29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.

options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞

B. As x → –∞, y → –∞, and as x → +∞, y → –∞

C. As x → –∞, y → +∞, and as x → +∞, y → +∞

D. As x → –∞, y → –∞, and as x → +∞, y → +∞

Answers

Answer 1

Answer:

  C.  As x → –∞, y → +∞, and as x → +∞, y → +∞

Step-by-step explanation:

The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.

_____

When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.

When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.


Related Questions

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a function f, then

Answers

If there is such a scalar function f, then

[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]

[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]

Integrate both sides with respect to y :

[tex]g(y,z)=4ye^{4z}+h(z)[/tex]

Plug this into the equation above with f , then differentiate both sides with respect to z :

[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]

Integrate both sides with respect to z :

[tex]h(z)=C[/tex]

So we end up with

[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]

Determine which is the appropriate approach for conducting a hypothesis test. ​Claim: The mean RDA of sodium is 2400mg. Sample​ data: n​150, ​3400, s550. The sample data appear to come from a normally distributed population.

Answers

Answer:

Use the student t distribution

Step-by-step explanation:

Here is the formula

t = (x - u) ÷(s/√N)

From the information we have in the question:

n = 150

s = 550

x = 3400

u = mean = 2400

= 3400 - 2400÷ 500/√150

= 1000/44.9

= 22.27

At 0.05 significance level, df = 149 so t tabulated will be 1.65.

We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.

8÷2(2+2)=?
I asked a few people some say it’s 1 and some say 16....

Answers

Answer:

16

Step-by-step explanation:

Follow the rules of PEMDAS

8÷2(2+2)

Parentheses

8÷2(4)

Exponents

we have none

Multiply and Divide from left to right

4(4)

16

Then Add and Subtract from left to right

Answer:

16

Step-by-step explanation:

In order to understand the answer to the problem, we need to know the correct order of operations, through the acronym PEMDAS

PEMDAS

P: Parentheses

E: Exponent

M: Multiply

D: Divide

A: Add

S: Subtract

First add everything in the parentheses to get 4

Then divide 8 by 2 to get 4

4 times 4 = 16

8/2= 4

2+2=4

4 x 4 = 16

-50 POINTS- (5/5) Which scatter plot represents the following data?

Answers

Answer:

B is plotted correctly

Step-by-step explanation:

A point (1,2) is plotted at (1,3)

B is plotted correctly

C point (1,2) is plotted at (1,3)

D point (1,2) is plotted at (1,3)

Answer:

B.

Step-by-step explanation:

According to the table, there is a point at (0, 5), and a point at (1, 2).

A: The scatterplot has a point at (0, 5), but a point at (1, 3).

B: The scatterplot has points at (0, 5) and (1, 2).

C: The scatterplot has a point at (0, 5), but a point at (1, 3).

D: The scatterplot has a point at (0, 5), but a point at (1, 3).

Hope this helps!

Assume that blood pressure readings are normally distributed with a mean of 117and a standard deviation of 6.4.If 64people are randomly​ selected, find the probability that their mean blood pressure will be less than 119.Round to four decimal places.

Answers

Answer:

0.9938

Step-by-step explanation:

We can find this probability using a test statistic.

The test statistic to use is the z-scores

Mathematically;

z-score = (x-mean)/SD/√n

from the question, x = 119 , mean = 117 , SD = 6.4 and n = 64

Plugging these values in the z-score equation above, we have;

z-score = (119-117)/6.4/√64

z-score = 2/6.4/8

z-score = 2.5

The probability we want to find is;

P(z < 2.5)

we can get this value from the standard normal distribution table

Thus; P(z < 2.5) = 0.99379

Which to four decimal places = 0.9938

Which equation is equivalent to StartRoot x EndRoot + 11 = 15?

Answers

Answer:

D  [tex]\sqrt{x} +11=15[/tex]

Step-by-step explanation:

Edge 2020

For the given expression √x + 11 = 15 the value of x will be equal to 16.


What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression √x + 11 =15. The expression will be solved as below,

√x + 11 =15

√x = 15 - 11

√x = 4

Squaring on both sides of the equation,

x = 4²

x = 16

To know more about an expression follow

https://brainly.com/question/25968875

#SPJ6

Alex has to pay his car insurance twice a year. Each Payment is 312. How much money should Alex budget for his insurance each month?

