Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. Σ n = 0 (x-3) 8⁰ (a) The radius of convergence is (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The interval of convergence is (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges only at x = OC. The series converges for all values of x. . (Type an integer or a simplified fraction.)
(b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges absolutely for. (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x = . (Type an integer or a simplified fraction.) C. The series converges absolutely for all values of x.
(c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The series converges conditionally for (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The series converges conditionally at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There are no values of x for which the series converges conditionally.

The speed of Neegan paddles in still water will be 6 miles/Hr, while the rate of the current will be 1 mile/Hr.

Neegan paddles a kayak 21 miles upstream in 4.2 hours.

As he is moving in Upstream, so during returning the flow will be downstream

Downstream refers to the direction of the flow's termination, which is at the other end of the canal from the source. You are travelling upstream, for instance, if you are sailing from Kingston to Toronto. You are travelling downstream if you are moving from Kingston to Cornwall.

Let the speed of Neegan paddles in still water = x miles/Hr.

Let the rate of the current be = y miles/Hr.

As Speed = Distance/Time

So, for Upstream speed, Speed will be = x-y

For downstream, the speed will be = x+y

From question,

(x-y) = 21/4.2 = 5-----(i)

(x+y)= 21/3 = 7 -----(ii)

Solving (i) and (ii)

2x = 12

=> x = 6

So, the value of y (From (i), will be = (x-5) = 6-5 = 1

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With the inclusion of randomness or exploration, some students might deviate from the dominant strategy which results in strategy evolution of longer cycles compared to the previous cycle.

The missing feature in the adjustment process that would prevent being stuck in the state (10,0,0) is the consideration of randomness or exploration. Currently, the adjustment process only relies on the information of the highest average payoff, without taking into account the potential benefits of exploring different strategies.

Including randomness or exploration would make the adjustment process more realistic because it allows for the possibility of discovering better strategies through experimentation. This reflects the idea that in real-life scenarios, individuals often try different approaches to find the most successful one.

As for identifying another cycle starting with the state (2,4,4), the dynamics of the system would involve periods of strategy switching based on the highest average payoff.

However, with the inclusion of randomness or exploration, some students might deviate from the dominant strategy in an attempt to discover a better one. This could lead to more complex patterns of strategy evolution and potentially longer cycles compared to the previous cycle.

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Answer:

2r2units

Step-by-step explanation:

Let a rectangle of dimensions x×y

Be inscribed in a circle of radius r.

Applying Pythagoras theorem on the right-angled triangle,

⇒x2+y2=(2r)2⇒x2+y2=4r2⇒y2=4r2−x2⇒y=4r2−x2−−−−−−−√

As dimensions of any shape cannot be negative so y=−4r2−x2−−−−−−−√

is not considered.

Area of the rectangle,

⇒A=x×y⇒A=x4r2−x2−−−−−−−√

Differentiating both sides with respect to x, we get –

dAdx=ddx(x4r2−x2−−−−−−−√)

Use the product rule to differentiate the above result –

A1(x)=xd(4r2−x2−−−−−−−√)dx+4r2−x2−−−−−−−√d(x)dxA1(x)=xd4r2−x2−−−−−−−√d(4r2−x2)d(4r2−x2)dx+4r2−x2−−−−−−−√(1)A1(x)=x124r2−x2−−−−−−−√(−2x)+4r2−x2−−−−−−−√A1(x)=−x2+4r2−x24r2−x2−−−−−−−√A1(x)=−2x2+4r24r2−x2−−−−−−−√

Now to get the maximum value, put A1(x)=0

−2x2+4r24r2−x2−−−−−−−√=0⇒4r2=2x2x2=2r2x=2–√r

The negative value of x is rejected.

⇒y=4r2−x2−−−−−−−√=r2–√

A(r2–√)=r2–√(4r2−2r2−−−−−−−√A(r2–√)=r2–√(r2–√)=2r2

The maximum area of a rectangle inscribed in a circle is 2r2units

and its dimensions are r2–√units×r2–√units

So, the correct answer is “ 2r2units ”.

The polynomial p(x) must have at least two zeros, since it has three relative extrema.

What is polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Here i would think that since there are only 3 critical points given and no other information other than that those are the only critical points that p(x) would not have any real zeros.

At each of the relative extrema, the value of the function changes from increasing to decreasing or vice versa, meaning that the function crosses the x-axis at that point, which is a zero. Therefore, p(x) must have at least two zeros.

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Answer:

we use ladder method

Then we multiple by two

Answer:

The answer will be 63cm²

Step-by-step explanation:

The length of this pendulum that makes one full swing is 3.93 meters.

Given the following data:

To determine the length of this pendulum that makes one full swing:

Mathematically, the time taken by this pendulum is given by this formula:

\(T=2\pi \sqrt{\frac{L}{32} }\)

Making L the subject of formula, we have:

\(T^2 = 4\pi ^2 \frac{L}{32} \\\\32T^2 =4\pi ^2L\\\\L=\frac{32T^2}{4\pi ^2}\)

Substituting the given parameters into the formula, we have;

\(L=\frac{32 \times 2.2^2}{4 \times (3.14)^2 } \\\\L=\frac{32 \times 4.84}{4 \times 9.8596 }\\\\L=\frac{154.88}{39.4384}\)

L = 3.93 meters.

