Answers
Answer:
a) 6x²/2x³-4
b) [tex]2ln (2x^3-4)+ C[/tex]
Step-by-step explanation:
a) Given the ln(2x³-4). We will use the chain rule in differentiating the function
If y = ln(2x³-4);
u = 2x³-4; du/dx = 3(2)x³⁻¹
du/dx = 6x²
y = ln u; dy/du = 1/u
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/u * 6x²
dy/dx = 1/2x³-4 * 6x²
dy/dx = 6x²/2x³-4
Hence, the derivative of the given function is 6x²/2x³-4
b) Given an integral function [tex]\int\limits {\frac{12x^2}{2x^3-4} } \, dx[/tex], the integral problem can be solved using integration by substitution method as shown below;
From the question, let y = 2x³-4... 1, dy/dx = 6x²
dx = dy/6x² ... 2
Substituting equation 1 and 2 into the question given;
[tex]\int\limits {\frac{12x^2}{y} } \,\frac{dy}{6x^2} \\\\= \int\limits {\frac{2dy}{y} } \\\\= 2 \int\limits {\frac{dy}{y} }\\\\= 2lny + C\\substituting\ y = 2x^3-4\ into\ the \ resulting\ function\\\\= 2ln (2x^3-4)+ C[/tex]
Related Questions
What is the arithmetic mean of the following numbers? 6 , 4 , 1 , 9 , 3 , 8 , 3 , 5 , 10
Answers
Answer:
5.4Step-by-step explanation
First find the mean of the numbers which you do by adding the numbers all together and then you will get 49.Then you have to divide 49 by the amount of numbers there are so there are 9 numbers so you do 49 ÷ 9 and you will get 5.4.Answer = 5.4The arithmetic mean of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 5.4
What is arithmetic mean?The arithmetic mean is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
According to the given question we have
A data set 6, 4, 1, 9, 3, 8, 3, 5, 10
The total numbers in the given data set is 9
Therefore, the arithmetic mean of the given data set is given by
Arithmetic mean = [tex]\frac{6 +4+1+9+3+8+3+5+10}{9}[/tex]
⇒ Arithmetic mean = [tex]\frac{49}{9}[/tex]
⇒ Arithmetic mean = 5.4
Hence, the arithmetic mean of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 5.4
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Jackson is attending a lacrosse game that is halfway through the first quarter.
4) What fractional part of the game is left?
5) If 7 minutes of playing time have past, how many total minutes of playin
time are there in the game?
6) How many minutes of playing time are left in the game?
(I'll also need help on the shading for the fraction picture)
Answers
Answer:
4) 1/8
5) 56
6) 49
First shaded boxes = 4/7
Second shaded boxes = 1 out of 8 boxes are shaded = 1/8
Step-by-step explanation:
1/2x1/4=1/8
7X8=56
59-7=49
First shaded boxes = 4 out of 7 are shaded = 4/7
Second shaded boxes = 1 out of 8 boxes are shaded = 1/8
The fractional part of the game is left [tex]\frac{7}{8}[/tex] , total minutes of playing time 56 mins and playing time are left in the game is 49 mins .
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
According to the question
Jackson is attending a lacrosse game that is halfway through the first quarter
i.e, Game played = [tex]\frac{1}{2} *\frac{1}{4}[/tex]
Game played = [tex]\frac{1}{8}[/tex]
a) fractional part of the game is left
Game left = 1 - [tex]\frac{1}{8}[/tex] (treated complete game as 1 )
= [tex]\frac{7}{8}[/tex]
b) If 7 minutes of playing time have past,
i.e [tex]\frac{1}{8}[/tex] part of game is completed in 7 mins
therefore,
1 whole will complete in 7*8 = 56 mins
c) Minutes of playing time are left in the game
As,
total time to complete the game - game played time
= 56 - 7
= 49 mins
as in the fraction of shading question
a) [tex]\frac{4}{7 } is shaded[/tex]
b) [tex]\frac{1}{8}[/tex] is shaded
Hence , the fractional part of the game is left [tex]\frac{7}{8}[/tex] , total minutes of playing time 56 mins and playing time are left in the game is 49 mins .
