Integrate \(e^{4x}\sqrt{1+e^{2x} } dx\) please show work so i can learn
Answers
Answer:
\((\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C\)
Step-by-step explanation:
Step(i):-
Given that the function
f(x) = \(e^{4x} \sqrt{1+e^{2x} }\)
Now integrating on both sides, we get
\(\int\limits{f(x)} \, dx = \int\limits{e^{4x} \sqrt{1+e^{2x} } dx\)
= \(\int\limits{e^{2x} e^{2x} \sqrt{1+e^{2x} } dx\)
Step(ii):-
Let \(1 + e^{2x} = t\)
\(e^{2x} = t -1\)
\(2e^{2x}dx = d t\)
\(e^{2x}dx = \frac{1}{2} d t\)
= \(\int\limits{( \sqrt{1+e^{2x} }) e^{2x} e^{2x} dx\)
= \(\int\limits {\sqrt{t}(t-1)\frac{1}{2} dt }\)
= \(\frac{1}{2} \int\limits {\sqrt{t} (t) -\sqrt{t} ) dt }\)
= \(\frac{1}{2} \int\limits {(t^{\frac{1}{2} } t^{1} +t^{\frac{1}{2} } ) } \, dx\)
\(= \frac{1}{2} \int\limits {(t^{\frac{3}{2} } +t^{\frac{1}{2} } ) } \, dx\)
= \(\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{3}{2}+1 } + \frac{t^{\frac{1}{2} +1} }{\frac{1}{2}+1 } )+C\)
= \(\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{5}{2} } + \frac{t^{\frac{1}{2} +1} }{\frac{3}{2} } )+C\)
= \(\frac{1}{2} (\frac{t^{\frac{5}{2} } }{\frac{5}{2} } + \frac{t^{\frac{3}{2} } }{\frac{3}{2} } )+C\)
= \((\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C\)
Final answer:-
= \((\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C\)
Related Questions
HELPPP I DONT UNDERSTAND
Answers
Answer:
\(\boxed{\bf \angle B = 58^{o}}\)
Step-by-step explanation:
The cyclic quadrilateral sum of the opposite angle is 180°. From the given figure....
\(\bf \angle B + \angle D= {180}^{o} \)
Where....
~\(\bf \angle B = 3x+7\)
~\(\bf \angle D = 6x+20\)
\(\bf 3x+7+6x+20 ={180}^{o} \)\(\bf 9x+27=180^{o}\)\(\bf 9x=180-27\)\(\bf 9x=153\)\(\bf x = \cfrac{153}{9} \)\(\boxed{\bf x=17^{o}}\)Now, that we found x, let's find angle B....
\(\bf \angle \: B = 3x + 3\)\(\bf 3(17) + 7\)\(\bf 58^{o}\)\(\sf Therefore, \: \boxed{\sf \angle B = 58^{o}}\)
8. Given AABC~AEDC
What is the value of x?
C. 30
D. 20
A. 15
B. 12
A
E
60
X
C
D
10
40
B
Answers
Answer:
790
Step-by-step explanation:
7098uuilu4645
8 + 3x=29 +2x
I need answer ASAP
Answers
Answer:
x = 21
Step-by-step explanation:
8 + 3x = 29 + 2x
8 + 3x - 2x = 29
8 + x = 29
x = 29 - 8 = 21
x = 21
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answers
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home. Find the margin of error for this poll if we want 95% confidence in our estimate of the percentage of new home buyers who hired movers.
Answers
Answer:
The margin of error M.O.E = 2.5%
Step-by-step explanation:
Given that;
The sample size = 1500
The sample proportion \(\hat p\) = 0.60
Confidencce interval = 0.95
The level of significance ∝ = 1 - C.I
= 1 - 0.95
= 0.05
The critical value:
\(Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96\) (From the z tables)
The margin of error is calculated by using the formula:
\(M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}\)
\(M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}\)
\(M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}\)
\(M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}\)
M.O.E = 0.02479
M.O.E ≅ 0.025
The margin of error M.O.E = 2.5%
Estimate 147+14+85 by first rounding each number to the nearest ten.
Answers
Answer:
250
Step-by-step explanation:
because 147 rounded is 150 14 is 10 and 85 is 90 these added together are 250
A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = 2x3 + 11x2 – 23x – 14. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = x2 + 11x + 28. After how many days does the retailer start making money?
3
7
1
2
Answers
The retailer starts making money after approximately 2 days. The correct answer is option 4: 2 days. To determine the point at which the retailer starts making money, we need to find the value of x when the revenue (R(x)) exceeds the cost (C(x)).
