Answers
Step-by-step explanation:
According to the quotient rule of differentiation, if [tex]y(x) = u(x)/v(x),[/tex] then its derivative is given by
[tex]\dfrac{dy}{dx} = \dfrac{v\dfrac{du}{dx} - u\dfrac{dv}{dx}}{v^2}\:\:\:\:\:\:\:\:\:(1)[/tex]
We can see that
[tex]u(x) = \ln (4x^2 + 1)[/tex]
[tex]\dfrac{du}{dx} = \dfrac{8x}{4x^2 + 1}[/tex]
[tex]v(x) = 2x - 3[/tex]
[tex]\dfrac{dv}{dx} = 2[/tex]
Plugging the above expressions into Eqn(1), we find that the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{8x(2x - 3)}{(4x^2 + 1)} - 2\ln (4x^2 + 1)}{(2x - 3)^2}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{8x}{(4x^2 + 1)(2x - 3)} - \dfrac{2\ln (4x^2 + 1)}{(2x - 3)^2}[/tex]
Related Questions
Kendra has already prepared 15 kilograms of dough and will continue preparing 1 kilogram
of dough every hour. How many hours did Kendra work if she prepared 23 kilograms of
dough?
Answers
hour 0 she has 15
hour 1 she has 16
hour 2 she has 17
hour 3 she has 18
hour 4 she has 19
hour 5 she has 20
hour 6 she has 21
hour 7 she has 22
hour 8 she has 23
6. Find the areas of the rectangles with the following side lengths.
C.
a. 5 in and 1/3 in
Answers
9514 1404 393
Answer:
5/3 in²
Step-by-step explanation:
The area of a rectangle is the product of length and width.
A = LW
A = (5 in)(1/3 in) = 5/3 in² = 1 2/3 square inches
Is [tex]2 \frac{2}{3} [/tex]
a rational number
Answers
If AB= x+4, BC=2x-10, and AC=2x+1, then find the value for AB
Answers
Answer:
x+4→AB=7+4=11
Step-by-step explanation:
342,475 plus 71,925
Thank you
Answers
Answer:
414,400
Step-by-step explanation:
[tex]342.475 + 71.925[/tex]
[tex] = 414.400[/tex]
what is the slope of the line
Answers
Answer:
i think zero but i suck at slope
Step-by-step explanation:
pew pew
verizon's plan costs $75 per month and gives you unlimited talk, and 500 messages per month, and no dataplan. If you send more 500 text messages, on top of the $75 it will cost $.10 per text overage. Write the piecewise function for the following situation. If you send 800 text messages, then how much will your bill be?
Answers
$.10x 300=$30
$75+$30= $105
Sets question with option answers. Help please
Answers
Answer:
best bet is 6
Step-by-step explanation:
Find the equation of the line with slope m
= -1/2 that contains the point (-10, 1).
In slope intercept form
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 4
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~~
m = - [tex]\frac{1}{2}[/tex]
( - 10, 1 )
y - 1 = - [tex]\frac{1}{2}[/tex] [ x - ( - 10 )]
y - 1 = - [tex]\frac{1}{2}[/tex] x + ( - [tex]\frac{1}{2}[/tex] )(10)
y = - [tex]\frac{1}{2}[/tex] x - 4
Jane bought 23 pounds of flour for $11 how many pounds of flour did she get pre dollar
Answers
Answer:
2.090 pounds
Step-by-step explanation:
11 dollars
23 pounds
dollars ÷ pounds = pounds per dollar
23 ÷ 11 = 2.090 pounds8
Answer:
Step-by-step explanation:
23 lbs / $11 = 2.09 lb/$
MN has endpoints at M(2,5) and
N(-4, 3). In what quadrant is the midpoint
of MN?
A Quadrant |
B Quadrant II
C Quadrant IIl
Answers
Answer:
quad 2
Step-by-step explanation:
Midpoint = (x1 + x2)/2,(y1 + y2)/2
x1 = 2
x2 = - 4
y1 = 5
y2 = 3
midpoint = (2 - 4)/2,(5 + 3)/2
midpoint = -2/2, 8/2
midpoint = -1,4
-1 for x puts you in quad 2 or 3
4 for y puts you in quad 2 because you are going up.
The final answer is in quad 2
Which of the equations is shown by the shaded area of the model? A. 0 . 29 + 0 . 37 = 0 . 63 B. 0 . 34 + 0 . 23 = 0 . 57 C. 0 . 36 + 0 . 27 = 0 . 63 D. 0 . 24 + 0 . 33 = 0 . 57
Answers
Answer:
is there anyway you could show the Shaded area of the model because I can't answer it without is that part of the picture showing. Thank you
19. Subtract: 5 - 3 1/3
A. 3 1/3
B. 2 1/3
C. 1 2/3
D. 2 2/3
Answers
C. 1 2/3
Step-by-step explanation:
5 - 3 1/3
We can also convert 5 into a fraction with the same denominator like this:
Since we’re trying to make 5 a fraction with a denominator of 3, leave 4 as the whole number and 3/3 as the fraction
4 3/3
4 3/3 = 5 because 3/3 = 1 and 4 + 1 = 5
Now we can subtract!
