The sum of two consecutive even integers is 26. What is the product of the two integers?
A) 168
B) 160
C) 132
D)120

The area of the shaded sector is 144π units squared.

To find the area of the shaded sector:

Given - The central angle of the sector is, θ [tex]=\frac{8\pi }{9} rad[/tex].

The radius of the circle is, [tex]R=18 units[/tex].

We know that the area of a sector of a circle of radius 'R' and central angle θ is given as:

[tex]A=\frac{1}{2} R^{2}[/tex]θ

Insert, θ [tex]=\frac{8\pi }{9} ,R=18[/tex] and obtain:

[tex]A=\frac{1}{2} *18^{2} *\frac{8\pi }{9} \\A=\frac{(324*4)}{9} \pi \\A=(36*4)\pi \\A=144\pi units^{2}[/tex]

Therefore, the area of the shaded sector is 144π units squared.

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The complete question is given below:

The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared

By the ratio test, the series converges for all [tex]x[/tex], since

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]

Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.

The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.  

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β

Here aₙ = (n²/n!) xⁿ⁺³  and  aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴

Now limit is taken,

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]  

                      =   [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex]  = 0 < 1

Since the limit is less than 1 the series is converging.

We get that,

interval of convergence = (-∞, ∞)

radius of convergence R = ∞

Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.

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Answer:

  1.314 MJ

Step-by-step explanation:

As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.

There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.

The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.

The mass of the water being raised is the product of the volume of the cone and the density of water.

The cone volume is ...

  V = 1/3πr²h . . . . . . for radius 2 m and height 8 m

  V = 1/3π(2 m)²(8 m) = 32π/3 m³

The mass of water in the cone is then ...

  M = density × volume

  M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg

The center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.

The discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...

  W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J

As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.

  V(y) = (32π/3)(y/8)³

The differential volume at height y is the derivative of this:

  dV = π/16y²

The work done to raise this volume of water to a height of 10 m is ...

  (9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J

The total work done is the integral over all heights:

  [tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]

It takes about 1.31 MJ of work to empty the tank.

Answer:

Read explanation

Step-by-step explanation:

I answered another one of your questions just like this in detail so I'll keep this one shorter.

Domain: (-∞, 0]

Range: (-3,∞)

x-intercept: Approximately -3.75

y=intercept: -3

Answer:

Step-by-step explanation:

a. d^2 - 7d + 6 = 0

(d - 1)(d - 6) = 0

d - 1 = 0,  d - 6 = 0 therefore:

d = 1,  6.

b, x^2 + 18x + 81 = 0

(x + 9)(x + 9) = 0

x = -9  multiplicity 2.

c   u^2 + 7u - 60 = 0

(u + 12)(u - 5) = 0

u = -12, 5.

It will cost $375 to hire the doctor for 45 minutes

The doctor charges $500 for an hour

60 minutes makes 1 hour

60 minutes= $500

Therefore the amount that will be charged for 45 minutes can be calculated as follows

60 minutes= $500

45 minutes= x

Cross multiply both sides

60x= 500×45

60x= 22500

x= 22500/60

x= 375

Hence it will cost $375 to hire the doctor for 45 minutes

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Explanation: The 4th one is the distributive property because it shows an     equal sign and the 5th one is the inverse property of addition because it uses more than addition.

Answer: 4th one is distributive property 5th one is inverse property of addition

P.S. I am sure 95% sure that I am correct.

Answer:

They are all true except for D

Step-by-step explanation:

What they are asking you to do, is take your rectangle and flip it over the top.  QR would stay right where it is and line ST would now be on top and line QR would be the bottom.  If you can picture that, you can see that all the statements would be true but D.

Answer:

x= -4 + radical 13

Step-by-step explanation:

Solving a linear equation, we conclude that the book has 276 pages in total.

From pages 1 to 9, each page needs one digit, so at this point we have 9 digits.

From page 10 to 99, each one needs 2 digits. Then in these pages we have:

(99 - 9)*2 = 180 digits.

So at this point we have 180 + 9 = 189 pages.

Now, for each page after this point, we will add 3 digits more.

So if there are x pages after this point, the total number of digits will be:;

N = 189 + x*3

Now we need to solve this linear equation for N = 720 digits, then:

720 = 189+ x*3

720 - 189 = x*3

531 = x*3

531/3 = x = 177

So there are 177 pages after page number 99, this means that the book has:

99 + 177 = 276 pages in total.

