verify, using the definition of convergence of a sequence, that the following sequences converge to the proposed limit. (a) lim 2n 1

The values for the variables a and b in the parallelogram are 2 and 3 respectively.

The parallelogram STVW have two pairs of parallel sides hence VW = TS and TV = SW.

We shall evaluate for variables a and b as follows:

3a + 11 = a + 15

3a - a = 15 - 11 {collect like terms}

2a = 4

a = 4/2 {divide through by 2}

a = 2

3b + 5 = b + 11

3b - b = 11 - 5 {collect like terms}

2b = 6

b = 6/2 {divide through by 2}

b = 3

Therefore, the values for the variables a and b in the parallelogram are 2 and 3 respectively.

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Answer:1,283.803

Step-by-step explanation:

By the quotient rule the derivative of all functions can be found in an easy way,

(1) [tex]f'(x)=\frac{x^6+128x^3-3x^2}{(x^3+32)^2}[/tex]    

(2)  [tex]f'(x)=\frac{5}{(2+x)^2}[/tex]

(3)  [tex]f'(t)=\frac{4t}{(t^2+1)^2}[/tex]

The Quotient Rule in calculus is a technique for figuring out a function's derivative (differentiation) as the ratio of two differentiable functions. It is a formal rule applied to issues involving differentiation where one function is split in half by another function. The definition of the limit of the derivative is followed by the quotient rule. Keep in mind that the bottom function is where the quotient rule starts and where it finishes.

The quotient rule is similar to the product rule. A Quotient Rule is stated as the ratio of the quantity of the denominator times the derivative of the numerator function minus the numerator times the derivative of the denominator function to the square of the denominator function. In short, the quotient rule is a way of differentiating the division of functions or the quotients

We have the functions

(1) [tex]f(x)=\frac{x^4+1}{x^3+32}[/tex]

derivative with respect to x by the quotient rule.

[tex]f'(x)=\frac{(x^3+32)(4x^3)-(x^4+1)(3x^2)}{(x^3+32)^2}\\\\f'(x)=\frac{4x^6+128x^3-3x^6-3x^2}{(x^3+32)^2}\\\\f'(x)=\frac{x^6+128x^3-3x^2}{(x^3+32)^2}[/tex]

2) derivative with respect to x of the below function

[tex]f(x)=\frac{3x+1}{2+x}\\\\f'(x)=\frac{(x+2)(3)-((3x+1))}{(2+x)^2}\\\\f'(x)=\frac{5}{(2+x)^2}[/tex]

3)

[tex]f(t)=\frac{t^2-1}{t^2+1}[/tex]

derivative with respect to t,

[tex]f'(t)=\frac{(t^2+1)(2t)-(t^2-1)(2t)}{(t^2+1)}\\\\f'(t)=(2t^3+2t-2t^3+2t)/(t^2+1)^2\\\\f'(t)=4t/(t^2+1)^2[/tex]

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C = 45 + 0.25t. The 45 represents the baseline amount that she is charged per month. The t represents each additional text, and the 0.25 represents how much she is charged for each additional text.

The volume of a pyramid can be calculated using integration is [tex]V = (1/3)(7*282 - 2*282) = 224 cubic units..[/tex]

The formula for the volume of a pyramid with a rectangular base with dimensions l and w, and height h is given by V = (lwh)/3. Using this formula, the volume of a pyramid with a rectangular base with dimensions 2 and 7 and height 28 can be calculated to be 224 cubic units.

To calculate this using integration, we can use the formula V = (1/3)∫b a y2dx, where a and b are the lower and upper limits of the rectangular base, and y is the height of the pyramid. In this case, a = 2, b = 7, and y = 28. Therefore, V = (1/3)(7*282 - 2*282) = 224 cubic units.

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The statement that is true when comparing the two accounts after 10 years is: A: "Hannah's account has more money than Frank's account".

To compare the amount of money in the two accounts after 10 years, we can use the formula for continuous compound interest:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal (initial amount), r is the annual interest rate (expressed as a decimal), and e is the mathematical constant approximately equal to 2.71828.

For Frank's account, we have:

A = 2500e^(0.05410) = 4244.96 dollars (rounded to the nearest cent)

For Hannah's account, we have to take into account the quarterly compounding. The formula for quarterly compound interest is:

A = P(1 + r/n)^(nt)

where n is the number of compounding periods per year (4 for quarterly compounding), and t is the time in years. Thus, we have:

A = 3000*(1 + 0.032/4)^(4*10) = 4412.09 dollars (rounded to the nearest cent)

Therefore, the amount of money in Hannah's account after 10 years is greater than the amount in Frank's account.