4 3/3 - 3 1/3 = 1 2/3
Step 1. Subtract the whole numbers
Step 2. Subtract the numerator
Step 3. Leave the answer with the same denominator
About: Classifying Rational Numbers
Question: Write each rational number in the form a-t (fraction) where a and b are integers.
Offering 30 points for a answer!
0.7 -29 and 8|1-3 (fraction)
Answers
Answer:
i dont know how to use sign
Supervisor: "You have been averaging 55 sales per day. Per our new policy, everyone
needs to increase his or her sales per day by 10% in the next month. Rounding up, by
next month you will need to be up to
sales."
Answers
Answer:
22
Step-by-step explanation:
Can any one solve it.Please
Answers
It's false. Consider f(x) = 1/x. This function is both continuous and decreasing on [1, ∞), and has a limit of 0 as x approaches infinity. But the integral diverges.
1/4 luke's marbles are white, 3/8 are blue, and the rest are 30 yellow marbles. How many of the marbles are white.
Answers
Answer:
It is 20 white marbles
step by step explanation:
Fraction of the yellow marbles:
[tex]1 - \frac{1}{4} - \frac{3}{8} = \frac{3}{8} [/tex]
let total number of marbles be x :
[tex]{ \sf{ \frac{3}{8} \: of \: x = 30 \: yellow \: marbles}} \\ \\ \frac{3}{8} \times x = 30 \\ \\ 3x = 30 \times 8 \\ 3x = 240 \\ x = 80[/tex]
Total marbles = 80 marbles
for white marbles:
[tex] = \frac{1}{4} \times 80 \\ \\ = 20[/tex]
Titik ( 2,3 ) ditranslasi oleh (3 4) Koordinat bayangannya adalah
Answers
Answer:
6,2 kordinat 34,5 h2 semoga membanti
6. If there are 60 studensts in a class, 20 students are absent. Then, find the percentage of absent students.
Answers
Answer:
60:20
100:?x
60×x=100×20
=33.333 %
Find the slope that is PARALLEL and PERPENDICULAR to the equation of the line y = -1/2x+6.
Answers
Step-by-step explanation:
the slope that is PARALLEL to the equation of the line y = -1/2x+6 is -1/2.
and the slope that is PERPENDICULAR to the equation of the line y = -1/2x+6 is :
-1 ÷ -½ = 2
A share of stock is now worth 20% of its value from a year ago. If it is now worth $44,250, what was it worth a year ago?
Answers
Answer:
$8850
Step-by-step explanation:
44250 divided by 0.2 (output value converted from percentage to decimal)
Similarly, if you want to add percentage, multiply instead of divide!
A restaurant serves soda pop in cylindical pitchers that are 6 inches in diameter and 8 inches tall. if the pitcher has1-inch head of foam, how much soda is lost as a result? ( ROUND YOUR ANSWER TO TWO DECIMAL PLACES.)
Answers
Questions relating Word Problems can sometimes be resolved by taking note of the definition of given clues
The amount of soda lost is approximately 28.27 in.³
The reason the above value is correct is as follows:
The known parameters about the the soda pop served by the restaurant are;
Diameter of the cylindrical pitcher in which the soda pop is sold, D = 6 inches
The height of the cylindrical pitchers, h = 8 inches
Thickness of the head of foam in the pitchers, t = 1 inches
Required:
The amount of soda lost as a result of the head of foam
Method:
Define a pitcher
Calculate the volume occupied by the head of foam
Solution:
A pitcher holds drink and usually has a lip and handle, therefore, the drink is filled level with the pitcher
The volume occupied by the head of foam = The amount of soda lost
The volume occupied by the head of foam, [tex]\mathbf{V_{(head \ of \ foam)}}[/tex] = The volume of 1 inch height of the foam in the cylindrical pitcher
Volume in a cylinder = Base area × Height
[tex]\mathbf{Base \ area\ in \ a \ cylinder} =\dfrac{\pi \cdot D^2}{4}[/tex]
The height of the foam = The thickness of the foam = t
∴ [tex]V_{(head \ of \ foam)} =\mathbf{\dfrac{\pi \cdot D^2}{4} \times t}[/tex] =
Plugging in the values of D, and t, gives;
[tex]\mathbf{V_{(head \ of \ foam)}} =\dfrac{\pi \times (6 \ in.)^2}{4} \times 1 \ in. = \pi \mathbf{\times 9 \, in.^3}[/tex]
The volume of the head of foam, given to two decimal places is presented as follows;
[tex]V_{(head \ of \ foam)}[/tex] = π × 9 in.³ ≈ 28.27 in.³
The volume of the head of foam = The amount of soda lost ≈ 28.27 in.³
Learn more about calculating volumes in a cylinder here:
https://brainly.com/question/12368492
https://brainly.com/question/12550991
Find the equation of the line that is parallel to y = 2x - 3 and passes through the
point (0,7).
