Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by


T(x) = 7-9(x-2)2-3(x-2)3


a. find f(2) and f '' (2).


b. Is there enough information given to determine wheather fhas a critical point at x = 2?


If not, explain why not.


If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.


c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?


If not, explain why not.


If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.


d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.

Answer:

(A) B h(x)= -2x-5.5

(B) The y intercept is (0,-5.5)

(C) The rate of change is -2

(D) The x intercept is (-2.75,0)

The composite functions fog and g • f are not equal to x. The function fog simplifies to 4x² - 20x + 25, while g • f simplifies to 45. Therefore, neither composite function equals x.

To determine whether the composite functions fog and g • f are equal to x, we need to evaluate each expression separately and compare the results.

1. fog (or f(g(x))):

f(g(x)) = f(2x - 5)

To compute f(2x - 5), we substitute (2x - 5) into the function f(x) = x²:

f(2x - 5) = (2x - 5)²

Expanding this expression, we get:

f(2x - 5) = 4x² - 20x + 25

Therefore, fog is not equal to x since f(2x - 5) simplifies to 4x² - 20x + 25, not x.

2. g • f (or g(f(x))):

g(f(x)) = g(25)

To compute g(25), we substitute 25 into the function g(x) = 2x - 5:

g(25) = 2(25) - 5

g(25) = 50 - 5

g(25) = 45

Therefore, g • f is not equal to x since g(25) evaluates to 45, not x.

In conclusion, neither fog nor g • f is equal to x. The composite functions do not simplify to x; fog simplifies to 4x²- 20x + 25, and g • f simplifies to 45.

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In simple linear regression, we desire the residuals to have certain characteristics. Specifically, we want the residuals to be:

Random: The residuals should not follow a specific pattern or exhibit any systematic behavior. Random residuals indicate that the model captures the underlying relationship between the variables adequately.

1. Normally distributed: The residuals should follow a normal distribution. This assumption allows for the use of statistical inference and hypothesis testing techniques based on normality.

2. Zero mean: The average of the residuals should be close to zero. A zero mean indicates that, on average, the model is not biased and accurately represents the data.

3. Homoscedastic: The residuals should have constant variance across all levels of the independent variable. Homoscedasticity ensures that the model's performance is consistent throughout the range of values.

By satisfying these criteria, we can ensure that the model is valid, reliable, and provides accurate predictions.

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Answer:

x = 30

Step-by-step explanation:

2x + x = 90

3x = 90

x = 30

Answer:

Circumference is about 182.21

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is 29. Plug 29 into the formula 2(pi)r to find the Circumference. The answer is 182.21

The equation of the circle is [tex]\rm(x-3)^2+(y+2)^2=29^2[/tex].

The equation of the circle is given by;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where r is the radius and h and k are the centre of the circel.

The radius of the circle is;

[tex]r=\sqrt{(23-3)^2+(19-(-2))^2} \\\\r=\sqrt{(20)^2+(21)^2} \\\\r=\sqrt{400+441}\\\\r =\sqrt{841}\\\\r=29[/tex]

The equation of the circle is;

[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-3)^2+(y-(-2))^2=29^2\\\\ (x-3)^2+(y+2)^2=29^2[/tex]

Hence, the equation of the circle is [tex]\rm(x-3)^2+(y+2)^2=29^2[/tex].

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Answer:

I believe the answer to be 5 and 4

The exterior angles of the given triangle are angles 4 and 5

A triangle is a polygon with three sides, angles and vertices.

Given that, a triangle, with angles, 1, 2, 3, 4, 5 we need to find the exterior angles,

An exterior angle of a polygon is the angle that lies outsides of the polygon,

Here, we can see, that only two angles 4 and 5 lies outsides of the triangles

Therefore, the exterior angles are 4 and 5

Hence, the exterior angles of the given triangle are angles 4 and 5

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The Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).

Given function is f(t) = i Se^4t

Here, Laplace transform of the function f is given by:

L(f)(s) = ∫[0,∞) e^(-st) f(t) dt

On substituting the given function in the above equation, we get:

L(f)(s) = ∫[0,∞) e^(-st) i Se^(4t) dt

L(f)(s) = i S ∫[0,∞) e^(t(4-s)) dt

We know that the Laplace transform of e^(at) is 1/(s-a).

Therefore, Laplace transform of e^(t(4-s)) = 1/(s - (4-s)) = 1/(2s - 4).

Therefore,L(f)(s) = i S * ∫[0,∞) e^(t(4-s)) dt

L(f)(s) = i S * 1/(2s-4) * [-e^(-(4-s)t)]_0^∞

L(f)(s) = i S * 1/(2s-4) * [0 - (-1)] (since the exponentials evaluated at ∞ is zero)

L(f)(s) = i S * 1/(2s-4) * 1

L(f)(s) = i S / (2s-4)

Therefore, the Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is  L(f)(s) = i S / (2s-4).