"

Complete question

frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. which of the following statements is true when comparing the amount of money in the two accounts after 10 years?

A: Hannah's account has more money than Frank's account

B: : Frank's account has more money than Hannah's account

"

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Answer:

50+50=100
50/2=25
125km in 2 and a half hours

Step-by-step explanation:

Umm I'm assuming this isn't a trick question and saying just add 50+50 for 2 hours and then divide 50 by 2 to get 25. so 125 I hope i'm right :')

Answer:

Step-by-step explanation:

The man would walk 125km.

Explanation: The man would walk 125km, because if every hour he is walking 50km then if he walks for 2.5 hours, then all you have to do is multiply 50km by 2.5 hours.

The volume of the pyramid is mn, where m and n are positive integers, and n is not divisible by the square of any prime then m+n is 803.

Let the triangular base be ΔABC with

AB = 24, Altitude to the side AB is 16

Area of ΔABC is 24x16/2 = 192

Let fourth vertex of Tetrahedron be P and let the midpoint of AB be M

ΔABC will pass through circumcenter of Δ ABC which we will call O

OM + OC = 16

OM = d

d = √d² + 144 = 16

2d² + 2d√d² + 144 = 112

2d(d + √d² + 144) = 112

d = 7/2

Now, we find √d² + 144 = 25/2

Theorem , on the triangle AOP, BOP, COP

25² = h² + (25/2)²

625 = h² + 625/4

h = 25√3/2

Finally the formula for volume of Pyramid from

V = Ah/3

= 192 (25√3/2) / 3

= 800√3

m + n = 800 + 3

m + n = 803

Therefore, the value of m+n is 803.

The volume of a aggregate depends upon the type of aggregate’s base, whether it's a triangle, square or cube. A aggregate is a polyhedron figure which has only one base.

The base of the aggregate is a poly sided figure. Hence, the formula to find not only volume but also the face area of a aggregate will be grounded on the structure of its base and height of the aggregate.

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Answer:

See below for answers

Step-by-step explanation:

Part A

[tex]\displaystyle V=\pi\int\limits^d_c {(R^2-r^2)} \, dy\\=\pi\int\limits^3_0 {\biggr(\biggr(\frac{y^2}{9}\biggr)^2-\biggr(\frac{y}{3}\biggr)^2\biggr)} \, dy\\=\pi\int\limits^b_a {\biggr(\frac{y^4}{81}-\frac{y^2}{9}\biggr)} \, dy[/tex]

Make sure to write the functions in terms of y since you rotate on a vertical axis.

Part B

[tex]\displaystyle V=\pi\int\limits^b_a {(R^2-r^2)} \, dx\\=\pi\int\limits^1_0 {((3-3\sqrt{x})^2-(3-3x)^2)} \, dx\\=\pi\int\limits^1_0 {((9-18\sqrt{x}+9x)-(9-18x+9x^2))} \, dx\\=\pi\int\limits^1_0 {(-18\sqrt{x}-9x-9x^2)} \, dx[/tex]

Make sure to fix the radii so they start at y=3.

Clinical Chemistry Principles, Techniques, and Correlations 7th ed. Bishop is False.

A typical analytical technique (the method used to determine a chemical or physical property of a chemical substance, chemical element, or mixture.) for dissolving a chemical combination into its constituent parts so that each part may be carefully examined is called "chromatography."

The liquid or gaseous medium that moves the items to be separated over the stationary phase of a chromatography device at varying speeds is called as mobile phase.

In chromatography, the stationary phase can be either a solid or a liquid matrix. The mobile phase, which moves through the stationary phase, typically occurs in a liquid or a gas.

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Answer:

20

Step-by-step explanation:

Easiest way to solve is to consider the formula for the area of the trapezoid, which is 0.5h(a+b), where h is the altitude and a and b are the two bases.

Here we know the area, the altitude and one base so let's sub these in to find the other base:

92=0.5*8*(3+b)

92=4(3+b)

23=4+b

b=20

AB line segment correctly represents the perpendicular bisector of line segment XY.

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

There are 4 doted lines are shown.

Now, From all dotted line;

Line segment AB divides the line segment XY into two equal parts.

