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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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
Answer:
A. f(x) = -3x - 4
Step-by-step explanation:
Evaluate the following algebraic expression, if (x = 5, y = 3)
x² +9y - 5
Answer: 47
Step-by-step explanation:
simply substitute the constants with 5 and 3.
(5)^2 + 9(3) - 5 = 47
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
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
Which of the following describes the transformation from Figure 1
1
to Figure 2
2
?
5 units to the right and 3 units down
ITS FOR A TESTT I NEED THE ANSWER
Answer:
I believe the answer is $1.52. hope this helps
Which pair of angles is congruent?
Answer:
Option 2
Step-by-step explanation:
Corresponding Angles Theorem
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?
Answer:
B
Step-by-step explanation:
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༎ຶ`)
Answer:
64%
Step-by-step explanation:
512/800=.64
Answer: The exact answer is 62.5 but rounded its 63.
What are the restrictions for y for the following equation? X=10/5+y
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
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?
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 is the decimal equivalent of 2/3
A. 0.23
OB. 0.32
O c. 0.3
O
D. 0.6
Help me Please !!!! You will receive Brainliest!!!
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.
Answer:
C. Yes,because it is still less likely to have an outcome of drawing a Twix.
Step-by-step explanation:
Cos^4x csc^2x = csc^2 x sin^2 -2
Answer:
0
Step-by-step explanation:
i think im not sure the way this question is written doesn't make a lot of sense
i dont know how to do this I tried so many times and got it wrong please help if you can
Answer:
14
Step-by-step explanation:
Answer:
I don't see the paper so how can i help u
Step-by-step explanation:
20 = x/4 - 13 help plz thank you
Answer: x = 132 daw
Step-by-step explanation: believe me
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?
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
pls subtract the first polynomial from the first one
(42m^(4)+21m^(2))+10) (-8m^(4)-12m^(3)-15m^(2)+9)
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.
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
Answer:
Answer
Given equation is:
x
2
−9x+20=0
⇒x
2
−5x−4x+20=0
⇒(x−4)(x−5)=0
⇒x=4andx=5
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
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
Sin (61) = 24/ x
find x plz show work
Answer:
x=27.44
Step-by-step explanation:
sin(61)=24/x
x*sin(61)=24
x=24/sin(61)
x=27.44
help me pls im desperatew :p
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
If f(x) = x + 1, and g(x) = 2x,
then
gf(x)) = ?
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
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
Answer:
2 Triangles with the bilateral of the sun to the 2nd power of pie
Step-by-step explanation:
I took the test ;)
IsMepawsxD1234567890abcdef
IsMepawsxD1234567890abcdef
What is the value of the 8th term of the sequence 4, 8, 16, 32, ...?
128
2,048
512
1,024
Answer:
512
Step-by-step explanation:
A line with a slope of 2 passes through the point (2,4). what is its equation in slope-intercept form?
Answer:
y = 2x + 0
Step-by-step explanation:
What is the value of X ?
Answer:
i think x = 4
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.
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
Which of the following correctly shows the Pythagorean theorem?
Answer:
a²+b²=c²
Step-by-step explanation:
that is the formula for calculating pythagoras