Find value of K for which
Y=2x+K is tangent to
y=x²-4x+4

The power series expansion of\(f(x) = 6x^2 - 4\) centered at x = 0 is: \(6x^2 - 4 = -4 + 3x^2 + ...\)

To expand the function \(f(x) = 6x^2 - 4\) in a power series centered at x = 0, we can use the formula:

\(f(x) = ∑n=0^∞ an(x - 0)^n\)

where \(an = f^(n)(0) / n!\) is the nth derivative of f(x) evaluated at x = 0.

First, let's find the first few derivatives of f(x):

\(f(x) = 6x^2 - 4\)

f'(x) = 12x

f''(x) = 12

f'''(x) = 0

f''''(x) = 0

...

Notice that the derivatives of f(x) are zero starting from the third derivative. Therefore, we can write the power series expansion of f(x) as:

\(f(x) = f(0) + f'(0)x + f''(0)x^2 + ...\\= -4 + 0x + 6x^2 + 0x^3 + ...\)

Using the formula for an in the power series expansion, we get:

\(an = f^(n)(0) / n!\)

a0 = f(0) = -4 / 0! = -4

a1 = f'(0) = 0 / 1! = 0

a2 = f''(0) = 6 / 2! = 3

a3 = f'''(0) = 0 / 3! = 0

a4 = f''''(0) = 0 / 4! = 0

...

Substituting these coefficients into the power series expansion, we get:

\(f(x) = -4 + 0x + 3x^2 + 0x^3 + ...\)

Therefore, the power series expansion of\(f(x) = 6x^2 - 4\) centered at x = 0 is: \(6x^2 - 4 = -4 + 3x^2 + ...\)

Note that this power series converges for all values of x with |x| < 1.

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Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

\(\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx \)

Here 5 is a constant so it can come out . So that,

\(\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx \)

Now we can write √x as ,

\(\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx \)

Simplify ,

\(\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx \)

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

\(\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) \)

On simplifying we will get ,

\(\longrightarrow \underline{\underline{ I = 2 }}\)

Step-by-step explanation:

\(thank \: you\)

Answer:

value of x = 8

Step-by-step explanation:

well here,

line x is parallel to the line measuring 18

so the two triangles are similar to each other

hence ratio of their sides are equal

so 6/ 12 = x/ 16

=》1/2 = x/16

=》 x = 16 / 2

=》 x = 8

i hope u got it

have a nice day

Answer:

x = \(\frac{16}{3}\)

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{6}{6+12}\) = \(\frac{x}{16}\) , that is

\(\frac{6}{18}\) = \(\frac{x}{16}\) ( cross- multiply )

18x = 96 ( divide both sides by 18 )

x = \(\frac{96}{18}\) = \(\frac{16}{3}\)

Answer:

1. 3

2. 1

3. 9

4. 30

Step-by-step explanation:

1. 2*(18/12) = 3

2. 3*(5/15) = 1

3. 4*(45/20) = 9

4. 21*(10/7) = 30

Answer:

1. 2:x and 12:18

6

2. 2:15 and x:3

1

3. x:4 and 45:20

9

4. 21:x and 7:10

24

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

First, find the sides by looking at how many squares are filled. Using that you add to find the perimeter. (In this case, it was 8.5) Take the perimeter and multiply it by 2. Then you have your answer. (17.) If it was the other way around you would multiply by 1/2.

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

QRN=128°

Step-by-step explanation:

MNR+RNP = 180

52 + RNP = 180

RNP= 180 - 52

RNP = 128° = QRN

Or MNR= QRL = 52

QRL= NRS = 52 —> Opposite angles

QRN+NRS=180

QRN+52=180

QRN=180-52

QRN=128

I hope I helped you^_^

Answer:

Since there are a total of six friends and they each use a $2 off coupon then what you first want to do is multiply:

2 times 6 = 12

Then you want to add:

42 + 12 = 54

So the total that they would have spent without the discount would be $54.

Step-by-step explanation:

Hope it helps! =D

Answer:

1. The cost increases $0.30 each time 1 goldfish is

added.

