Consider the function defined by f(x) lnx/x^4 for x > 0 and its graph y = f(x).
The graph of f has a horizontal tangent at point P. Find the coordinates of P.

Answers

Answer 1

Answer:

[tex]\sqrt[4]{e};\frac1{4e}[/tex]

Step-by-step explanation:

The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.

[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]

Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.

[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]

At this point we Replace the value we found in the equation to find it's y coordinate

[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]


Related Questions

Solve using area model. 53x95

Answers

53x95 = 5035!


hopes this helps! ^^

Answer:

5605

Step-by-step explanation:

50 POINTS NEED HELP
If u = 3 inches, v = 4 inches, w = 7 inches, x = 7 inches, y = 8 inches, and z = 4 inches, what is the area of the object?
A.
52 square inches
B.
53 square inches
C.
56 square inches
D.
54 square inches

Answers

Hey so I have a question do u need to explain?

PLS HELP ME I WILL MARK THE BRAINLIEST

Answers

#1

First the rectangle

L=18mB=7m

Area

18(7)126m^2.

For semicircle

d=7m=>r=3.5m

Area

=πr^2/2=12.25π/2

Total area

126+2(12.25π/2)126+12.25πm^2

#2

r=15fttheta=332°=332×π/180=0.92π

Area:-

r^2\theta15^2(0.92)207ft^2

Number 3. (Look at the Image) Using the formula ū = ||T||(cos o 7 + sin 0 j) Il, find the magnitude and direction of ū= (3,-V3).
Magnitude should be written in simplified radical form.
ů= 11 ull (cosoit sin 63
ů
find magnitude and direction of
ů - <333)

Answers

Answer:

its 54

Step-by-step explanation:

1+2=3 3x5=15 15x2=30 30+16=46 46+8=54

The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?

Answers

Answer: 0.27

Population density of the species in water:

Population density of a species in the water is given by the expression,

       Density =Given in the question,

Number of goldfish in the tank = 12

Volume of the tank = 45 cubic feet

Substitute these values in the expression,

Density =

            = 0.267

            ≈ 0.27 goldfish per cubic feet

      Therefore, density of the tank will be 0.27 goldfish per cubic feet.

Find two integers having a product of positive 27 and a sum of negative 12.

Answers

I know you're looking for an answer but i'm doing a challenge where i have to answer 10 questions by the end of today, I'm sorry! :(

Question
Find the perimeter of the figure to the nearest hundredth.

Answers

Answer:

50.29in

Step-by-step instructions:

First find the semi-circular part:- 1/2×2πr

=1/2×2×22/7×9

=28.29

Find whole perimeter:- 28.29+5+5+12 = 50.29 in

What transformation did Tory perform?

Answers

Answer:

She translated each vertex of Figure 1 seven units to the right.

Step-by-step explanation:

find the value of (0.81÷0.09)+(0.81÷9)

Answers

Answer:

9.09

Step-by-step explanation:

[tex]\frac{0.81}{0.09} + \frac{0.81}{9}[/tex]

= 9 + [tex]\frac{0.81}{9}[/tex]

= 9+ 0.09

= 9.09

I hope this helped!! If so please rate and mark brainliest <3!!

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain? ; 13.5 mg ; 34.6 mg ; 0.2 mg ; 4.6 mg

Answers

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

What is the fromula for he amount of a radioactive substance remaining after t years?

The amount of a radioactive substance remaining after t years is given by the function  

[tex]f(t)=m(0.5)^{t/h}[/tex]............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

[tex]f(10)=50(0.5)^{10/5.3}[/tex]

Therefore  the required equation  f(10) = 13.52 mg .

To learn more about the mass of radioactive substance visit:

https://brainly.com/question/25793075

Answer:

The required equation f(10) = 13.52 mg remains.

We have given that ,

m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60

What is the fromula for he amount of a radioactive substance remaining after t years?

The amount of a radioactive substance remaining after t years is given by the function  

............ (1),

where m = initial mass and h= half-life in years.

Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,

then from equation (1) we get,

Therefore  the required equation  f(10) = 13.52 mg .

To learn more about the mass of radioactive substance visit:

brainly.com/question/25793075

cereal set roster notation

Answers

Answer:

Step-by-step explanation:

Notation for Cereal Set Roster

The roster form is one of the simplest ways to represent the set. The elements of a set are represented in a row and separated by a comma in roster form. For example, the first five positive even numbers are denoted as A = 2, 4, 6, 8, 10.

A = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 is an example of roster notation: A = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.

Hope that helps you understand :)

3. What is the area of the triangle below?
6.0 ft^2
8.6 ft^2
15.0 ft^2
17.2 ft^2

Answers

Answer:

6.0 ft^2

Step-by-step explanation:

hope this helps

3. How many 3 digit all even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Answers

Step-by-step explanation:

Only 3 numbers are possible at units place (2, 4 & 6) as we need even number.

But at tens & hundreds place all 6 are possible

Number of 3 digit even numbers

= 3x6x6 = 108

Answer:

36

Step-by-step explanation:

[tex]Solution:[/tex]

[tex]6\times6=36[/tex]

[tex]such\ as:[/tex]

[tex]11\ \ \ 22\ \ \ 33\ \ \ 44\ \ \ 55\ \ \ 66\\ 12\ \ \ 21\ \ \ 31\ \ \ 41\ \ \ 51\ \ \ 61\\ 13\ \ \ 23\ \ \ 32\ \ \ 42\ \ \ 52\ \ \ 62\\ 14\ \ \ 24\ \ \ 34\ \ \ 43\ \ \ 53\ \ \ 63\\ 15\ \ \ 25\ \ \ 35\ \ \ 45\ \ \ 54\ \ \ 64\\ 16+263646+56\\ 6+6+6+6+6+6\\ =36.[/tex]

I hope this helps you

:)

PLEASE HELP! DUE TODAY! TY!
Use the diagram to find measure of Arc HJ.
Work:
(HJ) =

Answers

Answer: 44 degrees

Step-by-step explanation:

Terrence measured an Italian restaurant and made a scale drawing. The scale of the drawing was 7 centimeters = 2 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.

Answers

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

A robot vacuum cleans a dirty floor using multiple passes. During each pass, 24% of the dirt is removed. If the floor initially has 550 ml of dirt, write a function to find out how much dirt will remail after 10 passes?

please include function and value.​

Answers

The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml

How to solve an exponential function?

Let y represent the amount of dirt on the floor after x passes.

The floor initially has 550 ml of dirt, hence a = 550.

During each pass, 24% of the dirt is removed. Hence b = 100% - 24% = 76% = 0.76

The equation is given by:

y = 550(0.76)ˣ

After 10 passes:

y = 550(0.76)¹⁰ = 35.36 ml

The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml

Find out more on exponential function at: https://brainly.com/question/12940982

In a school there are 1970 pupils. If there are 799 boys, how many more girls are there than boys?

Answers

372.




Explanation:


Subtract 799 from 1970, and you get 1171.



Subtract 799 from 1171 and you get your answer, which is 372.

As per linear equation, there are 372 more girls in school than boys.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant."

Given, there are 1970 pupils.

There are 799 boys in the school.

Therefore, the number of girls in the school is

[tex]= (1970-799)\\= 1171[/tex]

Therefore, the number of girls more than boys in the school is

[tex]= (1171-799)\\= 372[/tex]

In that school , there are 372 more girls than total number of the boys.

Learn more about linear equation here: https://brainly.com/question/11897796

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Solve 7x -4 = 5x + 15 for x.

19/12

11/2

19/2

Answers

Answer:

Third option

Step-by-step explanation:

Given the following question:

[tex]7x-4=5x+15[/tex]

To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.

[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]

Your answer is the third option or "19/2."

Hope this helps.

Please help I will give brainliest.

Answers

You're given the typical position function H=-16t2+Vt+S

You're also given that V=20

So the only thing to figure out is what is S? Well, the frog essentially leaps from the top of the water since he is on a lilly pad so his initial height is 0 since he started from the ground.

Your position polynomial would be H= -16t2+20t+0

When the frog hits the water you would simply set H equal to 0 since he will be at the ground when this happens.

So 0= -16t2+20t → 0=(-16t+20)t

Sowe know that we have the following:

t=0s
16t=20 → t=5/4s



possibly. let me know?