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Answer:

4

Step-by-step explanation:

Answer: March to April shows the least increase of average temperature.

Answer:

It’s d

Step-by-step explanation:

Answer:

five miles

Step-by-step explanation:

taxi A: for one mile: 10.75

taxi B: for one mile: 11.75

two miles: A: 12.25 B: 13

three miles: A: 13.75 B: 14.25

four miles: A: 15.25 B: 15.5

five miles: A: 16.75 B: 16.75

Answer:

It stands for "Nothing But Trouble"

Step-by-step explanation:

Answer:

Step-by-step explanation:

The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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Answer:

cost per mile = $2.

Step-by-step explanation:

Given the cost function, c(m) = 2m + 4,

Where the m represents the number of miles traveled, and $2 is the cost per mile of the cab. The $4 represents the flat rate, a set fee, or the initial value.

Therefore, the cost per mile of the cab is $2.  

Answer:

15/8

Hope it helps

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Thank you

ANSWER:

The y-intercept is:

STEP-BY-STEP EXPLANATION:

We have to calculate the equation in its slope-intercept form, which is the following

we calculate the slope with the following formula:

we replace the points (34, -52) and (68, -78)

now, for b, with the point (51, -65)

Answer:

0, -26

Step-by-step explanation:

khan academy

The given function is f(x) = 2x - 1.

The original function is f(x) = 2x - 1. To translate this function up by 9 units, we need to add 9 to the function's output or f(x) + 9. Therefore,

g(x) = f(x) + 9

So, g(x) = 2x - 1 + 9

g(x) = 2x + 8

Therefore, the function g that represents a translation of f up 9 units is g(x) = 2x + 8.

Hence, Option C is correct.

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The predicted number of calories in a sandwich containing 32 grams of fat is 559.

In algebra, the slope-intercept form of a linear equation is a typical approach to express a line on a graph. A linear equation is written as y = mx + b in standard form.

The y-intercept, or place where the line crosses the y-axis, is represented by the letters b and m, respectively. The point where the lines contacts the y-axis is known as the y-intercept, and the slope is a measurement of how steep the line is. Because it explicitly displays the slope and y-intercept, this equation's form is known as the slope-intercept form.

y = mx + b

Where m is the slope, x is the value of the independent variable, and b is the y-intercept. In this case, the slope is 13 and the y-intercept is 143. So, the equation of the line of best fit is:

y = 13x + 143

To predict the number of calories in a sandwich containing 32 grams of fat, you can plug in 32 for x in the equation:

y = 13 * 32 + 143

y = 416 + 143

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Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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Let's denote the number of books Eva has read each year as 'B'.

According to the given information, Eva has read over 25 books each year for the past three years.

To represent this as an inequality, we can write:

B > 25

This inequality states that the number of books Eva has read each year (B) is greater than 25.

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Answer:

12x^2+17x-5

Step-by-step explanation:

(4x-1)(3x+5)

12x^2-3x+20x-5

12x^2+17x-5

Answer:

The translation rule is;

Explanation:

Given the graph attached;

Let us pick a corresponding edge(point) on the preimage and image respectively;

The change on the x and y axis is;

Therefore, the translation rule is;

The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

3.5

Step-by-step explanation:

7/3= 3.5 or 3 1/2

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The equation for the lines whose graph is depicted below is y = x/2.

In order to write the equations for these straight lines, we would have to determine the slope of the straight lines.

Mathematically, the slope of any straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

From the graph (see attachment), we have the following data:

Points on x-axis = (0, 2).

Points on y-axis = (0, 1).

Substituting the given points into the formula, we have;

Slope, m = (1 - 0)/2 - 0)

Slope, m = 1/2.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (2, 1), we have:

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

y - 1 = x/2 - 1

y = x/2 - 1 + 1

y = x/2.

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There are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$. For a number to end in the digit $3$ in base-$b$ representation, it must be congruent to $3$ modulo $b$.

We can rewrite $2013$ as $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$. Now, if $2013$ is congruent to $3$ modulo $b$, it means that $2 \cdot 10^3 + 0 \cdot 10^2 + 1 \cdot 10^1 + 3 \cdot 10^0$ is also congruent to $3$ modulo $b$.

Simplifying the expression, we have $2000 + 0 + 10 + 3$. Since the base-$b$-representation is formed by multiplying each digit by the corresponding power of $b$, we can rewrite the expression as $2 \cdot b^3 + 1 \cdot b^1 + 3 \cdot b^0$. We can now observe that the constant term $3 \cdot b^0$ will always be congruent to $3$ modulo $b$. However, the other terms $2 \cdot b^3$ and $1 \cdot b^1$ will not be congruent to $3$ modulo $b$ for any positive value of $b$. Therefore, the base-$b$-representation of $2013$ cannot end in the digit $3$ for any value of $b$.

Hence, there are no values of $b$ for which the base-$b$-representation of $2013$ ends in the digit $3$.

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According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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Answer:

the pattern is adding the number before it  21, 34, 55

Step-by-step explanation:

Answer:

x = 10, -4

Hope this helped!