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according to a recent study the probability that a randomly selected individual wears glasses is 0.23. suppose you ask a random sample of 18 individuals if they wear glasses and count the total. how many individuals out of 18 would you expect to wear glasses, on average?
Answers
Answer:
4
Step-by-step explanation: 18x.23 = 4.14
Answer:
4
Step-by-step explanation:
What is the remainder in the synthetic division problem below?
O A. 5
O B. 9
O O. 3
O D. 7
Answers
Answer:
The answer is option D.
I hope it's what you require.
Answer:
D) 7
Step-by-step explanation:
1 / 4 6 -3
4 10
4 10 7
Step 1: Carry down the first number 4 as it is
Step 2: Multiply 4 by 1 [4 * 1 = 4] and write down this 4 under the next number 6 and then add. 6 + 4 = 10
Step 3: Multiply 10 by 1 [10 * 1 = 10] and write down this 10 under the next number -3 and then add. -3 + 10 = 7
And now 7 is the remainder
Determine if the statement is always, sometimes or never true. The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle. always
Answers
Answer:
I believe it is never
Step-by-step explanation:
Sorry if I'm wrong ...
May someone please explain what a central tendency is I do not understand what it exactly means
Answers
median, the mode and the range.
2) If Mike fell from (0.35) to (20, 0), determine the slope of his fall.
Answers
Answer:
-7/4.
Step-by-step explanation:
I'll take it to mean (0, 35)
The slope = (y2-y1)/(x2-x1)
= (0-35)/ (20-0)
= -35/20
= -7/4.
a hummingbird flies forward 149 meters backward 57 meters and forward 23 meters write an equation that can be used to find how far forward the hummingbird flew.
Please help due today
Answers
Answer:
X=149-57+23
Step-by-step explanation:
X=149-57+23
Answer:
distance = 149 -57 +23
(-) is backward
(+) is forward
A school administrator bought 6 desk sets. Each set consists of one table and one chair. He paid $48.50 for each chair. If he paid a total of $663 for the 6 sets, the cost of each table is
$
.
Answers
Answer:
c
Step-by-step explanation:
Answer:
$62
Step-by-step explanation:
[tex]if \sqrt{p ^{2} } +1= \frac{5}{4} .Find the postive value of p[/tex]
Answers
Answer:
Positive value of p = 1/2
Step-by-step explanation:
Given:
[tex]\sqrt{p^2}+1=\frac{5}{4}[/tex]
Find:
Positive value of p
Computation:
[tex]\sqrt{p^2}+1=\frac{5}{4}\\\\\sqrt{p^2}=\frac{5}{4}-1\\\\\sqrt{p^2}=\frac{5-4}{4}\\\\\sqrt{p^2}=\frac{1}{4}\\\\p = \frac{1}{2}[/tex]
Positive value of p = 1/2
can somewon help me i eally need help
Answers
Answer: The answer should be 1/2
Step-by-step explanation:
Answer:
i say 1/6 but pleaseeee dont go off my answer im not 100%
Step-by-step explanation:
Write an equation and solve it to answer each question:
A pile of 55 coins, consisting of nickels and dimes, is worth $3.90. find the number of each.
You have to Answer like this:
If there are x nickels, then the equation is______
The number of nickels is_____
the number of dimes is______
Answers
Answer:
there are 25 nickels and 30 dimes
Write the other side of this equation so it's true for no values of x;
1/2(6x-10)-x =
Answers
Answer:
1/2(6x-10)-x = 2x +3
Step-by-step explanation:
1/2(6x-10)-x =
Distribute
3x -5 -x
2x -5
We need to other side to be of the form 2x - constant where the constant is not equal to 5
2x-5 = 2x+3
Subtract 2x from each side
-5 =3
This is not true so there is no solution
this one question so plz don't think it is two
Answers
It's point A. 4 vertical units away from point M.
Answer: Point A
Step-by-step explanation:
Point M has the same x value as point A and point A is 4 units below it.
