Answers
Answer:
[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Step-by-step explanation:
We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]
Therefore, we want to separate the [tex]y[/tex] from the equation.
[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]
[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]
Now we can calculate the derivative. By the chain rule,
[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]
Now
[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]
Therefore
[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Related Questions
Tropical dried fruit costs $1.50 per pound and regular dried fruit costs $0.90 per pound. You want to create a mixed bag of tropical dried fruit and regular dried fruit that is worth $1.30 per pound. How many pounds of tropical dried fruit do you need if you have already purchased 50 pounds of regular dried fruit?
Answers
t = total amount of lbs of Tropical dried fruit
m = total amount of lbs of mixed bag
[tex]\begin{array}{lcccl} &\stackrel{fruit}{lbs}&\stackrel{per~lb}{price}&\stackrel{total}{price}\\ \cline{2-4}&\\ \textit{tropical fruit}&t&1.50&1.5t\\ \textit{regular fruit}&50&0.90&45\\ \cline{2-4}&\\ \textit{mix bag}&m&1.30&1.3m \end{array}~\hfill \begin{cases} t+50=m\\ 1.5t+45=1.3m \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{substituting on the 1st equation}}{1.5t+45=1.3\stackrel{m}{(t+50)}}\implies 1.5t+45=1.3t+65\implies 0.2t+45=65 \\\\\\ 0.2t=20\implies t=\cfrac{20}{0.2}\implies \boxed{t=100}[/tex]
A bakery sold a total of 500 cupcakes in a day, and 190 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?
Answers
Answer: 50/19
Step-by-step explanation:
I'm no math genius however I believe this is division.
500/190 gave me a fraction which is 50/19.
There are 400 bricks used to build a wall that's 15 feet high. How many bricks will be used to build a wall that's 36 feet high?
Answers
Based on the information given
36x400 divided 15
The ratio of the distances a driver and a 2-iron will drive a
golf ball is 5 to 4. If a golfer averages 240 yards with a 2-
iron, how far should she average with a driver?
Answers
The average distance is 300 yards
How to determine the average distance?The ratio is given as:
Driver : 2-iron = 5 : 4
When the iron driver is 240 yards, we have:
Driver : 240 = 5 : 4
Express as fraction
Driver/240 = 5/4
Multiply both sides by 240
Driver= 300
Hence, the average distance is 300 yards
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If a cylinder has a volume of 648pi cm3( 3rd power) and a height of 8 cm, what is the radius?
Answers
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=\stackrel{cm^3}{648\pi }\\ h=8 \end{cases}\implies 648\pi =\pi r^2(8) \\\\\\ \cfrac{648\pi }{8\pi }=r^2\implies 81=r^2\implies \sqrt{81}=r\implies \boxed{9=r}[/tex]
The simplified equation after clearing the decimals is
-12.2 + 2.8w - 8.8 = 1.05w
Answers
Answer:
-21=-4w
w=5.25
but you don’t want decimals
so- you round down
w=5
Step-by-step explanation:
You combine like terms, and then make sure your variable is alone, the only way to get it alone from a ”mixed number” is to divide
you do the same thing to both sides
so divde each side by -4
-21/-4 = 5.25
or with it rounded down since it’s under a five
It’s 5 with the decimals removed
i hope this helps
There are 300 students in the 6th grade class. 252 of the students have received dragon
tickets. What is this as a percent?
Answers
The percentage of students in the 6th grade class that have received dragon tickets is 84%.
Given the following data:
Total number of students = 300 studentsNumber of students with dragon tickets = 252 studentsTo determine the percentage of students in the 6th grade class that have received dragon tickets:
A percentage is used to describe or represent a portion of a given population or total number of something.
Mathematically, the percentage for the given number of students is:
[tex]D = \frac{Students}{Total\;students} \times 100\\\\D = \frac{252}{300} \times 100\\\\D=0.84\times 100[/tex]
D = 84%
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send help send help send help
Answers
Answer:
B answer answer
[tex]the \: answer \: is \: b[/tex]
What is the value of a on the triangle below?
Answers
Answer: answer 56 I’m the goat lol
Step-by-step explanation:
subtract 107 from 180 and you get 73 that’s one corner 73 +51 =124 and 180 - 124 = 56
5x + y = 11
3x − y = 9
Answers
Answer:
x = 5/2y = -1.5Step-by-step explanation:
5x + y = 113x − y = 9
=> 5x + y = 11+3x − y = +9
=> 8x = 20=> x = 20/8=> x = 5/2=> 5(5/2) + y = 11=> 25/2 + y = 11=> 12.5 + y = 11=> y = 11 - 12.5=> y = -1.5Therefore, the answers are:
x = 5/2y = -1.5Hoped this helped.
[tex]BrainaicUser1357[/tex]
If you spend 3/5 of your $40 gift card, how much money will be left on it?
Answers
Answer:
$16
Step-by-step explanation:
1-⅗=⅖
40×⅖=16
Here's the answer
Suppose a worker makes $286.08 in one week. If he is paid $5.96 an hour for the first 36 hours he works and then $8.94 an hour in overtime pay for each additional hour, how many hours did he work overtime
Answers
Answer:
5.96 x 36 = 214.56.
286.08 - 214.56 = 71.52
71.52 divided by 8.94 = 8.
He worked 8 additional hours.
Answer:
The worker worked about 8 hours overtime.
Step-by-step
First we figure out how much they made without overtime.
Multiply 5.96 x 36 and you would get 214.56
Then we figure out how many hours he worked overtime
Multiply 8.94 times 8 and you would get 71.52
Then take 214.56 and add 71.52, you would get 286.08, the answer is 8 hours overtime.
through: (-5,1), parallel to y = -2/3x +2
Answers
Answer:
y = -2/3x-1
Step-by-step explanation:
The difference between two numbers is 8. if 2 is added to the bigger number the result will be three times the smaller number. Find the numbers.
