Does the series shown below converge or
diverge?
If convergent, find its sum.

Does The Series Shown Below Converge Ordiverge?If Convergent, Find Its Sum.

Answers

Answer 1

Answer: Diverge Reasoning I took the test


Related Questions

can someone help me really quick

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Answer:

18$

Step-by-step explanation:

this is so i can reach twenty characters.

Two trains are 525 miles apart heading toward each other on parallel tracks. Train A is traveling east at 30 miles per hour, while Train B travels west at 45 miles per hour. When will the trains pass each other?​

Answers

The two trains will pass each other after 7 hours.

Both trains need to cover a distance of 525 miles before they cross each other.

We know, d = s × t

where d ⇒ total distance travelled

s ⇒ speed of the train

t ⇒ time taken for both trains to meet

For train A,

s = 30 miles per hour

Distance covered by train A in t hours = 30 × t

For train B,

s = 45 miles per hour

Distance covered by train B in t hours = 45 × t

As the total distance is 525 miles,

30t + 45t = 525

75t = 525

t = 7 hours

Hence, the trains will pass each other after 7 hours.

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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Answers

The length of the rectangular area is 800 yards and width is 800 yards

The perimeter of the rectangular area = 3200 yards

The perimeter of the rectangle = 2 (l + w)

Then the equation will be

2(l + w) = 3200

l + w = 3200 / 2

l + w = 1600 yards

w = 1600 - l

The area of the rectangular area = l × w

= l(1600 - l)

Since the area is maximizing the the rate of change of area will be zero

l × w = 0

1600 - 2l = 0

2l = 1600

l = 1600/2

l = 800 yards

Then

w = 1600 - l

Substitute the value of l in the equation

w = 1600 - 800

w = 800 yards

Hence, the length of the rectangular area is 800 yards and width is 800 yards

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a house is 13 ft tall. its shadow is 20 ft long at the same time the shadow of a nearby building is 170 ft long. find the height of the building.

Answers

The height of the building after using proportion is  110.5 ft.

What is proportion ?

The main conceptual underpinnings on which proportion is described are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers. For grasping the myriad concepts in science and mathematics, the ratio and proportion are crucial constructing elements. With the right amount of proportion, a variety of problems in daily life, such as those encountered in the kitchen or in business when processing transactions, can be resolved. It facilitates comparison by establishing a relationship between two or more quantities.

Here House height = 13ft

Shadow of the house height = 20 ft

Shadow of the building height = 170ft

Noe using proportion ,

=> [tex]\frac{House height}{shadow of the house} = \frac{building height}{shadow of the building}[/tex]

=> [tex]\frac{13}{20} = \frac{x}{170}[/tex]

=> x=[tex]\frac{13*170}{20}[/tex] =110.5 ft.

Hence the height of the building is 110.5 ft tall.

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A pe class has 484848 students. one group of 242424 students chooses to play volleyball. the teacher then divides the remaining students into as many groups of 555 as possible to shoot baskets. after that, the remaining students (not on a volleyball or basketball team) climb the rock wall. how many students climb the rock wall?

Answers

444 students will climb the rock wall.

Given, that A class has 484848 students, one group of 242424 students chooses to play volleyball.

Then the teacher divides the remaining students into as many groups of 555 as possible to shoot baskets.

After that, the remaining students (not on a volleyball or basketball team) climb the rock wall.

Now, we are asked that the students who climb the rock wall

So, from a class of 484848 students if One group of 242424 students is made to play volleyball then there will be 242424 students remaining.

Now, to divide 242424 students into groups of 555 students,

we need to divide 242424 by 555, then we get

242424/555 = 436.8

Now there will be 436 groups of 555 students who will shoot basket and remaining 444 students who will climb the rock wall.

Hence, 444 students will climb the rock wall.

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Direct or Inverse variation

3y=x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

Answers

The answers are as follows -

Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given are the following relations -

3y = x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

We can write -

x = 3y

as

y = (1/3)x

m = 1/3

Relation 3y=x represents direct variation.

For the relation - {(2,6),(3,9),(5,15)}, we can write -

We can write it as -

y = 3x

Relation {(2,6),(3,9),(5,15)} represents direct variation.

For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.

Therefore -

Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.

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Find the slope of the following graph

Answers

Answer:

3/2x

Step-by-step explanation:

Which function matches the table? Number of Days Rented 1 2 3 4 Rental Cost ($) 12 17 22 27 A. f(x) = 5x B. f(x) = 5 + 5x C. f(x) = 7 + 5x D. f(x) = 12 + 5x

Answers

Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The table is given below.

Number of Days Rented               Rental Cost ($)

                   1                                          12

                  2                                          17

                  3                                          22

                  4                                          27

At x = 1, the value of y is 12.

12 = m + c                      ...1

At x = 2, the value of y is 17.