Answer: 4 seconds

Step-by-step explanation:

The required linear function rule is W = (1/2) t.

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

here, we have,

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

At t = 0, W  =  0

At t = 20 minutes , W = 10 inches

W = k*t  

The y intercept = 0 because t = 0 W = 0

now,

10 inches = k * 20minutes

k = 10/20

k = 1/2 inches / minute

Hence, W = (1/2) t

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Answer:

It would be a diameter

Step-by-step explanation:

The diameter is also a chord.

The measure of ZAFD is 50 degrees.

Based on the given information:

ZCFE is congruent to ZCFA.

mZCFB = 68°.

mZEFD = 62°.

To find the measure of ZAFD, we can use the fact that angles in the same segment of a circle are equal.

Since ZCFE and ZCFA are congruent, angle ZCFE is equal to angle ZCFA.

Therefore, mZCFA = mZCFE.

Now, let's find the measure of angle ZCFE:

mZCFE = mZCFB + mZEFD (Angle Addition Postulate)

mZCFE = 68° + 62°

mZCFE = 130°

Since ZCFA is congruent to ZCFE, we can conclude that mZCFA is also equal to 130°.

Now, to find the measure of ZAFD, we need to consider the angles in the quadrilateral ZAFD.

The sum of the angles in a quadrilateral is always 360°.

mZAFD + mZAFB + mZBFD + mZBFA = 360°

We know that mZAFB and mZBFD are equal to 90° because they are right angles (angle AFB and angle BFD are right angles in the diagram).

Therefore, we can rewrite the equation as:

mZAFD + 90° + 90° + mZBFA = 360°

Simplifying:

mZAFD + 180° + mZBFA = 360°

Rearranging the equation:

mZAFD + mZBFA = 360° - 180°

mZAFD + mZBFA = 180°

We know that mZBFA is equal to mZCFA, which is 130°.

Substituting the known values into the equation:

mZAFD + 130° = 180°

Subtracting 130° from both sides:

mZAFD = 180° - 130°

mZAFD = 50°

Therefore, the measure of ZAFD is 50 degrees.

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Answer:

4/5

Step-by-step explanation:

Since we know that the first ratio that we have is 16:20, all you have to do is simplify by dividing and you get 4/5.

There you go.

A decision maker has to consider several factors when selecting a course of action. The options from which a decision maker chooses a course of action are generally influenced by several factors.

A decision maker has to consider several factors when selecting a course of action. The options from which a decision maker chooses a course of action are generally influenced by several factors. These factors may include the organization's objectives, resources available, legal and regulatory requirements, social and cultural norms, and other considerations. When making a decision, the decision maker has to weigh the pros and cons of each option and select the one that will best achieve the desired outcome.
In addition to the factors mentioned above, a decision maker may also need to consider the potential risks and benefits of each option. They may also need to consult with others who have expertise in the area, seek input from stakeholders, or conduct research to gather additional information. Once the decision maker has carefully considered all of these factors, they can then choose the course of action that best meets the needs of the organization.
The decision-making process can be a complex and challenging task. It requires careful thought, analysis, and evaluation of options to select the best course of action. A decision maker should also be aware of the potential consequences of their decision and take steps to minimize any negative impacts. Ultimately, the goal of the decision-making process is to make an informed choice that will lead to positive outcomes for the organization and its stakeholders.

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The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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Answer:

Step-by-step explanation:

To determine price per lb, divide dollar amount by lbs.

- Company A sells 2 1/2lbs (2.5lbs) for $32.50

So, Company A's price / lb = ($32.50/2.5lbs) = $13.00/lb

- Company B sells 2 3/4lbs (2.75lbs) for $35.00

And, Company B's price / lb = ($35.00/2.75lbs) = $12.73/lb

Therefore, Company B is offering the lowest price/lb at $12.73/lb.

Answer:

0.000602

Step-by-step explanation:

Sorry if that is wrong

Legend

The term that refers to the labels at the right of the graph indicating how each subcategory is represented is the Legend.

The Legend is a key that indicates what the different colors, lines, or other symbols in a graph represent. It is usually located at the right or bottom of the graph and provides a clear explanation of the different subcategories.

