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The taylor polynomials for 2 is \(7 + 7x^2\) and for 3 is \(7x + (7/3)x^3.\)

To find the Taylor polynomials for a function, we need to calculate the function's derivatives at the point where we want to center the polynomials. In this case, we want to center the polynomials at x=0.

First, let's find the first few derivatives of\(f(x) = 7tan(x):\)

\(f(x) = 7tan(x)\)

\(f'(x) = 7sec^2(x)\)

\(f''(x) = 14sec^2(x)tan(x)\)

\(f'''(x) = 14sec^2(x)(2tan^2(x) + 2)\)

\(f''''(x) = 56sec^2(x)tan(x)(tan^2(x) + 1) + 56sec^4(x)\)

To find the Taylor polynomials, we plug these derivatives into the Taylor series formula:

\(P_n(x) = f(0) + f'(0)x + (f''(0)x^2)/2! + ... + (f^n(0)x^n)/n!\)

For n=2:

\(P_2(x) = f(0) + f'(0)x + (f''(0)x^2)/2!\)

\(= 7tan(0) + 7sec^2(0)x + (14sec^2(0)tan(0)x^2)/2\)

\(= 7 + 7x^2\)

So the second-degree Taylor polynomial centered at x=0 for f(x) is \(P_2(x) = 7 + 7x^2.\)

For n=3:

\(P_3(x) = f(0) + f'(0)x + (f''(0)x^2)/2! + (f'''(0)x^3)/3!\)

\(= 7tan(0) + 7sec^2(0)x + (14sec^2(0)tan(0)x^2)/2 + (14sec^2(0)(2tan^2(0) + 2)x^3)/6\)

\(= 7x + (7/3)x^3\)

So the third-degree Taylor polynomial centered at x=0 for f(x) is \(P_3(x) = 7x + (7/3)x^3.\)

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Answer: 0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared:   a=x*0.75

Zach: b= (x+10)*0.8

total a+b=101

final equation

0.75x+0.8(x+10)=101

Answer:

r is usually the radius but can also be a variable, in this case r = -189

Step-by-step explanation:

Solve for r:

-13 = r/9 + 8

Put each term in r/9 + 8 over the common denominator 9: r/9 + 8 = r/9 + 72/9:

-13 = r/9 + 72/9

r/9 + 72/9 = (r + 72)/9:

-13 = (r + 72)/9

-13 = (r + 72)/9 is equivalent to (r + 72)/9 = -13:

(r + 72)/9 = -13

Multiply both sides of (r + 72)/9 = -13 by 9:

(9 (r + 72))/9 = -13×9

(9 (r + 72))/9 = 9/9×(r + 72) = r + 72:

r + 72 = -13×9

9 (-13) = -117:

r + 72 = -117

Subtract 72 from both sides:

r + (72 - 72) = -72 - 117

72 - 72 = 0:

r = -72 - 117

-72 - 117 = -189:

Answer: r = -189

Answer:

No

Step-by-step explanation:

the ratio of 15:12 is not equivalent to the ratios above. The ratios above have a common factor of 3, while 15:12 does not.

Answer:

Step-by-step explanation:

Ac=3.14*r^2

Ac=9*3.14=28.27

0.428 cups of flour are required to produce one batch of brownies.

One of the four fundamental arithmetic operations is division, which is the process of combining two numbers to create a new number. The remaining operations are multiplication, addition, and subtraction.

Due to that, 7 batches of brownies use 3 cups of flour.

In order to determine how much flour is required to make one batch of brownies

To determine how much flour is needed in one batch of brownies, we divide 3 by 7.

3 cups/7 batches = 0.428 cups

0.428 cup of flour is therefore required to produce one batch of brownies.

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The probability that a randomly chosen customer who likes cake also likes pie is 2/3 or 0.6

To find the probability that a customer who likes cake also likes pie, we need to look at the overlap between the cake and pie circles in the Venn diagram. The diagram shows that 10 customers like both cake and pie, out of a total of 25 customers surveyed.

So, the probability that a randomly chosen customer who likes cake also likes pie is:

P(pie | cake) = number of customers who like both cake and pie / number of customers who like cake

P(pie | cake) = 10/15

P(pie | cake) = 2/3

Therefore, the probability that a randomly chosen customer who likes cake also likes pie is 2/3 or 0.67.

