P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.

Answers

Answer 1

Answer:

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.

Step-by-step explanation:

Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of [tex]2\pi[/tex] radians. By this approach we find that:

[tex]\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}[/tex] (1)

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]T[/tex] - Period, measured in seconds.

Then, we solve (1) for [tex]T[/tex]:

[tex]\frac{8}{3} = \frac{2\pi}{T}[/tex]

[tex]T = \frac{6\pi}{8}\,s[/tex]

[tex]T = \frac{3\pi}{4}\,s[/tex]

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.


Related Questions

Find the sum of the measures of the angles in quadrilateral ABCD. (Hint: Draw diagonal AC. How can you use the figures you have formed to find the sum?)

Answers

The measure of four angles of quadrilateral is 360°.

What is quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles.

It is a type of polygon.

In order to create it, four non-collinear points are joined.

Quadrilaterals always have a total interior angle of 360 degrees.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is shown in the above image as an example.

A quadrilateral is a polygon with four vertices and four sides that each contain four angles, the sum of which is 360 degrees.

Two triangles are created when we draw a diagonal to a quadrilateral. These two triangles have a 180° angle sum.

As a result, the quadrilateral's total angle sum is 360°.

Hence, the measure of four angles of quadrilateral is 360°.

To know more about quadrilateral, click on the link

https://brainly.com/question/23935806

#SPJ1

Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60. What percent did she leave?

answer = _____%

Answers

The percentage of the tip that she leaves will be 20.02%.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60.

Then the percentage is given as,

P = [2.6 / 12.99] x 100

P = 0.2002 x 100

P = 20.02%

The percentage of the tip that she leaves will be 20.02%.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ1

To make a specific hair dye a hairstylist uses a ratio of one and 1/8 oz of red tone 3/4 oz of Gray tone and 5/8 oz of Brown tone if the stylist needs to make 20 oz of dye how much of each dye color is needed?

Answers

Answer: To make 20 oz of hair dye, the hairstylist needs to use 1 and 1/8 oz of red tone, 3/4 oz of gray tone and 5/8 oz of brown tone.

We can use proportionality to figure out how much of each dye color is needed.

Let's call the amount of red dye needed x, the amount of gray dye needed y and the amount of brown dye needed z.

According to the proportionality, we can write the following equation:

(1 + 1/8)x + (3/4)y + (5/8)z = 20

To find the amount of each dye color needed, we can solve this equation for x, y and z.

First, we can clear the fractions by multiplying all terms by 8:

(8 + 1)x + (6)y + (5)z = 160

Now we can solve for x:

9x + 6y + 5z = 160

x = (160 - 6y - 5z)/9

Similarly, we can solve for y and z:

y = (160 - 9x - 5z)/6

z = (160 - 9x - 6y)/5

Now we can substitute the desired amount of 20 oz into the equation and solve for x, y and z

Step-by-step explanation:

Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box. If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?

Answers

The total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

The total number of books that Jarrod packed into boxes can be found by multiplying the number of boxes he packed with the number of books per box.

In this case, Jarrod packed 6 boxes of science textbooks with 14 books per box, so the number of books in the science boxes is 614 = 84. He also packed math textbooks with 12 books per box, so the number of books in the math boxes can be represented by x*12, where x represents the total number of boxes he packed.

So the total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

Therefore, the equation that can be used to find the total number of books that Jarrod packed into boxes is: 84 + x*12 = Total number of books.

To learn more about Equations:

https://brainly.com/question/2972832

A ratio of 4 to 7 maybe written as the following, except 4:7 8:14 7/4 8/14 12:21

Answers

Answer:

except 7/4

Step-by-step explanation:


The ratio of 4 to 7 is the same as the fraction 4/7

7/4 is not equal to 4/7 and therefore they cannot be written in the same way.

The nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?

Answers

The nearest whole number to which the new height of the image is enlarged is 9cm.

What is scaling?

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are what we call scaled figures.

Given that the original size was in the ratio 4: 3.

When the image is enlarged the enlarged image will be in the similar ratio to the original size.

Hence, the ratio in which the enlarged image will be increased is 4x : 3x.

The new width is given as 12,

The value of 4x = 12

x = 3

Then the new height of the image is:

3 (3) = 9cm.

Hence, the new height of the image is 9cm.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

Algebra i need help asap

Answers

Answer:

Below

Step-by-step explanation:

Solutions are where the graphs intersect....they are equal at these points

(2,-3)  and (4,-1)  

There is likely one more point of intersection down and to the left which is not shown on the graph

Which method of solving for the variable could be used instead of cross multiplication?.