The Legend is an essential component of a graph, as it helps the viewer understand the information presented in the graph. Without the Legend, the graph can be confusing and difficult to interpret. It is important to ensure that the Legend is clear and easy to understand so that the viewer can quickly identify the different subcategories represented in the graph.

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Answer:

approx. 113.1

Step-by-step explanation:

Area formula: A= pi* (r^2)

12/2 = 6, so r=6

A= pi * (6^2)

A= pi * (36)

A = approx. 113.1

The distance from the earth to venus is an illustration of the sine ratio

The distance from the earth to venus at that time is 1.12 au

See attachment for the diagram that illustrates the complete question.

Start by calculating the angle V using the following sine ratio

SE/sin(V) = VS/sin(E)

This gives

1/sin(V) = 0.723/sin(39.4)

Take the inverse of both sides

sin(V)/1 = sin(39.4)/0.723

Evaluate the quotient

sin(V) = 0.8779

Take the arcsin of both sides

V = 61.4

Calculate the measure of angle S

<S + <V + <E = 180

This gives

<S  = - <V - <E + 180

Substitute known values

<S  = -61.4 - 39.4 + 180

<S  = 79.2

The distance (VE) is then calculated using the following sine ratio

VE/sin(S) = VS/sin(E)

This gives

VE/sin(79.2) = 0.723/sin(39.4)

Multiply bot sides by sin(79.2)

VE = sin(79.2) * 0.723/sin(39.4)

Evaluate the product

VE = 1.12

Hence, the distance from the earth to venus at that time is 1.12 au

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The possible values of the expression when the inequality is true, are:

(8, ∞).

Here we have the absolute value expression:

A = |x + 3|

And we know that x > 5, replacing that in the inequality, we will see that the lower bound of the possible values is:

A  >|5 + 3|

A > 8

Then the values allowed for the expression are all the values in the range (8, ∞).

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Answer:

-50

Step-by-step explanation:

The numbers are separated by three

Answer:

\(a_{n}\) = 3n - 87

Step-by-step explanation:

There is a common difference between consecutive terms , that is

- 81 - (- 84) = - 78 - (- 81) = - 75 - (- 78) = - 72 - (- 75) = 3

This indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 84 and d = 3 , then

\(a_{n}\) = - 84 + 3(n - 1) = - 84 + 3n - 3 = 3n - 87

The measure of each interior angle of the polygon is 150 degrees.

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Therefore, a regular polygon is a polygon with all sides equal to each other.

Therefore, the regular polygon above has 12 sides. Therefore, the polygon is dodecagon.

Measure of each interior angle of the regular polygon = 180(n - 2) / n

Measure of each interior angle of the regular polygon = 180(12 - 2) / 12

Measure of each interior angle of the regular polygon = 1800 / 12

Measure of each interior angle of the regular polygon = 150 degrees.

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 \(\textsf{Hey there!}\)

\(\mathsf{|2s| + 19= 13}\\\textsf{Solve both sides by -19}\\\mathsf{|2s|+19+ (-19)=13+(-19)}\\\mathsf{Cancel\ out:\ 19 + (-19) \ because\ that\ gives\ you\ 0}\\\mathsf{Keep: 13 + (-19)\ because\ that\ helps\ us\ solve\ for\ our\ answer}\\\mathsf{13 + (-19) = -6}\\\mathsf{Solve\ for\ absolute\ value: |2s| = -6}\\\mathsf{Any\ absolute\ values\ CANNOT\ be\ less\ than\ 0}\\\mathsf{\boxed{\boxed{\mathsf{Thus, \ this\ make\ your\ answer\ is: \boxed{\boxed{\bf{No\ solution}}}}}}}\checkmark\)

\(\textsf{Good luck on your assignment and enjoy your day!}\)

~\(\frak{LoveYourselfFirst:)}\)

Answer:

couldnt draw sorry but heres the answers for a

Step-by-step explanation:

for x = -2

x+y= 6

-2+8=6

so y=8

for x=-1 do the same and y= 7

for x =0 y=6

for x=1 y=5

for x=2 y=4

for x=3 y=3