ÷ 35 hours = 4.3 problems an hours,

which would then be rounded up to 5.

The length of RS is 6.32 unit (B).

To find the length of RS, we can use the distance formula:

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

where:

(x₁, y₁) = coordinate of point 1

(x₂, y₂) = coordinate of point 2

In this case, we have:

the coordinates of R: (-2, -4)

the coordinates of S: (-8, -6).

Plugging in these values into the distance formula, we get:

D = √[(-8 - (-2))² + (-6 - (-4))²]

D = √[(-6)² + (-2)²]

D = √[36 + 4]

D = √40

D = 6.32

Therefore, the length of RS is about 6.32 units.

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Answer:

12x - 29 + 4x + 1 = 180

Step-by-step explanation:

(12x - 29) and (4x + 1) are same- side interior angles and sum to 180° , then

12x - 29 + 4x + 1 = 180 ← is the equation to solve for x

16x - 28 = 180 ( add 28 to both sides )

16x = 208 ( divide both sides by 16 )

x = 13

To determine the stationing of PT on the horizontal curve, we need to consider the given information of the backsite bearing, deflection angle, and degree of curvature. By utilizing the stationing of PC, which is 6+88, we can calculate the stationing of PT.

The backsite bearing of N 10°E indicates that the tangent line extends 10° east of north. The deflection angle of 57° signifies the change in direction from the tangent line to the chord connecting PC and PT. The degree of curvature D, which is 5°, provides the angular change per station.

To calculate the stationing of PT, we need to determine the length of the curve between PC and PT. This can be done by dividing the deflection angle (57°) by the degree of curvature (5°) to obtain the number of stations. In this case, the length of the curve is 57° / 5° = 11.4 stations.

Next, we add the length of the curve (11.4 stations) to the stationing of PC (6+88) to find the stationing of PT. The stationing of PT is 6+88 + 11.4 = 18+28.4.

In summary, the stationing of PT on the horizontal curve, given a backsite bearing of N 10°E, a deflection angle of 57°, and a degree of curvature of 5°, is 18+28.4.

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Answer:

Step-by-step explanation:

∠CBD=1/2×88=44°

πr2 is an example of (D) a model.

Therefore, πr2 is an example of (D) a model.

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The complete question is given below:

Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?

A. a robot

B. a car

C. a telescope

D. a model

Using the long division method, the result of the division of the given polynomials is 3x² + 2x + 7.

Given is a polynomial division.

We have to find the result of the division using long division.

Dividend is 3x³ + 8x² + 11x + 14 which is divided by x + 2.

Now,

3x³ = 3x² × x

So the first term of the result is 3x².

3x² (x + 2) = 3x³ + 6x²    

Remainder is,                      

3x³ + 8x² + 11x + 14 - (3x³ + 6x²) = 2x² + 11x + 14

Now, 2x² = 2x (x)

So the second term of the result is 2x.

2x (x + 2) = 2x² + 4x

Remainder is,

2x² + 11x + 14 - (2x² + 4x) = 7x + 14

Now, 7x = 7 (x)

So the third term of the result is 7.

7 (x + 2) = 7x + 14

Remainder is,

7x + 14 - (7x + 14) = 0

Hence the result is 3x² + 2x + 7.

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Answer: y=2.5x+90

Step-by-step explanation:

idk

Answer: y =2.5x+90

Step-by-step explanation:

The composite function that can be used to calculate the final price of Jonah's car is f[c(p)] = 0. 9265p.

A composite function is a function that is in another function, such that on solving the composite function the result is the same as the function solve individually.

We know that the sale price of Jonah's car is c(p) = 0. 85p, where p is the original price of the car. Also, the tax on the car is 9% of the sale price, and the final price of the car is f(c) = 1. 09c, including tax, therefore, the composite function can be written as,

\(f(c) = 1.09 c\)

We already know the value of c, therefore,

\(f(c(p)) = 1.09 (0.85p)\\\\f(c(p)) = 10.9265(p)\)

Hence, the composite function that can be used to calculate the final price of Jonah's car is f[c(p)] = 0. 9265p.

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Both answers are "translation" which is the same as up/down/left/right shifting.

Refer to the diagram below to see how the reflections combine to form this shifting. A composition of two reflections always leads to a translation whenever the mirror lines are parallel. The direction of the shifting is perpendicular to the parallel lines. If the mirror lines intersected, then we'd have a rotation instead.

I used GeoGebra to create the diagram.

Answer:

put the -×+1 is y so yeah it equals 47×-746

Answer:

0.6

Step-by-step explanation:

1) 1.4-0.8 (A negative and a positive equals a negative, then you just subtract. On the number line you would start at 1.4 and go back)

hope this helps!

Answer:

Domain: (−∞,∞),{x | x ∈ R}

Range: [0,∞),{y|y≥0}

Step-by-step explanation:

The form of controls that are effective in eliminating, reducing, or minimizing hazards is called; Engineering controls

Engineering controls are defined as strategies that are designed to protect workers from hazardous conditions by placing a barrier between the worker and the hazard or by removing a hazardous substance through air ventilation.

Now, the reason why this is effective in eliminating, reducing, or minimizing hazards is because they are designed to remove the hazard at the source, before it comes in contact with the worker.

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Answer:

first of all the average score of students is 62.

and there are 27 students

so full marks scored by students are 27×62= 1674

and 1 new students added to that so his score would be 1674+ 53(his marks)= 1727

so now the mean of students are beause there are one more students so 27+1 = 28 then 28÷1727= 61.6 is the mean now

Answer:

To find the vertex and x-intercepts for the quadratic function f(x)=4.9x^2-28x+40:

First, we can find the x-coordinate of the vertex using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.

In this case, a = 4.9 and b = -28, so:

x = -(-28)/2(4.9) = 2.86

Next, we can find the y-coordinate of the vertex by plugging in this x value into the original function:

f(2.86) = 4.9(2.86)^2 - 28(2.86) + 40 = 6.65

So the vertex is at (2.86, 6.65).

To find the x-intercepts, we can set the function equal to zero and solve for x:

4.9x^2 - 28x + 40 = 0

We can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the coefficients, we get:

x = (28 ± sqrt(28^2 - 4(4.9)(40))) / 2(4.9)

Simplifying:

x = (28 ± sqrt(144.4)) / 9.8

x = 5.36 or 1.43

So the x-intercepts are (5.36, 0) and (1.43, 0).