if f'(x) = x^2/1 x^5 and f(1)=3 then f(4)

Answers

Answer 1

Therefore, the value of function f(4) is: f(4) = ln (1025^(1/5) * e^15 / 2) - ln 2^(1/5) ≈ 20.212.

We can solve this problem by integrating the given derivative to obtain the function f(x), and then evaluating f(4).

From the given derivative, we can see that f'(x) can be written as:

f'(x) = x^2 / (1 + x^5)

To find f(x), we integrate both sides of the equation with respect to x:

∫ f'(x) dx = ∫ x^2 / (1 + x^5) dx

Using substitution, let u = 1 + x^5, so that du/dx = 5x^4 and dx = du / (5x^4).

Substituting these into the integral, we get:

f(x) = ∫ f'(x) dx = ∫ x^2 / (1 + x^5) dx

= (1/5) ∫ 1/u du

= (1/5) ln|1 + x^5| + C

where C is the constant of integration.

To determine the value of C, we use the initial condition f(1) = 3. Substituting x = 1 and f(x) = 3 into the above expression for f(x), we get:

3 = (1/5) ln|1 + 1^5| + C

C = 3 - (1/5) ln 2

So the function f(x) is:

f(x) = (1/5) ln|1 + x^5| + 3 - (1/5) ln 2

To find f(4), we substitute x = 4 into the expression for f(x):

f(4) = (1/5) ln|1 + 4^5| + 3 - (1/5) ln 2

= (1/5) ln 1025 + 3 - (1/5) ln 2

= ln (1025^(1/5) * e^15 / 2) - ln 2^(1/5)

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Related Questions

pls subtract the first polynomial from the first one

(42m^(4)+21m^(2))+10) (-8m^(4)-12m^(3)-15m^(2)+9)

Answers

Answer:

34m^4+21m^3+6^2+19

Step-by-step explanation:

since there are no signs in between the bracket you just have to remove it a subtract and add like terms.

Evaluate the following algebraic expression, if (x = 5, y = 3)
x² +9y - 5

Answers

Answer: 47

Step-by-step explanation:

simply substitute the constants with 5 and 3.

(5)^2 + 9(3) - 5 = 47

answer is 49. explanation: substitute 5 in for x and 3 in for y to get
5 squared+9(3)-5. 5 squared is 25. 9(3) is 27. 25+27-3 equals 49

What is the value of X ?

Answers

Answer:

i think x = 4

Step-by-step explanation:

30/25 = 4x-4/20
25(4x-4)=30x20
100x-100=600
100x=700
x=7

Cos^4x csc^2x = csc^2 x sin^2 -2

Answers

Answer:

0

Step-by-step explanation:

i think im not sure the way this question is written doesn't make a lot of sense

X^2+10x+22=13 1. Rewrite the equation by completing the square your equation should look like (x+c)^2 = d or (x-c)^2=d 2. What was the solution to the equation?

Answers

Answer:

(x+5)² = 16

Solution: -1 and -9

Step-by-step explanation:

Given the quadratic equation X^2+10x+22=13

Subtract 22 from both sides

X^2+10x+22-22=13-22

x^2+10x = -9

Complete the square

Add the square of half of coefficient of x to both sides

coefficient of x = 10

half of coefficient of x = 10/2 = 5

square of half of coefficient of x= 5² = 25

Add 25 to both sides

x²+10x + 25 = -9+25

(x+5)² = 16

Hence the required equation is (x+5)² = 16

(x+5)² = 16

square root both sides

√(x+5)² = √16

x+5  = √16

x +5 = ±4

x = +4 - 5 and -4-5

x = -1 and -9

Hence the solution to the equation is -1 and -9

Which of the following describes the transformation from Figure 1
1
to Figure 2
2
?

Answers

5 units to the right and 3 units down

Sin (61) = 24/ x

find x plz show work

Answers

Answer:

x=27.44

Step-by-step explanation:

sin(61)=24/x

x*sin(61)=24

x=24/sin(61)

x=27.44

A line with a slope of 2 passes through the point (2,4). what is its equation in slope-intercept form?​

Answers

Answer:

y = 2x + 0

Step-by-step explanation:

Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.

Answers

Answer:

w = V/lh

Step-by-step explanation:

The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism.

Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.

volume of a rectangular prism,V = lwh

Where,

l = length of the base of the prism

w = width of the base of the prism

h = height of the prism

Rewrite the formula to find w

V = lwh

w = V/lh

That is,

width of the base of the prism = volume of the prism divided by length of the base of the prism multiplied by height of the prism


A rectangle is 2 feet wide and 4 feet long. A second rectangle is created by increasing the length and width of the first by a scale factor of
2.5. What is the area, in square feet, of the second rectangle?

Answers

Answer:

B

Step-by-step explanation:

A bag contains 4 Snickers bars and 1 Twix bar, and the outcome is drawing a Twix bar. Does the phrase that describes the probability of drawing a Twix bar change from Part A?
a: yes, because there are still only two possible outcomes.
b:No, because it is still less likely to have an outcome of drawing a Twix.
c: yes, because it is still less likely to have an outcome of drawing a Twix.
d:No, because there are still only two possible outcomes.