Hence, AB line segment correctly represents the perpendicular bisector of line segment XY.

Thus, ''AB line segment'' correctly represents the perpendicular bisector of line segment XY.

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5) The equation of population after year 2000 is expressed as;

P = 65x + 622

6) Population in the year 2012 is; P = 1402 students

The parameters given are;

Population in 2003 = 817

Population in 2006 = 1012

Thus;

Average population growth per year = (1012 - 817)/3

Average population growth per year =  65 people

Now, we see that the population of people in the year 2000 was 622.

Thus;

5) Equation of population is;

P = 65x + 622

where x is number of years after year 2000

6) Population in the year 2012 which is 12 years after year 2000 is;

P = 65(12) + 622

P = 1402

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Given that function f is defined and continuous on the closed interval [a,b], the correct statements are:

From the case we know that:

function f is on the closed interval [a,b]

c = relative maximum

A function reach its relative maximum when its first derivative function is equal to zero (0). Since c is the relative maximum of function f, then:

f'(c) = 0

The third statement is wrong because when c is the relative maximum point, then its second derivative function must be lower than zero (0), or:

f''(c) < 0

When the second derivative function is greater than zero (0), it indicates that the given critical point is the relative minimum.

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The equation for line 1 is y = x+6 and equation for line 2 is y= -x-4. The domain and range is as follows,

y = x+6 {(x,y)| x≤ -5 , y≤ 1}

y= -x-4  {(x,y) x≥-5, y≤1}

The line 1 passes through points (-6,0) and (-5,1).

Equation for a line is  y= Ax+B

Using two points we can formulate the following equations

-6A+B =0

-5A+B =1

Subtracting the two equations,

-A = -1, so A= 1

-6A+B = 0

-6 ×1 + B = 0

B= 6

So the equation for the line by substituting values of A and B is

y= x+6

The domain is all values ≤-5 and range is all values ≤1

The line 2 passes through (0,-4) and ( -5,1)

Formulating equations using points

B= -4

-5A+B =1

A = -1

Substituting in equation for line 2

y = -x-4

The domain is all values ≥ 5 and range is all values ≤1.

So the equation, domain and range of line 1 is y = x+6 {(x,y)| x≤ -5 , y≤ 1} and for line 2 is y= -x-4  {(x,y) x≥-5, y≤1}

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The complete question is included as image

-13y + 7 - 11 - 4y can be written as -17y - 11.

Expression is a way of conveying emotions, thoughts, or ideas through verbal or nonverbal means. It is often used to communicate an individual's feelings, beliefs, or opinions, and can be expressed through language, art, music, dance, and other forms of communication. Expression can be used to convey a wide range of emotions, from joy and excitement to anger and sorrow. Expression is an essential part of communication, and without it, we would not be able to effectively convey our thoughts, feelings, and desires. The way we express ourselves can also be a reflection of our personality and can give people an insight into who we are. Expression is also important for self-expression, as it allows us to explore our own thoughts and emotions, and express them in a way that may be more comfortable for us.


This can further be written as -17y × (-1) - 11. Therefore, the expression can be written as a multiplication as -17y × (-1) - 11.

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To calculate the distance traveled by the satellite, we need to find the circumference of the circle it traces in the sky. The circumference can be found using the formula:

C = 2 * π * r

where r is the radius of the circle (i.e., the distance from the center of the earth to the satellite), and π is pi, approximately equal to 3.14.

r = 36,000 km

C = 2 * π * 36,000 km

C = 72,000 * π km

Next, we need to find what fraction of the circumference the satellite has traveled in one hour. This is given by the fraction of the total circle the satellite has traced, which is equal to the angle it has formed divided by 360°.

fraction = 32° / 360°

Finally, we can multiply the circumference by the fraction to find the distance traveled by the satellite:

distance = C * fraction

distance = 72,000 * π * 32° / 360° km

Rounding the result to the nearest kilometer, the satellite has traveled approximately:

distance = 73,382 km

So, the satellite traveled approximately 73,382 km in one hour.

Answer:

Below

Step-by-step explanation:

Line DE grows to 5 as you move to the midpoints of  BC  and AC....

   go the the other half of the way to the end AB and it grows another 5  for a total of 10

The sets of numbers could not represent the three sides of a triangle is

{12, 17, 30}.

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.