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Answer:

x = 3

Step-by-step explanation:

Given the information from the question, we can deduce that:

3 - x = x - 3

Now our goal here is to find x.

3 - x = x -3

3 - x - 3  = x - 3 - 3

- x = x - 6

- x - x = x - 6 - x

- 2x = - 6

x = [tex]\frac{-6}{-2}[/tex] = 3

Answer: 3

Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.

x - 3 = 3 - x

Adding 3 to both sides, we have

x = 6 - x

Adding x to both sides we have

2x = 6

Dividing by 2 from both sides, we get

x = 3

1885.5 m^3 of water will fill the container.

To find how many cubic feet of water will it contain:

Given -

The pool comprises a 12-foot-radius cylinder with a height of 4.5 feet.

The volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed.

Therefore, 1885.5 m^3 of water will fill the container.

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The complete question is given below:

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14

A cylinder with a radius of 12 feet and a height of 4.5 feet.

Answer:

1/4

Step-by-step explanation:

To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4

In the point-slope form of a line, (y-y1)=m(x-x1)

'm' represents the slope of the line.

(x1,y1) represents a given point on the line.

(x,y) represents any point on the line.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

A straight line is represented using its slope and a point on the line using point slope form. This means that the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1,y1).

The point slope form's equation is (y-y1)=m(x-x1), where (x, y) is a randomly chosen point on the line and m is the slope.

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Answer:

1) (x1,y1)= a given point on the line

2)(x,y) = any given point on the line

3)m= a slope of a line

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:

T(t) = A · sin (2π · t / T + C) + B       (1)

Where:

The temperature amplitude and the middle temperature can be found by the following expressions:

A = (t' - t'') / 2      (2)

B = (t' + t'') / 2      (3)

Where t' and t'' are maximum and minimum temperatures, in degrees.

Then, we proceed to find each constant of the sinusoidal model:

A = (45 - 7) / 2

A = 38 / 2

A = 19

B = (45 + 7) / 2

B = 52 / 2

B = 26

We assume a period of 24 hours (T = 24).

If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:

7 = 19 · sin [(π / 12) · 0 + C] + 26

- 19 = 19 · sin C

sin C = - 1

C = π

T(t) = 19 · sin (π · t / 12 + π) + 26

Then, the temperature at 9 AM is: (t = 4)

T(4) = 19 · sin (π · 4 / 12 + π) + 26

T(4) ≈ 9.545

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

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The measure of the central angle of the circle BC = 176°

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the three points be represented as A, B and C

Now , the measure of angle ∠BAC = 88°

And , the measure of the central angle is given by

Central Angle = 2 x Angle in other segment

On simplifying the equation , we get

The measure of central angle BC = 2 x 88°

The measure of central angle BC = 176°

Hence , the measure of central angle is 176°

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Answer: 50

Step-by-step explanation:

50% of the class passed the first test, so that 25% that passed both test has to be part of the 50% that passed the first test. 25% that passed both is 50% of the 50% that passed the first test. Hopefully that makes sense.

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

To find the order of matrix:

To prove:

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.

The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.

Increasing the price by 15% would mean we exist taking 100% of the value + another 15%

100 + 15 = 115%

115% = 115/100 = 1.15.

Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.

Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.

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Answer:

C - by multiplying each entry by 1.15

Step-by-step explanation:

Edmentum.

Answer:

(2 dimes + 6 pennies)

(4 nickels + 6 pennies)

(1 dime + 2 nickels + 6 pennies)

( 2 dimes + 1 nickels + 1 penny)

(1 dime + 3 nickels + 1 penny)

5 different ways that Jamie can make 26 cents.

Answer:

23.  216

24.  56

25.  52

26.  -7

27.  5

Step-by-step explanation:

Work out the differences between the terms until the differences are the same:

[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]

    [tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]

        [tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]

As the third differences are the same, the sequence is cubic and will contain an n³ term.  The coefficient of n³ is always a sixth of the third difference.  Therefore, the coefficient of n³ = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^3[/tex]

So the next term in the sequence is:

[tex]\implies a_6=6^3=216[/tex]

Work out the differences between the terms until the differences are the same:

[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]

     [tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+n[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+7=56[/tex]

Work out the differences between the terms until the differences are the same:

[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]

     [tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+3[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+3=52[/tex]

Given numbers:

-1, 2, -3, 4, -5, 6

As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]

From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.