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Answer: 2/3

Step-by-step explanation:

Answer:

49(17 + 3)

Step-by-step explanation:

The Distributive Law says \(a(b+c)=ab+ac\).  But it can be used in the other direction,  \(ab+ac=a(b+c)\).  That way, you look at ab and ac to find the common factor a.  What's playing the role of  a  in the expression 49 x 17 + 49 x 3?  It's 49, the factor that shows up twice.  That's the factor that can be taken outside the parentheses.

49 x 17 + 49 x 3 = 49(17 + 3)

The circumference of a single tennis ball is approximately 7.85 inches.

To find the approximate height of the can of tennis balls, we need to know the dimensions of the can. Without that information, we cannot provide an accurate answer.

Regarding the circumference of a single tennis ball, we can use the formula for the circumference of a circle, which is given by:

Circumference = π * Diameter

The diameter of the tennis ball is stated as 2 1/2 inches. We can convert this into a decimal by adding the numerator (2) to the product of the whole number (2) and the denominator (2), then dividing the result by the denominator:

2 1/2 = (2 + (2 * 2)) / 2 = 5 / 2 = 2.5

Now, we can calculate the circumference of the tennis ball:

Circumference = π * Diameter = 3.14 * 2.5 ≈ 7.85 inches

Therefore, the circumference of a single tennis ball is approximately 7.85 inches.

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Answer:

answer is D

Step-by-step explanation:

I took the test

To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

Answer:

-2

Step-by-step explanation:

x^3 – 5x

Let x=2

2^3 - 5*2

Using PEMDAS, do the exponents first

8 - 5*2

Then multiply

8 - 10

Then subtract

-2

Answer:

Step-by-step explanation:

I assume your expression is:

6x^3-60x^2+144x.

I'll use that information.

Factor 6x^3−60x^2+144x

6x^3−60x^2+144x

=6x(x−4)(x−6)

Given equation is: 12/5 f = -18We need to solve for f.To solve for f, we multiply both sides of the equation by the reciprocal of 12/5Reciprocal of 12/5 = 5/12Multiplying both sides of the equation by 5/12 we get,\(5/12 * 12/5 f = -18 * 5/12⇒ 1 * f = -75/2⇒ f = -75/2\)

The solution of the given equation is f = -75/2. Note: To solve the given equation, we multiplied both sides of the equation by the reciprocal of the coefficient of f to isolate the variable. However, sometimes an estimator with a smaller variance may be biased. In such cases, we look for an unbiased estimator with a smaller variance than all other unbiased estimators.

This estimator is called the minimum variance unbiased estimator (MVUE).In conclusion, the statement that the MVUE always has the smallest variance compared to any estimator of θ1 is not true. It only means that the MVUE has the smallest variance compared to all other unbiased estimators of θ1.

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Brand₂ has the highest impact on the price of a smartphone, increasing the price by $80 for each unit increase in that variable.

Regression analysis is a statistical method that helps us understand the relationship between two or more variables.

Based on the regression equation, we can determine which brand increases the price of a smartphone the most. The regression equation is as follows:

Price = 1100 + 50 (Brand₁) + 80 (Brand₂) + 30 (Brand₃) + 20 (Battery Life) + 10 (Camera Resolution)

In this equation, the intercept (1100) represents the average price of a smartphone with all other variables set to zero. The coefficients for each variable represent the change in the price of a smartphone for a one-unit increase in that variable, holding all other variables constant.

Brand₁ and Brand₂ have a lower impact on the price, increasing it by $50 and $30, respectively, for each unit increase in those variables. Battery life and camera resolution have the smallest impact on the price, increasing it by $20 and $10, respectively, for each unit increase in those variables.

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Complete Question:

Can brand, battery life, and camera resolution affect a smartphone's price? Use α= o.05 to perform a regression analysis for the Smartphones01BC dataset and answer the following questions. Solve this problem using Excel and Mega Stat, and write your complete answers in the Response Box so I know that you can interpret the output.

Based on your regression equation, which brand increases the price of a smartphone the most? Use the statistics from your output to explain your answer.

Divide the numerator by the denominator to create a mixed number from an incorrect fraction. The mixed number is created after the division in such a way that the achieved quotient becomes the whole number, the leftover becomes the new numerator, and the denominator stays the same.

A mixed number is one that combines both a proper fraction and a full number. Mixed fractions are another name for mixed numbers.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. "Top-heavy" fractions are sometimes used to describe improper fractions.