Answers

Answer: multiplying by denominators

Step-by-step explanation: not sure if this is the right answer in this context but i hope it helps

technically cross multiplying basically is multiplying by denominators, but depending on the math level they are sometimes considered different methods

again, this may not be correct so if you want a more clear answer could you provide a bit of context? sorry, hope it helps anyway though.

Can someone help me with this please?

Answers

By using the triangle inequality theorem, the possible side lengths for the third side is equal to: D. 4 < c < 42.

What is the triangle inequality theorem?

In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:

b - c < a < b + c

23 - 19 < a < 23 + 19

4 < a < 42.

Read more on Triangle Inequality Theorem here: brainly.com/question/26037134

#SPJ1

PLEASE HELP!!! I NEED HELP WITH MY HOMEWORK!!!!
(GEOMETRY)
WILL MARK BRAINLIEST!!!!!

Answers

Answer:U: 1.98 V: 1.4 And also the other side, square root symbol: 1.4

Step-by-step explanation:

I hope this helps man, i havnt done this stuff in a while...

Do all exponential functions pass through 0 1?

Answers

All exponential functions pass through (0, 1)

We know that the exponential function f with base b is defined as:

f(x) = b^x

where b > 0 and b is not equal to 1

and x is any real number.

For x = 0,

f(0) = b^0

f(0) = 1

This means, the graph of function f(x) passes through (0, 1)

For example consider an exponential function f(x) = 2^x

For x = 0,

f(0) = 2^0

f(0) = 1

the graph of f(x) = 2^x passes through (0, 1)

so, the characteristics of the graphs of all exponential functions:

The graphs contain the point (0, 1).

The x-axis is an asymptote.

Learn more about the exponential function here:

https://brainly.com/question/3127939

#SPJ4

Pls, Help!! My assignment is due tomorrow!

Answers

Mina will receive $13.33 after converting her 18 Pounds GBP to Dollars USD

What is conversion?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used

To change 18GBP to USD at the current exchange rate of 1.35GBP to 1 USD

Divide the Amount being converted by the exchange rate

that is, 18GBP/1.35

=13.33USD

Hence, 13.33USD is the amount that Mina will receive after converting her 18 GBP

Learn more about conversion at:https://brainly.com/question/97386

#SPJ1

Write and solve an equation to find the value of x below.​

Answers

Answer:

Equation:

[tex]7x + 10 = 150[/tex]

Value of x:

[tex]x = 20[/tex]

Step-by-step explanation:

In the figure, we are given 2 angles, 150° and (7x+10)°.

These 2 angles are vertical angles because they are directly opposite of each other and formed by intersecting lines.

Vertical angles are congruent, which means the same.

Thus, to make an equation to solve for x, we need to set the angles equal to each other.

Equation: [tex]7x + 10 = 150[/tex]

Solving for x:

[tex]7x + 10 = 150[/tex]

⇒ [tex]7x = 140[/tex] . . . . . . . . . subtract 10 from both sides of the equation

⇒ ∴ [tex]x = 20[/tex] . . . . . . . . . divide both sides by 7 to isolate x

if this response helped you, please mark it the "brainliest"!

Answer:

Step-by-step explanation:

Using VAT:

Angles opposite each other are consider equal.

Therefore : 7x+10 = 150

Solve for x: 7x= 150-10

                    x= 140/7

                    x= 20

To check : 7x+10 = 150

                 7(20)+10=150

                 140+10=150

                 150=150 (correct)

What is 14/10 reduced??

Answers

The reduced form of 14/10 is 7/5. The answer is obtained using the method of simplifying fractions.

What is meant by simplifying fractions?

Making a fraction as simple as possible is referred to as simplifying (or reducing) a fraction.

To do this, we divide the denominator and numerator by the biggest number that can be divided exactly into both numbers. In other words, we choose the biggest common number between the top and bottom and divide it by that.

In a fraction, the numerator and denominator are referred to as the "terms." Thus, when we simplify a fraction, we cast it in its most basic mathematical form.

Now, to reduce 14/10, we will find the highest common factor of 14 and 10.

The highest common factor is 2 i.e. both numerator and denominator are divisible by 2.

So, on dividing both the terms by 2, we get

(14÷2)/(10÷2)= 7/5

Hence, the reduced form of 14/10 is 7/5.

