(a)The antiderivative of f(x) = 1/x with C=0 is ln|x|.
(b)The antiderivative of g(x) = 5/x with C=0 is 5 ln|x|.
(c)The antiderivative of h(x) = 4 - 3/x with C=0 is 4x - 3 ln|x|.
What are the antiderivatives, with C=0, of the functions: a. f(x) = 1/x^bb. g(x) = 5/x^c c. h(x) = 4 - 3/x?a. To find the antiderivative of f(x) = 1/x^b, we use the power rule of integration. The power rule states that if f(x) = x^n, then the antiderivative of f(x) is (1/(n+1))x^(n+1) + C. Applying this rule, we get:
∫(1/x^b) dx = x^(-b+1)/(-b+1) + C
Simplifying the above expression, we get:
∫(1/x^b) dx = (-1/(b-1))x^(1-b) + C
Therefore, the antiderivative of f(x) = 1/x^b with C=0 is (-1/(b-1))x^(1-b).
b. To find the antiderivative of g(x) = 5/x^c, we again use the power rule of integration. Applying this rule, we get:
∫(5/x^c) dx = 5/(1-c)x^(1-c) + C
Simplifying the above expression, we get:
∫(5/x^c) dx = (5/(c-1))x^(1-c) + C
Therefore, the antiderivative of g(x) = 5/x^c with C=0 is (5/(c-1))x^(1-c).
c. To find the antiderivative of h(x) = 4 - 3/x, we split the integral into two parts and use the power rule of integration for the second part. Applying the power rule, we get:
∫(4 - 3/x) dx = 4x - 3 ln|x| + C
Therefore, the antiderivative of h(x) = 4 - 3/x with C=0 is 4x - 3 ln|x|.
Learn more about antiderivative
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in a 5th grade class, 9/10nof the students like going to the movies. Of those students 4/5 like popcorn. Of the students that like popcorn, 2/3 of them also like candy. what fraction of the students class like popcorn at the movies? What faction lf the students in class like popcorn and candy at the movies?
Answer:
48%
Step-by-step explanation:
9/10 of the students like going to the movies.
4/5 of 9/10 is 72/100 or 72%.
2/3 of 72 is 48.
So, 48% of the students like popcorn, candy, and going to the movies.
Having trouble solving this
opt1.
667/1000
=66.7
hope u understand
Answer:
more like dividing the up ones with bottom ones
EX 717/1000=0.717
#every one when im in public be like
Answer:
lol
Step-by-step explanation:
can someone properly explain the multiplier method I need help for revision
Answer:
yes
Step-by-step explanation:
I'm ready to help anyone in maths
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
[tex] = 2\pi \: r \: h \\ 2 \times \pi \times 4 \times 9 \\ = 226 .19 {cm}^{2} [/tex]
Can I have the brainliest please?
Answer:
9 X 4 = 36
Step-by-step explanation:
not really the answer sorry pls dont be mad
How might a change in the environment affect plants differently than it would animals?
Answer:
Some plants need certain things in their environment, so if their environment changes it could make the plants not grow. Animals would most likely either move to a different area or would get used to the change.
Find the area of the figure below. 7 cm
Answer:
Area tells us the size of a shape or figure. It tells us the size ... The rectangle above has an area of 15 square units. The area of a ... Area = 7 cm x 6 cm = 42 cm2.
Step-by-step explanation:
plz help, just look at the picture
Answer:
<2, <3, <4
Step-by-step explanation:
You have parallel lines cut by a transversal, so alternate interior angles are congruent. Also, alternate exterior angles are congruent. Corresponding angles are congruent.
Vertical angles are always congruent.
I'll write each congruent angle and the reason.
<2, vertical
<3, corresponding
<4, alternate exterior angle
Each earbud is 4/7 of an inch long. If you put 8 earbuds end to end, how long would they be from beginning to end?
Answer:
4 4/7
Step-by-step explanation:
4/7x8/1
4x8/7x1
32/7
4 4/7
Answer:
The answer is 4 4/7.
Step-by-step explanation:
4/7 x 8 = 32/7
32/7 = 4 4/7
does anyone know how to do this ?