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Options :

A.

33.5%

B.

20,000 and 33.5%

C.

500 and 20,000

D.

20,000

Answer:

A.) 33.5%

Step-by-step explanation:

A statistic value is simply a numerical statistical estimate or value which is obtained from the sample data or value. Here the statistic is the statistical value which is obtained the sample of 500 customers selected from the about 20000 population value 500 itself is the sample size while 33.5% is the sample. Proportion of supermarket customers who do not buy store-brand products.

20,000 = population size ;

500 = sample. Size

33.5% =. Statistic

To make the 2% solution of tetracaine hydrochloride isotonic, a 0.9% solution of sodium chloride should be used.

The amount of the 0.9% sodium chloride solution needed can be calculated by setting up a proportion based on the concentration percentages.

Let's assume x represents the volume of the 0.9% sodium chloride solution needed in milliliters.

Since the 0.9% solution is isotonic, it means that the concentrations of tetracaine hydrochloride and sodium chloride should be equal. Therefore, the proportion can be set up as follows:

(0.9 / 100) = (2 / 100) * (x / 30)

Simplifying the proportion, we have:

0.009 = 0.02 * (x / 30)

To solve for x, we can multiply both sides of the equation by 30 and divide by 0.02:

x = (0.009 * 30) / 0.02

x ≈ 13.5 mL

Therefore, approximately 13.5 milliliters of the 0.9% sodium chloride solution should be used in compounding the prescription to make the 2% tetracaine hydrochloride solution isotonic.

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Answer:

huh?

Step-by-step explanation:

did you forget a pic?

Answer:

whatdo u need help with love?

Step-by-step explanation:

Answer:

n= 1

Got it right on my test \(￣︶￣*\))

Answer:

i think you're right- you seem to have all numbers squared correctly, also every negative value squared becomes a positive number, which means that your answers are correct.. what is your issue?

Step-by-step explanation:

The scheme procedure "heap-insert" adds an element x to a heap h using the first-order relation f to determine the root element in each subtree.

The "heap-insert" procedure can be defined as follows in Scheme:

(define (heap-insert f x h)

 (cond

   ((null? h) (list x))

   ((f x (car h)) (cons x h))

   (else (cons (car h) (heap-insert f x (cdr h))))))

This procedure takes three arguments: f, x, and h. The first argument f is a first-order relation that determines the ordering of elements in the heap. The second argument x is the element to be inserted into the heap. The third argument h is the existing heap.

The procedure first checks if the heap h is empty. If it is, it simply creates a new heap with x as the only element. If the heap is not empty, it compares x with the root element (car h) using the relation f. If f determines that x should be the new root element, it adds x to the heap by consing x with h. Otherwise, it recursively calls the heap-insert procedure on the remaining elements (cdr h) until it finds the appropriate position to insert x.

In this way, the "heap-insert" procedure ensures that the new element x is inserted into the heap h while maintaining the heap property defined by the relation f.

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Answer:

12

Step-by-step explanation:

b-4x

Plug in 4 as b and -2 as x

= (4)-4(-2)

Multiply 4 and 2

= 4-(-8)

Two negatives make a positive

= 4+8

= 12

I hope this helps!

Answer:

21/20

Step-by-step explanation:

Answer:

3125

Step-by-step explanation:

first, find the unit rate.

2500/4=625

625= amount of oxygen needed to supply a family of one(or just one single person)

625*5=3125

***with these problems, always try to find the unit rate first which is the amount of something per one unit. it'll be helpful to solve the questions following it.

The approximate area under the curve from x = 2 to x = 5, using a left endpoint approximation with 3 subdivisions, is 13.5 square units.

To approximate the area under the curve, we divide the interval from x = 2 to x = 5 into three equal subdivisions, each with a width of (5 - 2) / 3 = 1. The left endpoint approximation involves using the leftmost point of each subdivision to approximate the height of the curve.

In this case, we evaluate the function at x = 2, x = 3, and x = 4, and use these values as the heights of the rectangles. The width of each rectangle is 1, so the areas of the rectangles are calculated as follows:

Rectangle 1: Height = f(2) = 2, Area = 1 * 2 = 2 square units.

Rectangle 2: Height = f(3) = 4, Area = 1 * 4 = 4 square units.

Rectangle 3: Height = f(4) = 7, Area = 1 * 7 = 7 square units.

Finally, we add up the areas of the three rectangles to obtain the approximate area under the curve: 2 + 4 + 7 = 13 square units. Therefore, the approximate area under the curve from x = 2 to x = 5 using a left endpoint approximation with 3 subdivisions is 13.5 square units.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

w = [tex]\sqrt{147}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

w² + 7² = 14²

w² + 49 = 196 ( subtract 49 from both sides )

w² = 147 ( take the square root of both sides )

w = [tex]\sqrt{147}[/tex]

Answer: 65

Step-by-step explanation:

8nn+7 is your given expression. Plug in 7 for n, the number of tickets: 8(7)+9=56+9=65

Answer:

∠1and∠5

Step-by-step explanation:

Hello There!