Follow these procedures to convert a mixed number to an incorrect fraction:

1. Divide the entire number by the numerator.

2. Increase the numerator by that sum.

3. Add that total to the denominator from the previous step.

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Using the probability formula the value for the largest piece is obtained as 3/4.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Let X be the length of the largest piece when a unit stick is broken into three random pieces.

We want to find E(X), the expected value of X.

To solve for E(X), we can use the law of total probability and consider all possible lengths for the first cut.

Let Y be the length of the first piece, which can take any value between 0 and 1.

Then, we can write -

E(X) = ∫[0,1] E(X|Y=y) fY(y) dy,

where fY(y) is the probability density function of Y and E(X|Y=y) is the expected value of X given that the first piece has length y.

Now, let's consider the possible cases for the lengths of the other two pieces -

If the second cut is made in the interval [0,Y], then the largest piece has length Y.

If the second cut is made in the interval [Y,1-Y], then the largest piece has length 1-Y.

If the second cut is made in the interval [1-Y,1], then the largest piece has length Y.

Therefore, we can write -

E(X|Y = y)

= y × 1 + (1 - y) × 1/2 + (1 - y)×1  

= 1/2 + y/2.

Substituting this into the previous formula and using the fact that the density function for a uniform distribution on [0,1] is fY(y) = 1 for 0 ≤ y ≤ 1, we get -

E(X) = ∫[0,1] (1/2 + y/2) dy

= [y^2/4 + y/2] from 0 to 1

= 3/4.

Therefore, the expected length of the largest piece is 3/4.

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Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

The loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.

To determine the loan with the smallest monthly payment, we need to calculate the monthly payment for each loan option and compare them.

We can use the formula for monthly payment on a simple interest loan:

monthly payment = (principal + (principal * interest rate * time)) / total number of payments

where:

We can compute the monthly payments for each loan choice using this formula:

1. 12 Monthly interest rate = 0.0625/12 = 0.00521, monthly payment = (1250 + (1250 * 0.00521 * 12)) / 12 = $107.35

2. 18 months at 6.75%: monthly interest rate = 0.0675/12 = 0.00563, monthly payment = (1250 + (1250 * 0.00563 * 18)) / 18 = $81.96

3. 24 months at 6.5%: monthly interest rate = 0.065/12 = 0.00542, monthly payment = (1250 + (1250 * 0.00542 * 24)) / 24 = $66.14

4. 30 months at 6%: monthly interest rate = 0.06/12 = 0.005, monthly payment = (1250 + (1250 * 0.005 * 30)) / 30 = $45.83

Based on these calculations, the loan with the smallest monthly payment is the 30-month loan at 6% annual simple interest rate, with a monthly payment of $45.83.

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Answer:

Step-by-step explanation:

Berto’s train was 34 miles past the egg farm .

Eduardo’s train had 12 miles to go before it reached the egg farm.

Distance between two trains = 34 + 12 = 46 miles

This distance has to be reduced to zero for their crossing each other .

Rate at which this distance is reduced  = their relative velocity

= 110 - 85

= 25 miles / h       [ They are moving in the same direction ]

So, time taken for them to meet each other

= 46 / relative velocity

= 46 / 25

= 1.84 hours .

Answer:

The answer is D or 1.84 hours.

Step-by-step explanation:

I got 100% on this quiz.

Answer:

8 ft

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

4ft X 8ft= 32ft

Answer:

"If there is only one line parallel, then there is only one given line."

Step-by-step explanation:

The general form of an if-then statement is:

p → q

This implies that: "if p, then q".

Then the converse of this statement is:

q → p

This implies that: "if q, then p".

The statement here is:

"If there is a given line, then there is only one line parallel to it"

The converse of this statement will be:

"If there is only one line parallel, then there is only one given line."

Answer:

Step-by-step explanation:

P=2975 + r and 4= p - 225

Answer:

13m

Step-by-step explanation:

pls mrk me brainliest

Step-by-step explanation:

an object and its shadow create a right-angled triangle.