Given the revenue function R(x) = 2x^3 + 11x^2 - 23x - 14 and the cost function C(x) = x^2 + 11x + 28, we can set up the following inequality:
R(x) > C(x)
Substituting the given functions into the inequality, we have:
2x^3 + 11x^2 - 23x - 14 > x^2 + 11x + 28
Simplifying the equation, we get:
2x^3 + 10x^2 - 34x - 42 > 0
Now, to find the point at which the retailer starts making money, we need to solve the inequality. This can be done by factoring, graphing, or using numerical methods.
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Answer: The Answer is option one, 3
Step-by-step explanation:
I took the test
what is 3.3 in fraction
Answers
Answer: 33/10
Step-by-step explanation:
=3.3 X 10/10
= 33/10
Answer done. 33/10 #
5+5 is what i can not even get it is hard
Answers
Answer:
Step-by-step explanation:
10 plzz give me brainliest see ya
solve for rational algebraic equation.
Answers
Step-by-step explanation:
Taking the provided equation ,
\(\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} \)
1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)
\(\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} \)
2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .
\(\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)\)
3) Multiplying the expressions.
\( \implies 5(3x^2+13x+2) = 40x + 120 \)
4) Opening the brackets .
\(\implies 15x^2+ 65x + 10 = 40x + 120 \)
5) Transposing all terms to Left Hand Side .
\(\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0\)
6) Solving the quadratic equation .
\(\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}\)
Answer:
\(x=2\\x=-\frac{11}{3}\)
Step-by-step explanation:
Solve the rational equation:
\(\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}\)
To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):
\(\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}\)
Operate and simplify:
\(\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)\)
\(\displaystyle 3x^2+4x+9x+12-10=8x+24\)
Rearranging:
\(\displaystyle 3x^2+4x+9x+12-10-8x-24=0\)
Simplifying:
\(\displaystyle 3x^2+5x-22=0\)
Rewrite:
\(\displaystyle 3x^2-6x+11x-22=0\)
Factoring:
\(\displaystyle 3x(x-2)+11(x-2)=0\)
\(\displaystyle (x-2)(3x+11)=0\)
Solving:
\(x=2\\x=-\frac{11}{3}\)
1. What concept does this picture illustrate?
A. radiation
B. conduction
c . contraction
D. convec
Answers
Answer:
c
Step-by-step explanation:
Answer:
Convection.
Step-by-step explanation:
Convection is where warm air rises and cool air falls. This picture is an example of Convection.
Which properties are used to add these complex numbers? Choose all that apply .
(4+3i)+(8+2i)=
Answers
Answer:
Associative property and Commutative
Step-by-step explanation:
Help please
9. Use the following information to answer questions 9 - 13.
Ray OB bisects ZAOC.
Find the value of x. Be sure to show all of your work!
Answers
Answer:
x = 5
Step-by-step explanation:
13x - 9 = 12x - 4
combine like terms
x = 5
Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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A child has a bottle full of pennies, nickels,dimes and quarters. There are twice as many quarters as pennies, four times as many nickels as pennies, and five times as many dimes as nickels. How many more dimes does the child have than quarters?
Answers
Answer:19x
Step-by-step explanation:
Take x as the value of pennies
If there are twice as many quarters as pennies then the explanation should be
Pennies =x
Quarters =2x
If there are 4 times as many nickels as pennies then the explanation is
Pennies =x
Nickels =4x
If there are 5 times as many dimes as nickels then the explanation is
Nickels =4x
Dimes=20x
So the values of them all is
Pennies =x
Nickels =4x
Dimes =20x
Quarters =2x
So to get how many more dimes does the child have than quarters you subtract
20x-2x=19x
The Number of dimes the child has more than quarters is; 10 times more.
Let number of pennies be P
Since he has twice as many quarters as pennies, then;
Number of quarters; Q = 2P
Four times as many nickels as pennies. Then;
Number of nickels; N = 4P
five times as many dimes as nickels. Then;
Number of dimes; D = 5N = 5(4P) = 20P
Since number of quarters = 2P
And number of dimes = 20P
Then;
Number of dimes the child has more than quarters is; 20P/2P = 10
Thus, the child has ten times as many dimes as quarters
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Gina made a
playlist of children's songs. In 1 hour,
how many more times could she play
"Row, Row, Row Your Boat" than "Twinkle,
Twinkle, Little Star"?
Answers
Here's li\(^{}\)nk to the answer:
bit.\(^{}\)ly/3HH\(^{}\)Mdaf
Pack of 50 stickers costs 4.50 what the uniy price
Answers
A researcher was interested in the impact of listening to different types of music on learning. She designed an extensive maze for rats and after she taught rats how to get through the maze, she randomly assigned each rat to run the maze while (a) listening to classical music, (b) listening to heavy metal music, or (c) in a quiet room (i.e., no music). The researcher measured the amount of time it took each rat to get through the maze and the number of errors made.
a. Independent Variable ? _________________ What are the levels? ________________________________
b. Dependent Variable ? _____________________________
c. What might be an extraneous variable?: ___________________________________
d. Control group? _________________ Experimental Group(s)?____________________
Answers
a.) The independent variable is the different types of music
b.) The dependent variable is the impact of listening felt by the rats
c.)An extraneous variable is the length of the maze.
d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.