Answers
Answer:
The bigger number is 13 and the smaller number is 5
given the equation f(x)=-2x²+4x+6 find the average rate of change from x=1 and x=2
Answers
Answer:
16
Step-by-step explanation:
1) Plug x=1 into equation
f(x) = -2(1)²+4(1)+6
f(x) = -2²+4+6
f(x) = 4+4+6
y = 14
(1,14)
2) Plug in x=2 into equation
f(x) = -2(2)²+4(2)+6
f(x) = -4²+8+6
f(x) = 16+8+6
y = 30
(2,30)
3) Use slope formula ([tex]\frac{y2-y1}{x2-x1}[/tex])
[tex]\frac{30-14}{2-1}[/tex]
[tex]\frac{16}{1}[/tex]
16
What is 50 million + 32 hundred thousands + 41 hundred
Answers
Answer:
82041000
Step-by-step explanation:
50,000,000 + 32,000,000 + 41,000
Y=-6x-5
Please find the slope
Answers
Answer:
-6
Step-by-step explanation:
this is in y=mx+b form, where m is the slope ! so m is -6
in a survey of 500 voters 430 said they would vote for the same candidate again what percent of the votes would vote the same way again
Answers
We figure 25 people will attend if it rains and 70 people will attend if it does not rain. The weather forecast indicates that there is a 20% chance of rain that day. What is the expected number of people who will attend the party?
Answers
Answer:
34
Step-by-step explanation:
20% of 70 + 80% of 25 = 14 + 20 = 34.
Answer:
61
Step-by-step explanation:
Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).
The expected number of people with a 20% chance of rain would be 61.
(hope it helps)
Determine the probability of the event.
A survey found that about 90% of the junior class is right handed. If 2 juniors are chosen at random out of
100 juniors, what is the probability that at least one of them is not right handed?
Give an exact answer as a decimal.
Answers
Answer:
The probability is 1/100
Step-by-step explanation:
This is because there are only ten left-handed juniors (on average). Therefore there isn't a great chance that you would end up with one.
When a number is divided by 5, it has a remainder of 4.
The number is between 35 and 40.
What is the number?
Answers
Answer:
37
Step-by-step explanation:
I plugged in the numbers between 35 and 40 and got this. No problem. :)
Grapes are 2.55 per pound and on two separate occasions Dana went to the store to
buy grapes. The first time she went to the store she bought 3.25 pounds of grapes
and during the second visit to the store she purchase 1.25 pounds of grapes.
Rounded to the nearest cent, what is the total amount that Dana paid for the grapes?
$7.25
$12.35
$11.48
$7.05
Answers
Answer: $11.48
Step-by-step explanation:
First of all, you have to multiply 3.25 by 2.55 because the grapes are 2.55 per pound. That makes 8.2875 for the first occasion. Next, you have to multiply 1.25 by 2.55 for the second occasion. That makes 3.1875. You then have to add 8.2875 and 3.1875. You get 11.47500, and that rounded to the nearest cent is $11.48.
use the result (a+b)²=a²+2ab+b² to find the value of 49²+98+1
pls help me
I will give brainliest
Answers
Answer:
2500
Step-by-step explanation:
a² + 2ab + b²
49² + 98 + 1
Comparing terms
a²= 49²
a= 49
2ab = 98
2× 49 × b = 98
98b = 98
b= 98/98
b = 1
or
b²= 1
b=√1
b= 1
a=49 and b= 1
Hence (a+b)²= (49+1)²
50²= 2500
Help me plzzzzzzzzzzzzz
Answers
Answer: It is D
Step-by-step explanation:
Need help. Sorry if the pic quality is bad…
Answers
how do i get more points? and why do i need it?
Answers
Answer:
You get more points by answering people's questions. You use points to get help from other people.
Answer: Answer people's questions to get points and use those points to get an answer to your question.
factorize completly Mn + np + or + rt
Answers
Answer:
n (m + p) + r (o + t)
Step-by-step explanation:
You have to split the expression in half.
First, focus on mn + np, the common factor would be n.
So the first part of the answer would be mn ÷ n and np ÷ n.
Leading to it being n(m + p).
Then you focus on the second half or + rt.
You find the common factor, which is r.
You divide both sides by r.
Hence why you get r(o + t).
Lastly, you put them together, n(m + p) + r(o + t).
Hope this helps :)
Please help!! Best answer gets brainliest<3
Answers
X= 29.70
Need help pls answer asap. Sorry the photo quality is bad.
Answers
Answer:
Step-by-step explanation:
1 + 3 = 4
so find the point 1/4 of the way from (-1, 2) to (7, 8)
x coordinate
Δx = ¼(7 - (-1)) = 2
x = x₀ + Δx
x = -1 + 2 = 1
y coordinate
Δy = ¼(8 - 2) = 1½
y = y₀ + Δy
y = 2 + 1½ = 3½
(1, 3½)
Use the drawing tools to form the correct answer on the graph.
What is the inverse of the function shown?
Click on a tool to begin drawing.
Delote
Undo
Reset
Drawing Tools
Select
iz
Point
10
Line Segment
8
6
4
2
x
6
-10
-8
-6
-4
-2
2
6
8
10
2
Answers
Answer:
i need to know this one fast i cant get past this mastery test
Step-by-step explanation:
The inverse of a function is the opposite of the function
From the graph, we have the following ordered pairs
(5,0), (8,3) and (2,-3)When the (x,y) coordinates are rewritten as (y,x), we have the following ordered pairs
(0,5), (3,8) and (-3,2)This means that the inverse of the function passes through the above points
See attachment for the graph of the inverse function
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