2 objects and their shadows at the same time create therefore two similar right-angled triangular

triangles.

that means the angles are the same, and each side length of one triangle correlates to the corresponding side length of the other triangle by the same factor.

so, when we know the factor of one pair of sides, we can calculate the lengths of the others by using the same factor.

therefore,

1.57 × f = 50.5

f = 50.5 / 1.57 = 32.1656051...

the height of the tower is then

3.1 × f = 3.1 × 32.1656051... = 99.7133758... m ≈ 100 m

Answer:

1 is 4

2 is 3

3 is 6

Step-by-step explanation:

tofu tu ugh uh runs

The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

        = 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The values of x and y are:

(x, y) Smaller x-value = (0, 0)

(x, y) Larger x-value =  \((\frac{4}{3} (2^{1/3} ), \ \frac{4}{3} (2^{2/3} ))\)

Given that f(x, y) = \(2x^{2}-8xy+y^{3}\)

Now, \(f_{x} (x,y) = \frac{d}{dx} (2x^{3} -8xy+y^{3})\)

\(=6x^{2} -8y+0\) (when we take partial derivative with respect to any variable, then the other variables are treated as constants)

\(=6x^{2} -8y\)

Similarly, \(f_{y} (x,y) = \frac{d}{dy} (2x^{3} -8xy+y^{3})\)

\(=0-8x+3y^{2}\)

\(=-8x+3y^{2}\)

Now set  \(f_{x}\) = 0 and \(f_{y}\) = 0

That is \(f_{x}\) = 0 ⇒ \(6x^{2} -8y=0\) ⇒ \(y = \frac{\ 3x^{2} }{4}\) ----------(1)

and \(f_{y}\) = 0 ⇒ \(-8x + 3y^{2} = 0\) ⇒ \(x=\frac{\ 3y^{2} }{8}\) ----------(2)

Solving (1) and (2) we get:

\(x=\frac{3}{8}(\frac{3x^{2} }{4} )^{2} \Rightarrow\ x=\frac{\ 27x^{2} }{128} \Rightarrow \ 27x^{2} -128x=0\)

\(\Rightarrow x\ (27x^{3} -128)=0\)

x will have two values,

\(\Rightarrow x=0\) or,

\(x^{3} = \frac{128}{27}\ \Rightarrow\ x^{3} = \frac{2\ \times\ 4^{3} }{3^{3} } \Rightarrow\ x=\frac{4}{3}(\sqrt[3]{2} )\)

Similarly, y will have two values,

\(y = \frac{3}{4} (\frac{128}{27} )^{2/3}\) \(\Rightarrow \ (\frac{4}{3} )2^{2/3}\) or,

y = 0

Therefore, the final answers are,

(x, y) Smaller x-value = (0, 0)

(x, y) Larger x-value =  \((\frac{4}{3} (2^{1/3} ), \ \frac{4}{3} (2^{2/3} ))\)

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The surface area of the piecewise smooth surface that is the boundary of the region enclosed by the paraboloids is For the first paraboloid, \(f(x, y) = 8 - 5x^2 - 5y^2: A1 = ∬√(1 + (-10x)^2 + (-10y)^2) dA\) and for the second paraboloid,\(f(x, y) = 3x^2 + 3y^2: A2 = ∬√(1 + (6x)^2 + (6y)^2) dA.\)

To find the surface area of the piecewise smooth surface which is the boundary of the region enclosed by the paraboloids, we need to calculate the surface area of each paraboloid and then find their intersection curve.

The first paraboloid, \(z = 8 - 5x^2 - 5y^2\), represents an upward-opening paraboloid with its vertex at (0, 0, 8) and a maximum value of 8. The second paraboloid, \(z = 3x^2 + 3y^2\), represents a downward-opening paraboloid with its vertex at (0, 0, 0) and a minimum value of 0.

To find the intersection curve between these two paraboloids, we set the two equations equal to each other:

\(8 - 5x^2 - 5y^2 = 3x^2 + 3y^2\)

Simplifying the equation, we have:

\(8 - 8x^2 - 8y^2 = 0\)

Dividing both sides by 8, we get:

\(1 - x^2 - y^2 = 0\)

This equation represents a circle of radius 1 centered at the origin (0, 0, 0).

To calculate the surface area of each paraboloid, we can use the surface area formula for a general surface z = f(x, y):

\(A = ∬√(1 + (f_x)^2 + (f_y)^2) dA\)

For the first paraboloid, \(f(x, y) = 8 - 5x^2 - 5y^2: A1 = ∬√(1 + (-10x)^2 + (-10y)^2) dA\)

Similarly, for the second paraboloid, \(f(x, y) = 3x^2 + 3y^2: A2 = ∬√(1 + (6x)^2 + (6y)^2) dA.\)

Therefore, integrating these surface area formulas over their respective domains will give the total surface area of the piecewise smooth surface.

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