Hope it helps <3
30 points high school geometry question
Answers
Answer:
x = 5
Step-by-step explanation:
9/15 = 3/x
x = 5
X would equal 5
I did this test in high school. smh
The baseball diamond at a playground is a square with sides that measure 60 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth. A baseball diamond represented by a square oriented so that the diagonal of the square running from home plate to 2nd base is vertical. 7,200 feet 60 feet 84.9 feet 120 feet
Answers
Answer:
84.853 ft
Step-by-step explanation:
A^2 + B^2 = C^2 | 60^2 + 60^2 = 84.853
Answer: 84.853 ft
Step-by-step explanation:
Consider points a, b, and c in the graph. Which point is the global maximum? Question 6 options: A) b B) c C) None of these D)
Answers
Answer:
point a is the maximum
Step-by-step explanation:I took the test
Given: f(x) = xand g(x) = x +1, find g[f(-2)].
1
5
-3
Answers
Answer:
-1
Step-by-step explanation:
f(x) = x
g(x) = x +1,
g[f(-2)].
First find f(-2) = -2
Then substitute into g(x)
g(-2) = -2+1
=-1
Hi. Please i need help with this question.
Please show workings.
Answers
Answer:
A =176 m^2
Step-by-step explanation:
The area of the floor is length times width
A = lw
A = 16* 11
A =176 m^2
Answer:
176 cm^2
Step-by-step explanation:
Given:
length=16m
width=11m
height=9m
We don't use the height in calculating since we are looking for the area of a rectangular carpet.
Required:
a=?
Formula:
a=l*w
whereas l is length and w is width
Solution:
a=l*w
a=16cm*11cm
a=176cm^2
A shortcut to find the answer:
16*11=1,1+6,6=176
Hope this helps ;) ❤❤❤
Find the output. y. when the input. . is -5.
Answers
Answer:
The answer is 7.
Step-by-step explanation:
You would find -5 on the graph and go up until you see the line, and where it ends, is your answer or output. 7.
Answer:
(-5, 7)
Step-by-step explanation:
Draw a vertical line through x = -5 and determine the point at which this line intersects the graph. You'll find that that point is (-5, 7).
which expression below would not be equivalent to 12n+ 6
1) 3(4n+2)
2) 2(6n+3)
3) 6(2n+1
4)12 (n +4)
Answers
Answer:
4)12(n+4)
=12n+48
Step-by-step explanation:
Answer:
4) 12(n + 4) = 12n + 48
Step-by-step explanation:
Estimate the solution to the system of equations.
Answers
Answer:
Find it in the explanation
Step-by-step explanation:
Equate the two solutions.
2x+3y=6 is exactly half of -4x+3y=12, so multiply 2x+3y=6 by 2.
Now we get
4x+6y=12 and
-4x+3y=12
Here what operation you use is your choice, but because I see a positive 4x and a negative 4x down below, I'm gonna use addition to cancel out the x.
Adding these two equations together, I get:
9y=24
y=24/9
in fraction form y= 2 and 2 thirds.
Plug that in any of the equations and solve for the value of x, which will be -1
Therefore, the coordinates are (-1, 2 and 2/3)
Answer:
The answer is x= -1/2 and y= 7/3 or 2whole 1/3.
hope it helps..
Select the correct answer from the drop-down menu. Emily is a geometry teacher. She asks each student to bring in a cutout of a parallelogram. She tells them that one angle must measure 50° and the length of one side must be 10 centimeters. Emily also states that the parallelogram must not be a rhombus, rectangle, or square. Using this information, each student can prepare parallelogram(s).
Answers
Answer:
50
Step-by-step explanation:
this is confusing and I'm a straight A student in highschool.I'm a junior to be exact
Answer:
the correct answer is that the students infinitely many parallelograms
An insurance company is considering implementing a plan based on mileage. The current plan, Plan A, charges a flat rate of $235.90 per month. Plan B charges a flat rate of $160.30 per month plus an additional $0.07 per mile driven the previous month. Using the inequality below, find the number of miles, x, where the cost of Plan B is less than the cost of Plan A. $160.30 + $0.07x < $235.90 A. x < 529 B. x < 5,660 C. x < 1,080 D. x < 2,160
Answers
Answer:
plan A
Step-by-step explanation:
Why Taraaaaaaa >:C Can somebody please help me?