9514 1404 393
Answer:
y = 21
Step-by-step explanation:
In straightforward fashion, we can find the midpoints of the two segments, and set the distance between them equal to 10.
M = midpoint of AB
M = (A+B)/2 = ((-1, 0) +(-3, 6))/2 = (-4, 6)/2 = (-2, 3)
N = midpoint of CD
N = (C+D)/2 = ((3, 1) +(5, y))/2 = (8, 1+y)/2 = (4, (1+y)/2)
Then the distance MN is given by the distance formula.
|N-M| = 10 = √((4 -(-2))² +((1+y)/2 -3)²) . . . . . distance formula*
100 = 36 +((1+y)/2 -3)² . . . . . square both sides
64 = ((1 +y)/2 -3)² . . . . . . . . . subtract 36
8 = (1 +y)/2 -3 . . . . . . . . . . . . (positive) square root
11 = 1+y/2 . . . . . . . . add 3
22 = 1+y . . . . . . . . . multiply by 2
21 = y . . . . . . . . . . . subtract 1
_____
* The distance formula is an application of the Pythagorean theorem. Basically, the differences of x- and y-coordinates are taken to be the legs of a right triangle. They length of the hypotenuse is the distance between the two points.
d² = (x2 -x1)² +(y2 -y1)² . . . . . . . from the Pythagorean theorem
d = √((x2 -x1)² +(y2 -y1)²) . . . . . the usual distance formula
URGENT!!! PLS GIVING BRAINLIEST!
A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 3 pounds of chocolate chps, the total cost is $16. For 6 pounds of walnuts
and 5 pounds of chocolate chips, the total cost is $34. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answer:
1 lb of chips cost $3.50
1 lb of walnuts cost $2.75
Step-by-step explanation:
c = $ chips
w = $ walnuts
System of Equations:
2w + 3c = 16
6w + 5c = 34
I multiplied the first equation by -3 to eliminate the 'w' terms to get
c = 3.5
I substituted 3.5 for 'c' to get 2.75 for 'w'
Cyril, the priest, created the English alphabet.
True
False
Answer:
its false
Step-by-step explanation:
.................,,,,,,,,,,,................
When I...
double my number ...
subtract six ...
take the square root and
add four
I get eight.
My number is:
Answer:
11
Step-by-step explanation:
Work backwards and reverse the operations to find the original number.
Reverse the operations for add four: 8 - 4 = 4
Reverse the operations for take the square root: 4² = 16
Reverse the operations for subtract six: 16 + 6 = 22
Reverse the operations for double the number: 22 ÷ 2 = 11
Jocelyn Smith has been injured by a local driver who was not paying attention to the road while he was texting on his cellphone. Jocelyn Smith decides to sue the driver. She believes that her own pain and suffering and other damages are worth more than $100,000. In which Florida court should she file her legal action against the driver?
Answer: florida circuit court
Step-by-step explanation:
Based on the information given, the Florida court that she should file her legal action against the driver is the Florida circuit court.
The Florida Circuit Court is a state court where cases such as civil cases, felony, juvenile cases, family law and probate issues are heard. Therefore, based on the scenario given, the Florida circuit court will be applicable here.
Calculate the result of operations, round the result to the tenth
5/2 + √2
Answer:
3.91421356237
nearest tenth
3.9
Step-by-step explanation:
Help please this is due in 10 minutes pleaseee I will mark you brainliest
QUESTIONS ARE DOWN BELOW!!! ALL HELP WILL BE APPRECIATED AND I WILL TRY TO MARK BRAINLIEST (IF I CAN)
Answer: 90 and 110
Step-by-step explanation:
Find the measure of the indicated angle to the nearest degree
Answer:
61.92°
Step-by-step explanation:
Sine Inverse of (75/85)
=61.92°
porque el factor común está relacionado con la propiedad distributiva
Answer:
El factor común se relaciona con la propiedad distributiva, ya que el factor común corresponde a la agrupación de expresiones comunes en una operación, de manera que éstas lleguen a ser simplificadas
What is StartFraction 4 Over 5 EndFraction divided by one-third A fraction bar. The top bar is labeled 1. 3 bars underneath the bar are labeled one-third. 5 bars underneath the 4 bars are labeled one-fifth. 15 bars underneath the 5 bars are labeled StartFraction 1 Over 15 EndFraction. The quotient is 2 and
HURRY PLEASE IM TIMED
Answer:
its 2/5
Step-by-step explanation:
What is Start Fraction 4 Over 5 End Fraction divided by one-third A fraction bar you may ask? The top bar is labeled 1.3 bars underneath the bars are labeled one-third. So, 5 bars underneath the 4 bars are labeled one-fifth. And 15 bars underneath the 5 bars are labeled Start Fraction 1 Over 15 End Fraction. The quotient is ??? well it would be 2 and all you have to do is figure it out so the answer is below.