Answers

Step 1:
312 • 2 = 624

Step 2:
624 divided by 12 months

Answer:
$52 a month

Answer:

$52

Step-by-step explanation:

$52. Since Alex pays for car insurance twice a year, divide the cost of each payment by 6, the number of months in half a year. This will tell you how much money Alex needs to set aside each month to cover his insurance costs.

312÷6=52

Find the area of the shaded triangle below.

Answers

Answer:

A = 12 square units

Step-by-step explanation:

Area of a Triangle = base * height / 2

The triangle might look weird and doesn't look like it has a base, but if you look at the left side you see there is a straight line which means there is a base, so we flip the picture until we see that the flat line on the bottom or the base.

The base is 4 units.

To find the height, we don't need a straight line, we just need to see how the tall the triangle is, to do that you must start from the lowest point and count up to the highest point.

You now get 6 units.

A = bh/2

A = 4*6/2

A = 24/2

A = 12 square units

What is the probability of drawing 3 kings and 2 aces in a 5 card hand of poker?

Answers

Answer:

the probability of getting 3 aces and 2 kings when you draw 5 cards from the deck is 24 / 2598960 = 9.234463016 * 10^-6.

Step-by-step explanation:

the number of ways you can get 3 aces out of 4 aces is c(4,3) = 4.

the number of ways you can get 2 kings out of 4 kings is c(4,2) = 6.

the number of ways you can get 2 kings and 3 aces is 4 * 6 = 24.

the number of ways you can get 5 cards out of a deck of 52 cards is c(52,5) = 2598960.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution is normal only if n30. B. The statement is false. A sampling distribution is normal if either n30 or the population is normal. C. The statement is true. D. The statement is false. A sampling distribution is never normal.

Answers

Answer: Choice B

The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.

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

Explanation:

If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).

Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".

Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.

How many times does 1/4 go into 3/8

Answers

Answer:

3/2

Step-by-step explanation:

3/8 ÷ 1/4

Copy dot flip

3/8 * 4/1

12/8

Divide top and bottom by 4

3/2

One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?

Answers

Answer:

The [tex]L_{ACL}[/tex] of the player is  [tex]L_{ACL} = 56.82 \ mm[/tex]

Step-by-step explanation:

From the question we are told that

       The relationship between the length [tex]L_{ACL}[/tex] to the height is  

            [tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]

       The height of the basketball player  is  [tex]h = 2.13 \ m = 2130 \ mm[/tex]

Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is

          [tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]

         [tex]L_{ACL} = 56.82 \ mm[/tex]

       

solve for x: 5x+3+8x-4=90

Answers

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.

[tex]5x+3+8x-4=90[/tex]

Combine like terms:

[tex]13x - 1 = 90[/tex]

Add 1 to both sides:

[tex]13x = 91[/tex]

Divide both sides by 13:

[tex]x = 7[/tex]

Hope this helped!

Answer:

x = 7

Step-by-step exxplanation:

5x + 3 + 8x - 4 = 90

5x + 8x = 90 - 3 + 4

13x = 91

x = 91/13

x = 7

probe:

5*7 + 3 + 8*7 - 4 = 90

35 + 3 + 56 - 4 = 90

8) The perimeter of a rectangle is 20x2 + xy - 7y2 and one of it's sides is
7x2 - xy. Find the other side.

Answers

Answer:

3x^2 + 3xy/2 - 7xy^2/2

Step-by-step explanation:

So we know the perimeter is 20x^2 + xy - 7y^2,

To find any perimeter you need 2l + 2w = P so,

One of the sides is 7x^2 - xy

First plug in the values,

2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2

Multiply,

14x^2-2xy + 2w = 20x^2 + xy - 7y^2

Subtract,

14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy

2w = 6x^2 + 3xy - 7y^2

w = 3x^2 + 3xy/2 - 7xy^2/2

Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.

Answers

Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.

Step-by-step explanation:

Dante is baking two recipes.

A cookie recipe, that needs 1.5 cups of sugar.

A brownie recipe, that needs 1.25 cups of sugar.

So the total sugar that he needs is:

The sugar for the cookies + the sugar for the brownies:

The equation is:

1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.

Factor the expression completely. 6×3- 4×2 – 16x A. 0 B. 2x(3×2 – 2x – 8) C. 2x(3x + 4)(x – 2) D. 4x(2x + 1)(x – 4) E. 2x(2×2 + 7x – 4) ill give brainliest

Answers

Answer:

The answer is option C

Step-by-step explanation:

6x³ - 4x² - 16x

To factorize the expression first factor out the GCF out

The GCF in the expression is 2x

That's

2x( 3x² - 2x - 8)

Next Factorize the terms in the bracket

To factorize write - 2x as a difference

that's

2x( 3x² + 4x - 6x - 8)

Factor out x from the expression

2x [ x( 3x + 4) - 6x - 8 ]

Next factor out - 2 from the expression

2x [ x ( 3x + 4) - 2( 3x + 4) ]

Factor out 3x + 4 from the expression

We have the final answer as

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

Hope this helps you

Which expression is equivaleny to 0.7 + p + 0.86p?