Answers
Answer:
4 hours
Step-by-step explanation:
3/5 of 8 hours
3/5 * 8 = 4.8 hours
Then she lost 1/6 of the 4.8 hours
4.8 * 1/6
.8
4.8 - .8 = 4
She got 4 hours of sleep
The desk is 1/2 as wide as it is long. If the desk is D meters long, how wide is the desk?
Answers
Answer:
1/2D meters
Step-by-step explanation:
I hope this helps
Answer:
(1/2)D
Step-by-step explanation:
The width is half the length, so is ...
(1/2)D or D/2 . . . meters wide
- (1 /-11 )( 77+1100)
Answers
-(1/-11)(77+1100)=107
Answer:
107
Step-by-step explanation:
-(1/-11)(77+1100)
1/11(1177)
=107
30. Three apples plus twice as many pears add up to one-half the number of grapes in a fruit basket. How many grapes are
in the basket?
(A) 8
(B) 18
c.28
d.38
Answers
Answer:
3 + 6 = 1/2(#grapes)
3 + 6 = 9
9 = 1/2(#grapes)
2(9) = 1(#grapes)
18 = # of grapes
Step-by-step explanation:
Hi. Please i need help with these questions ; 1. I spent 7/32 of my income housing , 1/4 of it on food and 1/8 of it on transport . What fraction of my income do i have left a . 7/32 b 9/32 c. 13/32 d. 15/32 e. 19/32 workings please
Answers
Answer:
C: 13/32
Step-by-step explanation:
Change 1/4 and 1/8 into 4/32 and 8/32 and add them up with the 7/32 and then subtract the top and you have your answer
Answer:
13/32 left over.
Step-by-step explanation:
First, you would want to convert the 1/4 and 1/8 to ?/32. You would get: 7/32 on housing, 8/32 on food, and 4/32 on transportation.
To get those numbers this is what you do: 1/4 was spent on food. 32 divided by 4 is 8. So that would be 8/32. I hope you understand, because I'm not that good at explaining!
Then you add those up: 7/32 + 8/32 + 4/32. You would get 19/32 as your total, which means you have 13/32 left over. I hope this helped!
Which equation could generate the curve in the graph below?
Answers
Answer:
The answer is option 1.
Step-by-step explanation:
In order to find the equation, you have to apply Discriminant Law, D = b² - 4ac. When D < 0, the equation has no real roots (no x-intercept). When D = 0, it has 2 and equal roots (1 x-intercept). When D > 0, it has 2 distinct roots (2 x-intercept).
Option 1,
[tex]y = 3 {x}^{2} - 2x + 1[/tex]
[tex]D = {( - 2)}^{2} - 4(3)(1)[/tex]
[tex]D = - 8[/tex]
[tex]D < 0[/tex]
Option 2,
[tex]y = 3 {x}^{2} - 6x + 3[/tex]
[tex]D = {( - 6)}^{2} - 4(3)(3)[/tex]
[tex]D = 0[/tex]
Option 3,
[tex]y = 3 {x}^{2} - 7x + 1[/tex]
[tex]D = {( - 7)}^{2} - 4(3)(1)[/tex]
[tex]D = 37[/tex]
[tex]D > 0[/tex]
Option 4,
[tex]y = 3 {x}^{2} - 4x - 2[/tex]
[tex]D = {( - 4)}^{2} - 4(3)( - 2)[/tex]
[tex]D = 40[/tex]
[tex]D > 0[/tex]
As you look at the graph, the curve does not meet x-axis so the discriminant must be less than 0.
The given curve in the graph is generated by the equation y =3x² - 2x +1. The correct option is A.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
In order to find the equation, you have to apply Discriminant Law, D = b² - 4ac. When D < 0, the equation has no real roots (no x-intercept). When D = 0, it has 2 and equal roots (1 x-intercept). When D > 0, it has 2 distinct roots (2 x-intercepts).
Option 1,
y =3x² - 2x +1
D = b² - 4ac
D = ( -2 )² - ( 4 x 3 x 1 )
D = 4 - 12
D = -6
D < 0
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