The image shown below shows an example of what corresponding angles look like

Properties of corresponding angles

angles 2 and 4 are on the same side of the transversal however they are supplementary angles not congruent

angles 2 and 4 are an example of adjacent angles therefore this is not the answer

angles 1 and 5 are on the same side of the transversal and they are most definitely congruent

This might be our answer but lets check the last answer just to be sure

Angles 3 and 6 are congruent but they are not on the same side of the transversal

angles 3 and 6 are an example of alternate interior angles therefore this is not the correct answer

So we can conclude that angles 1 and 5 are corresponding angles

Answer:

6,7

Step-by-step explanation:

the squre root of 41 is 6.403

Answer:

Step-by-step explanation:

The potential that satisfies the given boundary conditions in part (a) and (b) is: [tex]\[u(r, \theta) = \sin(\theta)\][/tex] and [tex]\[u(r, \theta) = \sin(\theta)\][/tex] respectively.

Consider the circular annulus (a plane figure consisting of the area between a pair of concentric circles) specified by the range:

[tex]$1 \leq r \leq 2$.[/tex]

a) Find the potential that satisfies the following boundary conditions:

[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(2\theta))\end{aligned}\][/tex]

b) Find the potential that satisfies the following boundary conditions:

[tex]\[\begin{aligned}u(1,0) &= \sin(\theta) \\u(2,0) &= 0 \\u(\theta, 1) &= 1 + (1 - \cos(20\theta))\end{aligned}\][/tex]

To solve this problem, we can use separation of variables and assume a solution of the form:

[tex]\[u(r, \theta) = R(r)\Theta(\theta)\][/tex]

Plugging this into Laplace's equation [tex]$\nabla^2u = 0$[/tex] and separating variables, we get:

[tex]\[\frac{1}{R}\frac{d}{dr}\left(r\frac{dR}{dr}\right) + \frac{1}{\Theta}\frac{d^2\Theta}{d\theta^2} = 0\][/tex]

Solving the radial equation gives us two solutions:

[tex]\[R(r) = A\ln(r) + B\quad \text{and} \quadR(r) = C\frac{1}{r}\][/tex]

For the angular equation, we have:

[tex]\[\Theta''(\theta) + \lambda\Theta(\theta) = 0\][/tex]

The general solution to this equation is given by:

[tex]\[\Theta(\theta) = D\cos(\sqrt{\lambda}\theta) + E\sin(\sqrt{\lambda}\theta)\][/tex]

To satisfy the boundary conditions, we can impose the following restrictions on [tex]$\lambda$[/tex] and choose appropriate constants:

For part (a)

[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]

Therefore, the potential that satisfies the given boundary conditions in part (a) is:

[tex]\[u(r, \theta) = \sin(\theta)\][/tex]

For part (b)

[tex]\[\begin{aligned}R(1) &= 0 \implies B = -A\ln(1) = 0 \implies B = 0 \\R(2) &= 0 \implies A\ln(2) + B = 0 \implies A\ln(2) = 0 \implies A = 0 \\\Theta(0) &= \sin(0) \implies D = 0 \\\Theta(0) &= \sin(0) \implies E = 1\end{aligned}\][/tex]

Therefore, the potential that satisfies the given boundary conditions in part (b) is:

[tex]\[u(r, \theta) = \sin(\theta)\][/tex]

Please note that in both parts (a) and (b), the radial solution does not contribute to the potential due to the boundary conditions at r=1 and r=2. Thus, the solution is purely dependent on the angular part.

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Answer:

69

Step-by-step explanation:

Answer:

Step-by-step explanation:

62.00

The ordered pair (2,3) is not a solution of the system

From the question, we have the following parameters that can be used in our computation:

−8x + 4y > 3

6x - 7y < −5

The solution is given as

(2, 3)

Next, we test this value on the system

So, we have

−8(2) + 4(3) > 3

-4 > 3 --- false

This means that (2,3) is not a solution of the system

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Answer:

m=3/4

Step-by-step explanation:

First, let us remind ourselves of the slope formula: m=rise/run=([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])

Let's pick two points from the graph to work with. Let's do (3,-6) and (-1,-9).

And let 3=[tex]x_{1}[/tex], -6=[tex]y_{1}[/tex], -1=[tex]x_{2}[/tex], -9=[tex]y_{2}[/tex].

1. Substitute the values into the slope formula: [-9-(-6)]/(-1-3)

2. simplify the expression: [-9-(-6)]/(-1-3)=(-9+6)/-4=-3/-4=3/4

3. As a result, the slope of the line is 3/4