Learn more about simplifying fractions from the given link

https://brainly.com/question/17220365

#SPJ1

What can you conclude about the following figure?

Answers

What we can conclude by the given triangle about similarity is;

ΔPQR ∼ ΔPST

How to Identify Triangle similarity theorem?

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, there are three types of similarity theorems for triangles namely;

Angle Angle(AA) Similarity

Side Angle Side(SAS) Similarity

Side Side Side(SSS) Similarity

We see that both triangles PQR and PST have equal angle R and angle T which are both 36 degrees. Thus, they are both similar by the AA Similarity theorem

Read more about Triangle similarity theorem at; https://brainly.com/question/21247688

#SPJ1

y= 2/3x -3 and x=-3 solution

Answers

y = 2/3*-3-3
y = 2/-9-3
* Unity of the denominator Multiply the number by 9
y = -29/9

What is the formula for finding the area of a sector of a triangle?

Answers

The formula for a sector's area is: 1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2) 3. A = (fraction of the circle) * (pi * r2)

The ratio used to find the area of the sector is that of how to know what fraction of the circle is the sector.

Ratio = (θ/360°)

θ is the angle subtended at the center of the circle by the arc, measured in degrees.

For this question,

θ = 60°

Ratio = (θ/360°) = (60°/360°) = (1/6)

Area of a circle is given as

Area of a circle = πr²

where

π = pi

r = radius of the circle = 8

Area of the circle = πr²

Area of the circle = π (8²) = 64π square units

Area of the sector is given as

Area of the sector = (Ratio) × (Area of the circle)

Ratio = (1/6)

Area of the circle = 64π square units

Area of the sector = (Ratio) × (Area of the circle)

Area of the sector = (1/6) × (64π) = (64π/6) = (32π/3) square units

learn more about of area here

https://brainly.com/question/29082330

#SPJ4

Which of the following represents the diameter of the circle below?

A. XY
B. O
C. X
D. YO

Answers

XY is the diameter because the diameter is the entire side to side while radius is from the middle to the side.

How to find the diameter of a circle?

The diameter is the entire side to side while radius is from the middle to the side.

The diameter of a circle is represented by the letter d.

here O is the center of the circle

radius of the circle is OX and YO

diameter of the circle is 2×radius

then here diameter of the circle is XY

To learn more about diameter of a circle refer to:

brainly.com/question/30221527

#SPJ1

Is dilation horizontal or vertical?

Answers

Dilation is neither horizontal nor vertical. Dilation is a transformation that changes the size of a shape but does not change its orientation.

It can be represented by a formula in coordinate geometry: (x, y) → (kx, ky), where k is a scale factor (greater than 0). The scale factor determines the amount of scaling that is applied to the shape. For example, if k = 2, then the coordinates of the original point (x, y) would be multiplied by 2, resulting in a new point (2x, 2y). This would result in the shape being twice as big as the original. Similarly, if k = 0.5, then the coordinates of the original point (x, y) would be divided by 2, resulting in a new point (0.5x, 0.5y). This would result in the shape being half as big as the original. Therefore, dilation can be used to scale shapes both up and down in size, but it does not alter their orientation.

Learn more about  dilation here:

https://brainly.com/question/13176891

#SPJ4

What is the formula for square units?

Answers

The formula for the area of a square is A = s², where A is the area of the square and s is the length of one of its sides.

To calculate the area of a square, multiply the length of one side by itself. For example, if the side of a square is 5 meters, the area of the square would be 25 square meters (5² = 25). If the side of a square is 8 feet, the area of the square would be 64 square feet (8² = 64). The area of a square is always equal to the length of one side multiplied by itself.

Learn more about area of a square  here:

https://brainly.com/question/11952845

#SPJ4

Can someone help me with this please?

A: Classify the triangle above by its sides

B: Classify the triangle above by its angles

C: Explain your answer to part a and b

Answers

A. I took the test and my teacher said astonishing. There is something to do with how it works on a calculator

How long do eyes stay dilated?

Answers

Depending on the patient and the strength of the eye drop, eye dilation caused by eye drops used for eye examinations typically lasts between 4 and 24 hours.

What is eyes dilation?

There are causes of dilated pupils besides underlying disease. Examples include a pitch-black room, sleep, fear, or adverse drug reactions.

When you get your eyes dilated, your doctor uses special drops to open your pupils wide.