Given:

a)  {12, 17, 30}

Using Triangle Inequality

12 + 17 < 30 This, measurement cannot give Triangle.

b) {15, 21, 33}

Using Triangle Inequality

15+ 21 > 33

21+33>15

33+15>21

This measurement give Triangle.

c)  {4, 6, 7}

Using Triangle Inequality

4 + 6 > 7

6+7>4

7+4 > 6

This measurement give Triangle.

d) {12, 27, 37}

Using Triangle Inequality

12+ 27 > 37

27+ 37 > 12

12 + 37 > 27

This measurement give Triangle.

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The solution to the system of equations is x = -1 and y = -3

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

-2x+2y=-4

3x + 3y = -18

Multiply (1) by 1.5

So, we have the following representation

-3x + 3y = -6

3x + 3y = -18

Add the equations

6y = -24

So, we have

y = -3

This means that

-2x + 2(-3) = -4

Evaluate

2x = -2

Divide

x = -1

Hence, the value of x is -1

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Answer:

C

Step-by-step explanation:

In table C, each time x increases by one, y increases by 26 correspondingly. This suggests that y = 26x. The other 3 tables do not show a consistent pattern or relationship between x and y.

Table A can be disproved because, though it seems at first to be a multiple of -2 for every x value, the third data value (3, -16) disproves this. It would have to be (3, -6) for this relationship.

Table B has no clear pattern; the difference from the y values corresponding to x=1 and x=2 is 23, while the difference between x=2 and x=3 is also 23. However, there is no x & y relationship that can be defined to find x or y when given the other.

Table D has no clear pattern; the difference between x=1 and x=2 is 6, but the difference between x=2 and x=3 is 7.

Answer: The correct answer is A. If the graph of the system shows parallel lines, then there are infinite solutions.

When two linear equations in the system have the same slope and different y-intercepts, the lines will be parallel and will never intersect. This means that there is no solution to the system.

On the other hand, when two linear equations in the system have different slopes, the lines will intersect at exactly one point, which is the unique solution to the system.

So, in summary:

Parallel lines: no solution

Intersecting lines: one solution

Infinite solutions: lines are the same.

Step-by-step explanation:

The informational text that is an expression of an opinion on a subject is an essay. That is option B

An essay is defined as the piece of writing or a literary write up that is used to represent the writer's opinion about a subject that is under study.

There are different types of easy written that includes the following:

Therefore, easy is an informational text that is an expression of an opinion on a subject.

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the question is mistake

Note that the measure of ∠AED is 123°. (Option D) This is arrived at using the properties of a 4 sided polygon and angles on a straight light postulate.

A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

We know that the sum of angles in a polygon is 360°

Since ∠ABD = 46°

That is Sum of Angles in ΔBDC Less (79+57) =

180 - (101)

= 46°

And ∠EDB = 180-79 (angles on a straight line)

⇒ ∠EDB = 101°

And ∠BAE = 90° (Given)

Thus,

∠AED = 360 - 90-46-101; Thus

∠AED = 123°

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3(3)-4 = 5

Hope this helped

Answer:

x = 24

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary.

             ∠B + ∠C = 180°

        5x + 2x + 12 = 180

                7x + 12 = 180

Subtract 12 from both sides,

                   7x = 180 - 12

                  7x  = 168

Divide both sides by 7,

                  x = 168 ÷7

                 [tex]\boxed{x = 24^\circ}[/tex]

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - 11 = (3/2)(x - 12)

Expanding and simplifying, we get:

y - 11 = (3/2)x - 18

y = (3/2)x - 7

Therefore, the equation of the line that passes through the point (12, 11) with slope 3/2 is y = (3/2)x - 7 in slope-intercept form or y - 11 = (3/2)(x - 12) in point-slope form.

The graph of the function f(x) = 3√(3 - x) is at the end of the answer.

We want to graph the function f(x) = 3√(3 - x)

To do so, we need to find some points on that line, to find the points we need to evaluate the function in some values of x

if x = -1

f(-1) = 3√(3 + 1) = 3*2 = 6

if x = 3

f(3) = 3√(3 - 3) = 3*0 = 0

if x = -6

f(-6) = 3*√(3 + 6) = 3*3 = 9

if x = -13

f(-13) =  3*√(3 + 13) = 3*4 = 12

Then the points are (-1, 6), (3, 0), (-6, 9), (-13, 12)

Now we can just graph these 4 points and connect them with a curve, the graph of the function is below.

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