17 = 2m + c                      ...2

Subtraction equation 1 from equation 1, then we have

2m - m = 17 - 12

m = 5

Then the value of 'c' is given as,

17 = 2 x 5 + c

17 = 10 + c

c = 7

Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.

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the average monthly rent for one-bedroom apartments in a particular city has been $770. because of a downturn in the real estate market, it is believed that there has been a decrease in the average rental. which is the correct hypotheses to be tested?

Answers

The set of values for Rents lesser than $700. So, rent 700 <y<0

Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.1) Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 7002) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment. Depending on the information received, it might be supported or might not be supported at all.

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Find the exact value of cosine (alpha beta) given sin alpha = two-fifths for alpha in quadrant ii and cosine beta = one-third for beta in quadrant iv. startfraction 8 startroot 2 endroot startroot 15 endroot over 15 endfraction startfraction 4 startroot 2 endroot startroot 21 endroot over 15 endfraction startfraction 4 startroot 2 endroot minus startroot 21 endroot over 15 endfraction

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The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV

we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for  quadrant 2 and 3). Since we know cos² a + sin² a = 1

for α, cos² α + sin² α = 1

=> cos² α = 1 - sin² α

=> cos² α = 1 - 4/25

=> cos α = √21/25

same for β, cos² β + sin² β = 1

=> sin² β = 1 -cos² β

=> sin² β = 1 -1/9

= 8/9

=2√2/3

substituting the known values in the above formula for cos (α+β)

=>cos α cos β - sin α sin β

=√21/25 *1/3- 2/5*2√2/3

=√21/25- 4√2/15

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Answer:

d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]

Step-by-step explanation:

The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!

Have a lovely day!

what is the difference between -3 and 10

Answers

Answer:

13

Step-by-step explanation:

-3-10, or 10+3 is equal to 13

Answer:

13

Step-by-step explanation:

-3+13=10

what is the distance between point P (-5,7) and point Q (6,7) ?

Answers

Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

Which shape has exactly 4 lines of symmetry?

Answers

Answer:

Step-by-step explanation:

its a square so choose the yellow square.

a man 6 ft tall walks at the rate of 5 ftsec toward a streetlight that is 16 ft above the ground. at what rate is the length of his shadow changing when he is 10 ft from the base of the light?

Answers

The rate at which length of shadow of person changing is 3 ft /sec.

What is meant by time rate?The literal formula for the relationship between distance, rate, and time is distance=rate×time=rt

H = Height of streetlight; 16 ft

h = Height of man; 6 ft

x = Length of man's shadow.

s = Distance from streetlight to man.

Using the similarities of the triangles.

H/h = (s + x)/x

Hx = h(s + x)

Differentiate with respect to 't' on both sides.

H(dx/dt) = h(ds/dt + dx/dt)

Put the values.

16(dx/dt) = 6(5 + dx/dt)

16(dx/dt) = 30 + 5dx/dt

10dx/dt = 30

dx/dt = 3 ft /sec

Thus, the rate at which length of shadow of person changing is 3 ft /sec.

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kendra ran 12 miles in 60 minutes. if the ratio of miles to minutes is constant how many more miles can she run in 90 minutes than in 60 minutes

Answers

Answer:

it is 18 mile

Step-by-step explanation:

12mile = 60 min

x = 90 min

we cris cross the equation and

we found x=18 mile

1.A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of oil are vinegar are needed to make 1/2 cup salad dressing?

Answers

Answer:

4 to 7 percent.

Step-by-step explanation:

We use the traditional oil-to-vinegar ratio: three parts oil to one part vinegar/acid, but this ratio can vary depending on your choice of vinegar/acid and personal taste. The less acidic the vinegar/acid, the less oil you need. It's all about balance!

Let's find 1/10 + 1/2

First write the addition so the fractions have denominator 10. Then add ​

Answers

1/10 + 1/2 = 1/10 + (1/2)*(5/5) = 1/10 + 5/10 = 6/10 = 3/5

Answer:

3/5

Step-by-step explanation:

Given problem,

→ (1/10) + (1/2)

Let's solve the problem,

→ (1/10) + (1/2)

→ (1/10) + (5/10)

→ 6/10

→ 3/5 {simplest form}

Thus, answer is 3/5.

NEED HELP ASAP!!!!!!!!!!!!!!

Answers

The number of solutions each polynomial has is 1, 5 and 3

What is a polynomial?

In mathematics, a polynomial is an equation made up of coefficients and indeterminates, sometimes referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be used to solve it. An example of a polynomial with one undetermined x is x2 4x + 7.

Polynomials are often employed in both mathematics and science. In fundamental chemistry and physics, economics, and social science, for example, they are used to define polynomial functions. They are also employed in calculus and numerical analysis to approximate other functions. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. polynomials' usage in complex maths.

The number of solutions of a polynomial is equal to the highest degree of the polynomial.