This let them get a look at your whole eye, including all the nerves and blood vessels at the back, to check for signs of diseases

When dilated, the pupil is unable to get smaller, and thus block out light in bright areas. This causes glare in your vision so you can't see things clearly.

The drops also make it difficult to focus on things up close, but usually don't affect distance vision.

So, Your eyesight will be impaired, so some experts say you should play it safe and not get behind the wheel will leads to affecting your driving

Hence, depending on the patient and the strength of the eye drop, eye dilation caused by eye drops used for eye examinations typically lasts between 4 and 24 hours.

To know more about eye dilation, click on the link

https://brainly.com/question/29794861

#SPJ4

i need help, i feel like i know how to do it but when i try it makes no sense. can someone explain this to me with steps?

Answers

Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.

What exactly is an X2?

X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .

heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!

To learn more about Square to refer:

https://brainly.com/question/14479322

#SPJ1

Aira got 76, 85, 81 and 77 in her four quizzes. What average score must she get in her next two quizzes to obtain an average of 83?.

Answers

Aira should must score a total of 179 combined in her next two quizzes in order to make the average of all the marks of the quizzes as 83.

Aira has got 76, 85, 81 and 77 marks in her 4 quizzes.

I have to give two more quizzes and the marks obtained in those two quizzes should be such that the average of all the quizzes should be 83.

We know that we can find the average of the data by taking the sum of all the given values and dividing that particular value by the number of data given to us.

Here in this case let assume that she obtained X marks in her next to test combined. Now this way total number of observation are 6.

Now, we can simply apply the formula to find the average of the data.

Average = (76 + 85 + 81 + 77 + X)/6

83 = (76 + 85 + 81 + 77 + X)/6

X = 179

So, Aira should obtain 179 marks in her next to quizzes in order to make the average of all the score equal to 83.

To know more about average, visit,

https://brainly.com/question/130657

#SPJ4

What do you call the total distance around a polygon, or 2-D shape?

A .area
B .perimeter
C .volume
D .width

Answers

Answer:

It is called the perimeter

Step-by-step explanation:

the length of a rectangle is 6 feet longer than the width. the perimeter is 28 feet. find the dimensions of the regtangle

Answers

The length of rectangle :10 feet

               The width of rectangle :  4 feet

       Given

        perimeter of the rectangle :28 feet

       let  width of the rectangle be :x

         and  length  of the rectangle be :  6+x   (as per given condition)

      therefore  

                      perimeter = 2(length +width)

                               28 = 2(6+x+x)

                               28 = 2(6+2x)

                               28 = 12+4x

                               28-12 = 4x

                                16  = 4x

                                 x = 4

  as width of rectangle  is : 4

similarly  length : 6+x

                            6+4

                            :10

The dimensions of the rectangle are : length =10

                                                               width = 4

verification :

perimeter =2(l+w)

28 = 2(10+4)

28 = 28

You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $4 hour and your sales job pays $8 per hour. You need to earn at least $120 each week to pay your bills. Write and graph a system of inequalities that shows the various numbers of hours you can work at each job.​

Answers

Let x be the number of hours you work at your housecleaning job and y be the number of hours you work at your sales job.

The first inequality represents the fact that you can work no more than 40 hours in total between the two jobs:
x + y ≤ 40

The second inequality represents the fact that you need to earn at least $120 per week:
4x + 8y ≥ 120

The third inequality represents the fact that you can only work positive hours at each job:
x ≥ 0
y ≥ 0

Graphically, this system of inequalities can be represented by a region on the xy-plane that is bounded by the lines x + y = 40, 4x + 8y = 120, x = 0 and y = 0.
This region is a triangle where x+y<=40, 4x+8y>=120 and x,y>=0

So, one possible solution is to work between 0 and 40 hours at the housecleaning job, and between 0 and 40 hours at the sales job, as long as the total number of hours worked is 40 or less and the total weekly income is $120 or more.

a function pairs each teacher with 30 students

Answers

On solving the provided question we can say that when each teacher is matched with 30 students, t is not a function.

what is function?

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

When each teacher is matched with 30 students, t is not a function.

This is true since it demonstrates a one-to-many link.

Therefore, this is the case because it shows a many-to-one relationship and multiple weights can have the same cost.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

If f(x)=6x-4 and f(x)=14, what is the value of x?

Answers

Answer:

Since, 6x -4 and 14 both are values of f(X)then,

6x-4=14

or,6x=14+4

or,X=18/6

:.X=3

*mark me brainliest

Answer: X=3 :)

Step-by-step explanation:

f(x)= 6x-4 and f(x)=14

6x-4=14

6x=4+14

6x=18

Divide both by 6

x=3

What is the answer of X² 6x 16?