A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p

Answers

Answer:

None of the above.

1.86p + 0.7

Step-by-step explanation:

Step 1: Write expression

0.7 + p + 0.86p

Step 2: Combine like terms

0.7 + 1.86p

None of those answer choices are correct unless you wrote the problem incorrectly.

what is the least common denominator of 1/8, 2/9, and 3/12

A. 864

B. 108

C. 72

D. 48

Answers

Answer:

c. 72

Step-by-step explanation:

you just have to see what is the lowest number the three denominators: 8, 9, 12, all go into

8 times 9=72 and 12 times 6=72, which makes answer choice C. &2 the least common denominator for the fractions 1/8, 2/9, and 3/12.

Answer:

c.72 he's right love you guys byeee you all welcome

Step-by-step explanation:

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

Answers

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

-----------------------

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

-------------------------

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

Solve the following equation using the square root property.
9x2 + 10 = 5

Answers

Answer: -5/81

Solving Steps:

9x^2+10=5
Simplify- 81x+10=5
Subtract 10 from both sides- 81x +10 -10= 5 -10
Simplify- 81x= -5
Divide both sides by 81- 81x/81= -5/81
Simplify- X= -5/81

Line k has a slope of 2/3. Find the slope of a line parallel to line k.

Answers

Answer:

We have to remember

slope = m

if the slope of line is parellel so it will be the same with other slope

m1= m2

2/3= 2/3

so the answer is 2/3

hope it helps ^°^

Answer:

2/3

Step-by-step explanation:

Parallel lines have the same slopes. Therefore,

[tex]m_{k} =m_{p}[/tex]

The slope of line k ([tex]m_{k}[/tex]) will be equal to the slope of the line parallel to k ([tex]m_{p}[/tex]).

We know that the slope of line k is 2/3.

[tex]m_{k}=\frac{2}{3}[/tex]

Therefore, the slope of the line parallel to line k is also 2/3.

[tex]\frac{2}{3}=m_{p}[/tex]

The slope of a line parallel to line k is 2/3.

Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)

Answers

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?




Sry if this is too much ​

Answers

Answer:

3 weeks

Step-by-step explanation:

6 quarts = 12 pints

12 divided by 3 = 4

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 2 x 6 = 12 pints

12 ÷ 4 = 3

He can have 3 weeks

A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The correct option is  D

Step-by-step explanation:

From the question the question we are told that

    The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.

Generally a confidence interval states to what extent the chances of the true population is within the a given range

 So the 95% confidence interval given in the question as 52.5% and 59.5%  means that the chances of the true population mean being with this given range is 95%

 So given that the the true population mean is within this range then it means that the population mean will be greater than 50%

   So  the statement that best describe and interprets this result is

The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.

Find the value of x.

Answers

Answer:

6x + 6 = 32

6x = 32 - 6

6x = 26

divide both sides by 6

6x/6 = 26/6

6x + 6 = 4.35

9x - 9 = 24

9x = 24 + 9

9x = 33

divide both sides by 9

9x/9 = 24/9

9x + 9 = 2.66

9x + 9 = 2.66

Answer: x=3

Step-by-step explanation:

[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]

For a trip, Eli packed 3 shirts, 3 pairs of pants, and 2 pairs of shoes. How many different outfits can Eli make? A. 6 outfits B. 8 outfits C. 9 outfits D. 18 outfits Please include ALL work!

Answers

Answer:

18 outfits

Step-by-step explanation:

To determine the number of outfits available

3 shirts * 3 pairs of pants * 2 pairs of shoes

3*3*2

18

Which polynomial function has zeros when ? A: B: C: D:

Answers

B BBbBbBBbBbBbBbbBbBbBbbBbBbBBbBbBb

If c o v (x comma space y )space equals space 1260, s subscript x squared equals 1600, and s subscript y squared equals 1225 , then the coefficient of determination is:

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The coefficient  is  [tex]r =0.81[/tex]

Step-by-step explanation:

From the question we are told that

      [tex]cov(x, y )= 1260[/tex]

      [tex]s_x^2 = 1600[/tex]

     [tex]s_y^2 = 1225[/tex]

Generally the coefficient of determination is mathematically represented as

      [tex]r = [ \frac{cov(x,y)}{ \sqrt{s_x^2} * \sqrt{s_y^2} } ]^2[/tex]

substituting values

      [tex]r = [ \frac{ 1260}{ \sqrt{1600} * \sqrt{1225} } ]^2[/tex]

     [tex]r =0.81[/tex]

Factor: 2(4-y)-j(4-y)

Answers

Answer:

(2-j)(4-y)

Step-by-step explanation:

Factoring using grouping,

(2-j)(4-y)

The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.