Answers

Answer:

C. Yes,because it is still less likely to have an outcome of drawing a Twix.

Step-by-step explanation:

What are the restrictions for y for the following equation? X=10/5+y

Answers

Answer:

y = -5

Step-by-step explanation:

The restriction for the value of y is the value of the variable that will make the function undefined

The function is undefined when the denominator is zero i.e when 5 + y is zero

5+y = 0

y = 0-5

y = -5

Hence the restrictions is at when y = -5

The school band has a goal of raising $800 for some new uniforms. If they
have raised $512 so far, what percent of their goal have they raised?
help please (;´༎ຶٹ༎ຶ`)

Answers

Answer:

64%

Step-by-step explanation:

512/800=.64

Answer: The exact answer is 62.5 but rounded its 63.

i dont know how to do this I tried so many times and got it wrong please help if you can

Answers

Answer:

14

Step-by-step explanation:

Answer:

I don't see the paper so how can i help u

Step-by-step explanation:

Which is the decimal equivalent of 2/3

A. 0.23
OB. 0.32
O c. 0.3
O
D. 0.6

Answers

The answer is d 0.6.......
The answer would be 0.6

help me pls im desperatew :p

Answers

Answer:

E)

Step-by-step explanation:

Because its gonna be a negative number and while using letters you should not use negative numbers you should use positive numbers or decimals

:) good luck

Which of the following correctly shows the Pythagorean theorem?

Answers

the pythagorean theorem is
a^2 + b^2 = c^2
which is D

Answer:

a²+b²=c²

Step-by-step explanation:

that is the formula for calculating pythagoras

If f(x) = x + 1, and g(x) = 2x,
then
gf(x)) = ?

Answers

Answer:

Step-by-step explanation:

If f(x)=x+1 and g(x)=2x then

g(f(x))=2(x+1)

g(f(x))=2x+2

2x(x+1)
Distribute
2x^2+2x

Mark is having his driveway paved. A diagram of his driveway is shown below. If the company he is using charges $3.50 per square foot, how much will he pay​

Answers

Answer:

He will have to pay $1412.25

Step-by-step explanation:

When you break down the area of the driveway, then add the areas of the different shapes it comes to have an area of 403.5. Multiply the area by the cost per square foot

In triangle Xyz the measure of angle YXZ is 14.5°, and the measure of angle XYZ is 75°. What is the measure of angle XZY in degrees

Answers

Answer:

90.5 degrees

Step-by-step explanation:

The sum of the angle in triangle XYZ is 180 degrees, hence;

m<XYZ + m<YXZ + <XZY = 180

Substitute the given angles

75 + 14.5 + <XZY = 180

89.5+m<XZY = 180

m<XZY = 180 - 89.5

m<XZY = 90.5 degrees

Hence the measure of angle XZY in degrees is 90.5 degrees

Help me Please !!!! You will receive Brainliest!!!

Answers

(-3, -3) and (2, 7).

The solutions to a graphed system of equations are where the two graphs cross each other. So in this case the two equations cross at (-3, -3) and (2, 7), and those points are the solutions to the system of equations.

IsMepawsxD1234567890abcdef​

Answers

IsMepawsxD1234567890abcdef​

4. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
IT'S NOT B

Write a rule for the linear function in the table.



A. f(x) = –3x – 4

B. f(x) = -1/3x - 4

C. f(x) = x – 7

D. f(x) = 3x + 4

Answers

Answer:

A. f(x) = -3x - 4

Step-by-step explanation:

20 = x/4 - 13 help plz thank you

Answers

Answer: x = 132 daw

Step-by-step explanation: believe me

okay so this is what i got very basic yup


ITS FOR A TESTT I NEED THE ANSWER

Answers

Answer:

I believe the answer is $1.52. hope this helps

Solve by factoring: x2 – 9x + 20 = 0

A. x = - 4 and x = - 5

B. x = 4 and x = 5

C. x = 20 and x = - 9

D. x = - 4 and x = 5

Show your work​

Answers

Answer:

Answer

Given equation is:

x

2

−9x+20=0

⇒x

2

−5x−4x+20=0

⇒(x−4)(x−5)=0

⇒x=4andx=5

Answer:
B.x = 4 x=5

Expiation:
x * (x-4)-5(x-4)=0
(x-4)*(x-5)=0
x-4=0
x-5=0
x1= 4 x2= 5

Rose and Carl share a 24-ounce bucket of clay. By the end of the week, Rose has used 3 8 of the bucket, and Carl has used 1 4 of the bucket of clay. How many ounces are left in the bucket?

Answers

Answer:Quantity of Clay left = 9ounce

Step-by-step explanation:

Quantity of clay in the bucket = 24 ounce

Quantity of clay used by rose=3/8 of 24 ounce = 4 x 3 = 9 ounce

Quantity of clay used by Carl= 1/4 of 24 ounce = 6 ounce

Therefore Quantity of Clay left = Quantity of clay in the bucket - (Quantity of clay used by rose+ Quantity of clay used by Carl

24 ounce - ( 9ounce + 6 ounce )

24-15ounce

= 9 ounce

PLEASE HELP I'M SOO CONFUSED AND IT'S DUE TODAY!!!!!!!!!!!!!...I HAVE A LOT OF WORK TO DO TODAY AND I JUST NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answers

Answer:

2 Triangles with the bilateral of the sun to the 2nd power of pie

Step-by-step explanation:

I took the test ;)

What is the value of the 8th term of the sequence 4, 8, 16, 32, ...?

128
2,048
512
1,024

Answers

Answer:

512

Step-by-step explanation:

512
Just keep doubling it and the 8th time it will be 512.

Which pair of angles is congruent?

Answers

Answer:

Option 2

Step-by-step explanation:

Corresponding Angles Theorem

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