Answers

The solution of (x^2 +  6x - 16) is ( x+8 )( x−2 ).

Lets solve the equation (x^2 +  6x - 16) in order to find its solution:

The equation is ( x^2 + 6x − 16 )

Now factorizing it

= ( x^2 + 8x − 2x − 16)

Taking x common from the first two terms and -2 common from the last two terms:

= [x (x+8) −2 (x+8) ]

Now,

= [ (x+8) (x−2) ]

Therefore, it is shown that the solution of the equation "(x^2 +  6x - 16)" is (x+8)(x−2) which is obtained through factorization.

You can learn more about equation at

brainly.com/question/22688504

#SPJ4

Other Questions
many retailers and some manufacturers use an omnichannel or multichannel strategy in which they sell in more than one channel, such as a store, catalog, or the internetT/F how many moles of electrons must be transferred through a cell in order to accumulate a total charge of 70,500 c? (a) if x is a normal n(, 2 ) = n(7, 64) distribution, find k such that p(k x 17) = 0.2957 Senator Stephen Douglas argued that the provisions of the Compromise of 1850 should be voted on as a package rather than individually to demonstrate national unity.T/F coenzyme involved in the conversion of proline to hydroxyproline: use the ratio test to determine whether the series is convergent or divergent. [infinity] (8)n n2 n = 1 identify an. evaluate the following limit. Suppose you're calculating the range of host IP addresses for a subnet (the targeted subnet). If the next subnet's network ID is 192.168.42.128, what is the targeted subnet's broadcast address?a. 192.168.42.255b. 192.168.42.96c. 192.168.42.0d. 192.168.42.127 What are the five main key points of chapter one of The Outsiders as a type of relationship tie, exploitation refers to such things as: in most cases, the longer the maturity of a bond, the higher is the cost of a bond to the issuer. people tend to feel more sympathy toward a person with a disability, and more likely to donate money or volunteer assistance, if/when passage.In which section of the passage does the author build tension surrounding WW?(3) "7t's my opinion, doctor," said the captain in a low voice, that this is the last time you or I will ever be at sea, oranywhere else, if our skipper don't look better after his men, for a more rascally crew I never set eyes on, and, from aword or two I have heard dropped now and then, I feel sure some mischief is in the wind. Come aft with me to a placewhere we ain't so likely to be overheard by eavesdroppers, and I'll tell you all about it."(4) Will Osten was so much astonished at his friend's remark, that he followed him to the after part of the ship withoututtering a word, and there sat down on the taffrail to listen to what he had to communicate....(5) "Doctor," said Captain Dall in a low whisper, taking Will Osten by the button-hole and bending forward until his eyeswere close to those of his young friend, "1 little thought when I set sail from England that, in a few weeks after, my goodship the Foam would come a wreck an' sink to the bottom of the Pacific before my eyes. Still less did I think that I shouldbe cast on a coral island, have to fight [and] be saved at last by missionaries... Yet all this has happened within a fewmonths."(6) At any other time Will Osten would have smiled at the solemn manner in which this was said, but there was somethingin the hour, and also in the tone of his friend's voice, which tended to repress levity and raise a feeling of anxiety in hismind(7) "Well, captain," he said, "what has this to do with the present evil that you seem to apprehend?"ResetNext The nurse is obtaining a medication history on a patient presenting with chest pain. What drug classification would necessitate the nurse informing the provider before beginning the prescribed nitroglycerin? Brenda types 15 words per minute. How long will it take her to type 750 words? Which of the following operating systems can be modified and the source code redistributed?Group of answer choicesAndroidiOSWindows MobileChrome OS a relational message makes a statement about how the parties feel toward one another.True or False? Generally, a board of directors has the power to do all of the following without shareholder approval, except Multiple Choice Declare dividends Appoint corporate officers Dissolve the corporationAll of the choices are correct using polar coordinates, evaluate the improper integral r2e4(x2 y2) dx dy. Use the Ratio Test to determine whether the series is convergent or divergent. [infinity] 9^n / (n+1)7^2n + 1 n=1Identify an ___________Evaluate the following limit.lim n -> [infinity] |an + 1 / an | how many teenagers (people from ages 13-19) must you select to ensure that 4 of them were born on the exact same date (mm/dd/yyyy)