Answers
Answer: [tex]y=2x+7[/tex]
Step-by-step explanation:
Let's introduce couple variables [tex]m_{1}[/tex] (slope of your equation) and [tex]m_{2}[/tex] (slope of the equation we need to find.
Parallel lines have the same slope, therefore: [tex]m_{1} = m_{2}[/tex], where [tex]m_{1}=2[/tex] and this means that [tex]m_{2} = 2[/tex] as well.
Given that we will use point-slope equation form with the point (0,7):
[tex]y-y_{1} =m(x-x_{1} )\\[/tex] where [tex](x_{1}, y_{1} )[/tex] is the point
Let's substitute:
[tex]y-7=2(x-0)\\[/tex]
And calculate:
[tex]y-7=2x\\[/tex]
Now we just need to isolate [tex]y[/tex] by subtracting 7 from both sides:
[tex]y=2x+7\\[/tex]
That's it!
Here's the graph to show the results:
Evaluate (y - 9) + (3 + x), when y = 15 and x = 5
Answers
Hi ;-)
[tex]y=15 \ and \ x=5\\\\(y-9)+(3+x)=(15-9)+(3+5)=6+8=\boxed{14}[/tex]
Answer:
14
Step-by-step explanation:
(y-9)+(3+x)
(15-9)+(3+5)
6+8
14
Francisco wrote these notes on one of the scientists who contributed to cell theory:
1838
Studied plants
Used a microscope
Concluded that plants are made of cells
Who are these notes about?
Virchow
Schleiden
Leeuwenhoek
Schwann
Answers
Answer:
Schleiden in 1838 said plants are made cells
Step-b
is statistics mathematics or science? defend your answer.
Answers
Answer:
Both
Step-by-step explanation:
Science and Math both are related in many concepts. I will say that Statistics is a mathematical science concept because it deals with the collection, analysis, interpretation or explanation, and presentation of data.
Answer:
Hello There!!
Step-by-step explanation:
The answer is=>Both, it is a mathematical science topic.
hope this helps,have a great day!!
~Pinky~
1 year is what fraction of a decade?
Answers
Answer:
It is 1/10
Step-by-step explanation:
One decade has 10 years
[tex]{ \sf{1 \: decade = 10 \: years}} \\ { \sf{ \frac{1}{10} \: decade = 1 \: year}}[/tex]
Answer:
10% , 1/10, or 10/100
Step-by-step explanation:
There are 10 years in a decade
1/10 represents the 1 year out of the 10!
A multiple choice test contains 25 questions with 5 answer choices. What is the probability of correctly answering 8 questions if you guess randomly on each question?
Answers
Answer: 0.0623
Step-by-step explanation:
The probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
It is given that multiple choice test contains 25 questions with 5 answer choices.
To find probability of correctly answering.
What is probability?The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Given that:
The probability of each correct answer is [tex]p_{s}[/tex][tex]=\frac{1}{5}[/tex]
The probability of 8 successful answers in 25 independent trials for a binomial probability distribution is:
p(k|n)=[tex]\frac{n!}{(n-k)!*n!}[/tex][tex]p_{s}^{k} (1-p_{s})^{n-k} \\[/tex]
p(8|25)=[tex]\frac{25!}{(25-8)!*8!}[/tex][tex]{\frac{1}{5} }^{k} (1-1/5)^{25-8} \\[/tex]
p(8|25)=0.062348
So, the probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
Learn more about probability here:
https://brainly.com/question/24385262
#SPJ2
Suppose that angle P = 3x + 14 and angle Q = 3x - 27. If these angles are supplementary, angle Q would need to be ___ degrees.
Answers
Answer:
Q = 69.5 degrees
Step-by-step explanation:
3x + 14 + 3x - 27 = 180
6x - 13 = 180
6x = 193
x = 32.1667
Q = 3(32.1667) - 27
Q = 69.5
un automóvil a recorrido 640 km a velocidad constante 4 horas Cuál es la velocidad del automóvil
Answers
Answer:
2,560
Step-by-step explanation:
necesitas sumar 4 veces 640 o multiplicar 4×640