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3 years ago

What are the coordinates of the inflection point on the graph of y=(x+1)arctanx

1 answer:

5 0

Inflection point is the point where the second derivative of a graph is zero.

y = (x+1)arctan xy' = (x+1)(arctan x)' + (1)arctan xy' = (x+1)/(x^2+1) + arctan xy'' = (x+1)(1/(1+x^2))' + 1/(1+x^2) + 1/(1+x^2)y'' = (x+1)(-1/(1+x^2)^2)(2x)+2/(1+x^2)y'' = ((x+1)(-2x)+1+x^2)/(1+x^2)^2y'' = (-2x^2-2x+2+2x^2)/(1+x^2)^2y'' = (-2x+2)/(1+x^2)^2

Solving for point of inflection: y'' = 00 = (-2x+2)/(1+x^2)^20 = -2x+2x = 1y(1) = (1+1)arctan(1) = 2 * pi/4 = pi/2

Therefore, E(1, pi/2).

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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bixtya [17]

Using an exponential function, it is found that f(5.5) = 19.8.

<h3>What is an exponential function?</h3>

An exponential function is a function in which the growth rate is a percentage, modeled by:

$y = ab^x$

In which:

a is the initial value.

b is the rate of change.

f(3.5) = 25 means that:

$ab^{3.5} = 25$

$a = \frac{25}{b^{3.5}}$

f(8.5) = 14 means that:

$ab^{8.5} = 14$

Hence:

$\frac{25}{b^{3.5}} \times b^{8.5} = 14$

$25b^5 = 14$

$b = \sqrt[5]{\frac{14}{25}}$

$b = 0.89$

$a = \frac{25}{0.89^{3.5}} = 37.59$

Hence, the function is given by:

$y = 37.59(0.89)^x$

Then, when x = 5.5:

$f(5.5) = 37.59(0.89)^{5.5} = 19.8$

More can be learned about exponential functions at brainly.com/question/25537936

7 0

2 years ago

HELP ME OUT PLEASE!!!!

vodka [1.7K]

Answer:

(3,-4)

Step-by-step explanation:

There is a graphing calculator called desmos that can help you answer questions like this, but, if you don't want to use that, you can just make a graph and imagine the transformation. Remember, when you reflect something over an axis, it is like you are folding the graph along the axis and your new point will be on the other side.

5 0

2 years ago

Read 2 more answers

ILL GIVE BRAINLIEST... HURRY PLZ

Alexeev081 [22]

12 Pairs

4 pairs = 8

2 pairs = 4

8 + 4 = 12

If you need total socks, there's 24 total

7 0

3 years ago

Will give 50 points!!! ASAP!!!!!!!!!!!

Nostrana [21]

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Since there are a total of 4 colors, and there are 5 of each colors, the total marbles in the bad would be;

5 x 4 = 20

If a color is selected at random the probability would be

$\frac{part}{whole}$

our part is 5

our whole is 20

so the probability would be;

$\frac{5}{20}$ or $\frac{1}{4}$ when reduced

Hope this helps!

5 0

2 years ago

Read 2 more answers

You have a total of $1760 to invest. Account A pays 7% annual interest and account B pays 4% annual interest. How much should

posledela

Answer:

You should invest $820 in account A and $940 in account B

Step-by-step explanation:

* Lets use the system of linear equations to solve the problem

- Simple Interest Equation I = Prt , Where:

# P = Invested Amount

# I = Interest Amount

# r = Rate of Interest per year in decimal; r = R/100

# t = Time Period involved in months or years

* Lets solve the problem

- The total money invested is $1760

- Account A pays 7% annual interest

- Account B pays 4% annual interest

- Let A represent the amount of money invested in the account A

- Let B represent the amount of money invested in the account B

- You would like to earn $ 95 at the end of one year

∴ The interest from both accounts at the end of one year is $95

- Lets write the equations

# Account A :

∵ Account A has $A invested

∴ P = $A

∵ Account A pays 7% annual interest

∴ r = 7/100 = 0.07

∵ t = 1 year

∵ I = Prt

∴ I = A(0.07)(1) = 0.07A

# Account B :

∵ Account B has $B invested

∴ P = $B

∵ Account A pays 4% annual interest

∴ r = 4/100 = 0.04

∵ t = 1 year

∵ I = Prt

∴ I = B(0.04)(1) = 0.04B

- The total amount of interest from both accounts at the end of one

year is $95

∴ I from A + I from B = 95

∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100

∴ 7A + 4B = 9500 ⇒ (1)

- The total money to invest in both accounts is $1760

∵ Account A has $A invested

∵ Account B has $B invested

∴ A + B = 1760 ⇒ (2)

* Lets solve the system of equations to find the amount of money

invested in each account

- Multiply equation (2) by -4 to eliminate B

∵ A + B = 1760 ⇒ × -4

∴ -4A - 4B = -7040 ⇒ (3)

- Add equation (1) and (3)

∵ 7A + 4B = 9500 ⇒ (1)

∵ -4A - 4B = -7040 ⇒ (3)

∴ 7A - 4A = 9500 - 7040

∴ 3A = 2460 ⇒ divide both side by 3

∴ A = 820

- Substitute the value of A in equation (1) or (2)

∵ A + B = 1760 ⇒ (2)

∴ 820 + B = 1760 ⇒ subtract 820 from both sides

∴ B = 940

- From all above

* You should invest $820 in account A and $940 in account B

6 0

3 years ago