Answer:

t = 0, and t = 4/5

Step-by-step explanation:

1. Write the equation in standard form:

-75t^2+60t=0

2. Solve with the Quadratic formula:

[tex]t_{1,2} = \frac{-60 +- \sqrt{60^2 - 4(-75)}0}{2(-75)} \\\\t_{1,2} = \frac{-60+-60}{2(-75)} \\\\3. Separate the fractions:\\t_{1} = \frac{-60+60}{2(-75)} , t_{2} = \frac{-60-60}{2(-75)} \\\\4. Solve for each:\\t_{1} = \frac{0}{-150} = 0\\t_{2} = \frac{-120}{-150} = 4/5[/tex]

hope this helps!

Can someone help me please

Answers

first add the ratio numbers which is 12

[tex] \frac{2}{12} \times 6000 = 1000[/tex]

then divide 1000 with 175

=5.71

5.71×2.25

=12.85 ruro

Identify C on the following diagram

Answers

Answer: X-axis

Step-by-step explanation: The arrow is pointing to the horizontal line on the on the graph. That horizontal line is the x-axis.

i need help with problem 1

Answers

If this parallelogram was straightened, since the lengths and widths are all the same, it would make a perfect rectangle.

Therefore, angle A and D are the same, and C and B are the same. Therefore,
x = 32°.

If VZ=p–7 and WY=p–21, what is the value of p?

Answers

Using the midline property;

[tex]2wy = vz[/tex]

[tex]2(p - 21) = p - 7[/tex]

[tex]2p - 42 = p - 7[/tex]

[tex]2p - p = - 7 + 42[/tex]

[tex]p = 35[/tex]

Two of which shape can make a circle

Answers

Answer:

2 semi circles put together

Step-by-step explanation:

just cut the circle in half

PLEASE HELP ASAP!!
A population of zombies in Happy Town, USA doubles every week. The number of zombies in Happy Town is currently 75. How many more zombies will there be after an additional 4 weeks? (no commas just numbers)

Answers

Answer:

1200

Step-by-step explanation:

since the first week has 75 doubling it is 150 doubling that is 300 doubling that is 600 doubling that for the final week is 1200.

1200 more zombies will there be after an additional 4 weeks.

What is Sequence?

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members (also known as elements or phrases), just like a set. The length of the series is the number of elements (potentially infinite).

At initial the zombies are= 75

Now, the zombies doubles at every week.

So, After 1 st week the population of zombies are

= 75 x 2

= 150

Then, After 2 nd week the population of zombies are

= 150 x 2

= 300

Then, After 3 rd week the population of zombies are

= 300 x 2

= 600

Then, After 4th week the population of zombies are

= 300 x 2

= 1200

Learn more about Sequence here:

https://brainly.com/question/30262438

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Which ordered pair is a solution of...
x-y = -3
2x+y = 0

a. (-3,0)
b. (-1,2)
c. (0,0)
d. (1,4)

Answers

It’s B
Explanation: because it’s B

Answer:

the answer to your question is B

The parabola y=x^2 is scaled vertically by a factor of 8

Answers

Answer:

2x8=16 so there for y=x^18

Step-by-step explanation:

Suppose that 18 inches of wire costs 72 cents.
At the same rate, how many inches of wire can be bought for 44 cents

Answers

72 divided by 18 is 4
Take 44 and divide it by 4 you get 11 inches worth of wire

Write a formula that shows the dependence of: the length of the side (a) of a cube on the surface area (S) of the cube

Write the formula for the parabola that has x-intercepts (-3-√2,0) and (-3+√2,0), and y-intercept (0,-5)

Answers

Answer:

Let a = side length of a cube

Let S = surface area of a cube

Area of a square = a²

Since a cube has 6 square sides:  S = 6a²

To make a the subject:

S = 6a²

Divide both sides by 6:

[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]

Square root both sides:

[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]

(positive square root only as distance is positive)

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

[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]

[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]

Therefore,

[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]  for some constant a

Given the y-intercept is at (0, -5)

[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]

[tex]\sf \implies a(9-2)=-5[/tex]

[tex]\sf \implies 7a=-5[/tex]

[tex]\sf \implies a=-\dfrac57[/tex]

Substituting found value of a into the equation and simplifying:

[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]

[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]

[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]

There are 30 students in Mrs. Jones class. 20% of the students received an A on the last math test. How many students received an A?

Answers

Answer:

20% of 30

= 20/100 * 30

= 6

hence 6 students recieved A grade

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