So,

1) y = -6x -9

Has 1 solution as highest degree = 1

2) y = 2x⁵-x⁴ +2x³-6x²+2x+4

Has 5 solutions as highest  degree = 5

3) y = -4x³-10x² +7x+5

Has 3 solutions as highest  degree = 3

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The population of a state was estimated to be
about 38,332,521 people. Write the estimated
population as a single digit times a power of 10.

Answers

The state population as a single-digit time power of 10 is approximately 4 × 10⁷.

What is estimation?

Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.

To estimate something is to approximate it as accurately as possible.

To acquire a quick and approximate response is obtained by rounding down the values used in the computation.

Given the state estimated population = 38,332,521

Divide and multiply by 10

So,

= 3,833,252.1 × 10¹

= 383,325.21 × 10²

So, similarly, we can write

= 3.8332521 × 10⁷

So, we can write the state population as approximately 4 × 10⁷

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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?

Answers

Answer:10.3

Step-by-step explanation:

16(5h-29)=360

80h-464=360

80h-464+464=360+464

80h/80=824/80

h=10.3

Explain why AB and AC are equal in length

Answers

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

∠ B + 72° + 36° = 180°

∠ B + 108° = 180° ( subtract 108° from both sides )

∠ B = 72°

Then

∠ B = ∠ C = 72°

this means the 2 base angles in Δ ABC are congruent , then the triangle is isosceles with the 2 legs being congruent , that is

AB = AC

what is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function?

Answers

(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.

Domain of the tangent function be, R - {(2n+1)π/2}

Range of the tangent function be, R

Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.

So, the restricted domain be (-π/2 , π/2).

In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.

So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

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What is the image of (-1,7) after a reflection over the line y = x

Answers

The image of (-1,7) after a reflection over the line y = x is (7, -1).

What is a line of reflection?

When reflecting a figure in a line or a point, the image and preimage coincide. A reflection converts each point in a figure from a point to an image via a set line. The reflection line is the name given to the fixed line.

Here, we have

Image : (-1.7)

Now,

Reflect over the line y = x:

When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.

Thus, the point (-1,7) maps to the point (7,-1) when reflected over y=x.

Hence, The image of (-1,7) after a reflection over the line y = x is (7, -1).

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I need help with this

Answers

Answer:

Yes.

Step-by-step explanation:

To decide if these triangles are similar, we need to check 2 criteria. The first is that the angles are all the same as their corresponding angles on the other triangle, which is true. The second is to check if the sides are all in the same proportional relationship. To do this, we need to put 40/50, 40/50, and 16/20 to see if they simplify to the same fraction (which is the proportion.) 40/50 and 40/50 simplify to the same fraction, 4/5. 16/20 also simplifies to 4/5, so the sides are all in the same proportion, which means the shapes are similar.

WXYZ is a kite. ∠WXY has a measure of 94° and ∠ZWX has a measure of 112°. Find the measure of ∠ZYW.

Answers

well, we know WXYZ is a kite, so is a quadrilateral, namely it has 4 sides, and it has two congruent angles, so

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 94+94+112+\measuredangle ZYW=360\implies \implies \measuredangle ZYW=60[/tex]

Check the picture below.

Two integers, a and b, have a product of 20. What is the least possible sum? pls help lol

Answers

The least possible sum wen the integers, a and b, have a product of 20 is 9.

How to calculate the sum?

From the information given, two integers, a and b, have a product of 20. It should be noted that the values that an give a product of 20 will be:

1 × 20 = 20

2 × 10 = 20

4 × 5 = 20

Therefore, the sum of the factors will be:

1 + 20 = 21

2 + 10 = 12

4 + 5 = 9

The least possible sum is 9.

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Convert 90°F into °C​

Answers

Answer:

32.2222

Step-by-step explanation:

Answer: 32.22 degrees Celsius.

I need help it’s due by 11:59pm
I need
Range=
Domain=

Answers

Answer:

Range:  [tex]\text{y} \ge 0[/tex]

Domain: [tex]\text{x} \ge 0[/tex]

Both involve "greater than or equal to 0".

==============================================

Explanation:

The domain is the set of allowed inputs (x). The smallest input allowed in this case is x = 0, as it corresponds to the left-most point (0,0) on the blue graph. There is no largest x value since it stretches forever to the right.

Either x = 0 or x > 0 which condenses to [tex]\text{x} \ge 0[/tex] and this is the domain as an inequality.

--------

The range will have us look at the possible y values or possible outputs. We have y = 0 as the smallest output possible, which corresponds to the lowest point (0,0).

There is no largest y value since the blue graph goes forever upward.

Either y = 0 or y > 0 to give us the range of [tex]\text{y} \ge 0[/tex]

The area of a square foot ball field is
16900cm². calculate the length of the field.

Answers

AREA OF A SQUARE= LENGTH* LENGTH

16900= L²

TAKE THE SQUARE ROOTS OF BOTH SIDES

√16900 =√L²

L= 130

THEREFORE THE LENGTH OF THE FIELD IS 130cm.

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