32 36 29 31 30 35 34 26 30

The 35th percentile of this data set is:________

a. 31
b. 32
c. 31.5
d. 30

Answers

Answer:

d. 30

Step-by-step explanation:

The computation of the 35th percentile of this data set is shown below:

Before that first we have to series the number in ascending number

S. No          Numbers

1                       26

2                      29

3                      30

4                      30

5                      31

6                      32

7                      34

8                      35

9                       36

Now use the formula

Here n = 9

Percentile = 100

[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]

= 3.5th

= 3th + 0.5 (4th - 3th)

= 3th + 0.5 (30 - 30)

= 3th + 0

= 30

Other Questions
Which of the factors below is NOT a cause of online disinhibition?O AnonymityO Lack of nonverbal cuesLack of tone of voiceSmartphones Samanthas college runs on a trimester schedule so she receives a bill 3 times a year for tuition. Each trimester costs $1,450, and Samantha must complete 2 years of college to receive her degree. The average cost for books each trimester is $350. Approximately what will be the total cost for Samantha to get her degree? MADs target capital structure is 60 percent debt and 40 percent equity. The yield to maturity on the companys new debt will be 10 percent. MADs beta is 1.7, the risk free rate is 4% and the required market return is 12%. If the companys tax rate is 30 percent, then which of the projects will be accepted? Make the biggest possible number using the digits below only once 3 , 1 , 3 answer 20. Fill in the blank in the following sentence with either the subjunctive or indicative form of the verb querer. Es obvio que Ral no _________ sacar una buena nota. Find all points having an x- coordinator of 5 whose distance from the point (-1,-3) is 10. (type an ordered pair. Use a comma to separate answers as needed.) Due Diligence refers to diligently monitoring the interview for lies or half-truths the interviewee might include. Select one: True False Please Help! Find the errors in this email. Hello, Robert, Thanks for your email. Hows it going? I have been really busy with the final exams, that's why I couldn't answer you quickly, sorry for that. Now I am freer and I can help you with what you mentioned last time, to be volunteer at a low-income school. Are you having a good time like a teacher? Children behave well? You have managed to awaken my curiosity and that I am interested in participating as an assistant. Anyway, I was also writing to tell you that I were accepted to university! I would like to celebrate with you, would you like to go eat ice cream on Saturday?I would like to see you ad heard your news, I hope you can come! Speak soon. Myle write 1,245 in word form find the perimeter of a square of length of 5cm Net sales$688,500 $450,000 Cost of goods sold 337,364 133,200 Determine the 2016 and 2017 trend percents for net sales using 2016 as the base year. ABCis reflected to form ABC. The vertices of ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of ABC are A(3, 1), B(4, 2), and C(6, 5). Which reflection results in the transformation of ABC to ABC? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=x Evaluate 5(14 - 2) +8 2.? Plz help me, will mark you as brainliest A. 26 B. 34 C. 44 D. 56 After winning power, the Jacobins sought strong leadership to face overwhelming challenges by asking for direction from Englands political leadership. deciding to form the Committee of Public Safety. using the leadership of former supporters of the monarchy. using the leadership of former supporters of the Church. the religion of Persia Label all of the Parts ofSpeech in the sentence.The first World Series wasplayed between Boston andPittsburgh Simplify the expression (x)^3(x^3y)^2 A) x^9y^2 B) -x^6y^2 C) x^5y^2 D) -x^9y^2 Problem 1. (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128101 feet. The ball is started in motion from the equilibrium position with a downward velocity of 2 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.) Because they do so much driving while visiting doctors' offices and hospitals, pharmaceutical sales representatives are often given company cars to drive. When a pharmaceutical company like Merck is preparing to purchase new company cars, sales reps' feedback will be sought on car models and features, but the final decision will be made by higher levels of management. What role(s) do the sales reps play in the buying center? Show that 12.34343434can be expressed in the form p/q