Well, the correct fraction would be 2 and 2/5 because this is what the model shows.
x²+8x-84=0
Formúla General
Answer:
[tex]x_{1} =-14\\\\x_{2} =6[/tex]
Step-by-step explanation:
[tex]x^{2} +8x-84=0\\\\x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=1; \: \: b=8; \: \: c=-84\\\\x=\dfrac{-8 \pm \sqrt{8^{2}-4 \cdot 1 \cdot (-84) } }{2 \cdot 1}=\dfrac{-8 \pm \sqrt{400 } }{2}=\dfrac{-8 \pm20}{2} =-4 \pm 10\\\\x_{1} =-14\\\\x_{2} =6[/tex]
Find the mean,median,mode, and range:5,2,5,2
Answer:
Mean = 3.5
Median = 3.5
Mode = 5, 2
Step-by-step explanation:
Hope that helps!
Mean: To find the mean, simply add the numbers together and divide by the amount of numbers in the set:
Mean: (5 + 2 + 5 + 2)/4
= (14)/4
= 3.5
Mean = 3.5
Median: To find the median, simply order from least to greatest, and find the middle number in the set. That is your median. In the case of an even amount of numbers in the set, find the mean with the two median numbers (as in this case):
Median: (2 + 5)/2
= 7/2
= 3.5
Median: 3.5
Mode: The Mode is the number that shows up the most frequently. As both given numbers show up the same amount of times (twice), there is no mode.
Mode: None.
Range: The Range is found by subtracting the greatest number with the least number:
5 - 2 = 3
Range: 3
Last year, 576 students attended a local middle school. This year, 721 students attended the school. What is the approximate percent increase in the number of students at the school?
x^5 ⋅ x^9
can someone help
Answer:
x^14
Step-by-step explanation:
[tex]x^{5}*x^{9}=x^{(5+9)}=x^{14}[/tex]
Answer:
x^14
Step-by-step explanation:
Use the power rule a^m a^n=a^m+n
x^5+9
add 5 and 9
x^14
For the given expression, use the Commutative Property of Addition to enter an equivalent expression.
x + 19 =
Answer:
x+19=19+x
Step-by-step explanation:
6.6=w-1.2 What is w??
Answer: 7.8
Step-by-step explanation:
1.2+6.6=7.8 so,
7.8-1.2=6.6
Type the expression that results from the following series of steps:
Start with
y
, subtract 7, divide by 3, then add 6.
John is measuring a piece of glass to fit in a triangular frame. he can only remember two sides of the brain, which are 6 cm and 11cm. Between what two numbers must the third side of the frame fall?
Answer:
yup right :)
Step-by-step explanation:
Answer: Your Correct
Step-by-step explanation:
radius:
diameter:32 meters
circumference:
area:
Given diameter is 32, radius would be 16 bc radius is always half of diameter, and circumference would be 2(pi)*radius, which would be 100.5309649.... and area is (pi)*radius^2 which would be 804.2477193........
2x - 5[4 + 3 (x + 2)] = 9
Step-by-step explanation:
i hope you will get the answer
Step-by-step explanation:
2x - 5 ( 4 + 3 ( x + 2 ) ) = 92x - 5 ( 4 + 3x + 6 ) = 92x - 5 ( 3x + 10 ) = 92x - 15x - 50 = 9-13x - 50 = 9-50 - 9 = 13x-59/13 = xMARK ME AS BRAINLIST