Therefore, the rule is:

[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]

[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]

So the next term in the sequence is:

[tex]\implies a_7=-7[/tex]

(since 7 is an odd natural number)

Given numbers:

5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5

The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:

Therefore, the next number of 5s will be five.  This means the next number in the list will be 5, since there are only four 5s after the last 3.

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Sariah has just begun training for a half-marathon, which is latex: 13.1 13 . 1 miles. since she was on vacation, she started the training program later than the rest of her running club. there are latex: 6 6 weeks of training runs remaining before the race. in her first week of training, sariah ran latex: 3 3 miles. she ran latex: 4.5 4 . 5 miles the second week and latex: 6 6 miles the third week. if she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance? describe how you would solve this problem using polya's four-step problem-solving method. complete each task as part of your response. be sure to number your answers task 1–task 4 so that your instructor can tell which part you are answering. otherwise, you may not receive credit. Understand the problem.

Task 1: Read the problem and restate in y0ur own words what the question asks.

2. Formulat3 a plan.

Task 2: Identify the model y0u would use to represent the problem and explain why y0u chose that model.

3. Implement th3 plan.

Task 3: Solve the problem and state y0ur answer.

4. Review th3 results.

Task 4: Explain the problem-solving process and how y0u know y0ur answer is correct.

Half of a marathon's distance, or 21.0975 kilometers (13 miles 192.5 yards), is covered during a half marathon. Using nearly the same course with a later start, an earlier finish, or shortcuts, a half marathon event is sometimes held alongside a marathon or a 5K race. If finisher medals are given out, they might not look exactly like the ones given out for the full marathon. Although these measurements are rounded and not officially correct, the half marathon is frequently referred to as a 21K, 21.1K, or 13.1 miles.

The International Association of Athletics Federations recognizes a half marathon world record.

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x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.

What is the linear equation in two variable?

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.

According to the given question

A recipe require 3.5 teaspoons of sugar to make a tart.

y represents the number of teaspoons of sugar.

x represents the number of tarts.

Now, for x tart 3.5y teaspoons of sugar required.

⇒  x = 3.5y

Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.

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The figure 980 inches can be written as 980.0 inches. It contains two non-zero digits and a zero trailing before the decimal point. Hence, it has three significant figures.

Rules to Determine Number of Significant Figures:

There are three fundamental rules that one can use to determine the significant figures in any given number or value. These rules go as follows:

For the portion followed by a decimal point, zeroes at the end are not counted, but zero between two non-zero digits and zero in the initial portion of the floating point are counted while taking note of the significant figures in a decimal value.

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The length of rectangle is 25 feet and the width  of rectangle is 135 feet.

According to the question,

The perimeter of a rectangle is 320 feet. The length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.

Odd integers that follow each other and they differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers. The perimeter of a rectangle is 320 feet. Let the length of a rectangle is x. The next consecutive odd integer is x+2.width = 5(x+2)

    =5x+10.

Let, Length - l:Width - w; l = 5w and the perimeter of a rectangle is 320 feet. Formula for perimeter of rectangle is 2(Length + Breadth). Perimeter of a rectangle is the sum of the length of all sides of the rectangle. The perimeter of a rectangle formula is,

P = 2(l + b)

In words, it is equal to the sum of two times the length and two times the breadth of the rectangle. Perimeter for any figure is defined as the length of its boundary.

2(length + width) = 320

Length+ width=160

x+5x+10=160

6x=150

x=25

Length = 25 feet

width = 5(25+2)=135 feet.

Hence, the length of rectangle is 25 feet and the width of rectangle is 135 feet..

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The root test is Divergent, for given [infinity] 1 nn n = 1.

The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.

The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate

Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.

explanation:

If tan is series

if Lim n root (1) = l

if l =<1 than it is convergent

if l = > 1 than it is divergent

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Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

Given that;

Hence 6 gems are gotten every  120sec and 30 seconds

Hence 6 gems are gotten every  150seconds

Next we convert 1 hour to seconds

1 hour = ( 60 × 60 × 1 )sec = 3600sec

Now,

6 gems can be gotten every  150seconds

x gems can be gotten every 3600 seconds

x = ( 6 × 3600 ) / 150

x = 21600 / 150

x = 144 gems

Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

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This might help a bit, i hope

Based on the given tast content; the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars.

Ratio of green cars to white cars = 24 : 48

= 24 / 48

= 1 / 2

Ratio of green cars to white cars = 1 : 2

Therefore, the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars

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