What is an independent and dependent variables?An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.
A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.
For question a.)
The independent variable is the different types of music
For question b.)
The dependent variable is the impact of listening felt by the rats
For question c.)
An extraneous variable is the length of the maze.
For question d.)
The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.
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What is the ratio of squares to circles in this picture?
Answers
Answer:
Step-by-step explanation:
since there is one square and 4 circles, the answer is 1/4
To make cranberry jam you need 12 cups of sugar for every 16 cups of cranberries. Find the amount of sugar needed for 4 cups of cranberries.
Answers
Answer:
It would be three cups
Step-by-step explanation:
16/12=4/x
Divide 16 by 4 to get 4 cups of cranberries, and do the same to the sugar
3=x
You can sand 4/9 square yard of wood in 1/2 hour. How many square yards can you sand in 3.2 hours? Justify your answer.
Answers
Answer:
4/9 = 1/2 x
Step-by-step explanation: 2.84 sands
Find . 144 pls help me who ever does first gets brainliest.
Answers
Answer:
12
Step-by-step explanation:
The square root of 144 is 12
an american put futures option has a strike price of 0.55 and a time to maturity of 1 year. The current future price is 0.60. The volatility of the futures price is 25% and interest rate is 6% per annum. Use a one-time step tree to value the option
Answers
The value of the American put futures option with a strike price of $0.55 and time to maturity of 1 year, using a one-time step tree, is $0.
The following is the one-time step tree for valuing the American put futures option:
Strike Price = $0.55, Volatility = 25%, Time to Maturity = 1 year, Interest Rate = 6% per annum, Current Futures Price = $0.60
The tree will be formed using the following equations:
u = e^(σ√t)
where σ is the volatility, t is the time and u is the up movement factor.
d = 1/u
N is the number of steps
r is the risk-free interest rate.
The values for these are:u = e^(0.25√1) = 1.2840d = 1/u = 1/1.2840 = 0.7787N = 1r = 6% per annum = 0.06First, calculate the futures price at time t=1 using the tree.
This will be used to determine whether to exercise the option or not at time t=1.Futures Price at time t=1:
From the tree:
Futures Price if Up = $0.60 x 1.2840 = $0.7704Futures Price if Down = $0.60 x 0.7787 = $0.4672
Using these values, calculate the risk-neutral probability of the futures price going up and down:
p = (e^(rt) - d) / (u - d)
= (e^(0.06x1) - 0.7787) / (1.2840 - 0.7787)
= 0.5679
The expected futures price at time t=1 is:
E(F) = p x $0.7704 + (1-p) x $0.4672
= 0.5679 x $0.7704 + 0.4321 x $0.4672 = $0.6157
Now we calculate the intrinsic value of the option. If the futures price at time t=1 is less than the strike price, then the option will be exercised. If not, then it will not be exercised.
Therefore, the intrinsic value is:Intrinsic Value = $0.55 - $0.6157 = -$0.0657
As the intrinsic value is negative, the option will not be exercised at time t=1.
Therefore, the option value at time t=0 is the expected value of the option at time t=1, discounted by the risk-free interest rate:
Option Value at t=0 = [pVu + (1-p)Vd] / (1+r)
= [0.5679 x 0 + 0.4321 x 0] / (1+0.06) = $0.
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Based on the graph, if Joe earned $400, how many hours did he work?
Answers
Please help 20 points please helpppp I don’t understand
Answers
Answer:
I think that its 58 degrees
Answer:
Angle CED=58°
Step-by-step explanation:
Angle CED=180-122 (adj angles on a str line)
=58°
Solve these linear systems using elimination <3
1. 4x-3y=8
5x-2y=11
2. -2x-5y=9
3x+11y=4
3. 7x-6y=-1
5x-4y=1
Answers
Answer:
1.x=3/4y + 2
Step-by-step explanation:
Add 3y to both sides then after youdidnt that divide both sides by 4 Thereyougo the answer.
i have school myself so i only did one.
please help! Write the equation of line that has a y-intercept of -6 snd a slope of 3
Answers
Answer:
y=3x+6
Step-by-step explanation:
the equation of a line in
slope-intercept form
is.
xy=mx+b
sanjana wrote the cross multiplication property for her proportion: xt=uy
Answers
Answer:
what does this mean. oh wAit iM dematerializinG mvxhkgd
hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd
h(x)=−2x+2
Find h(−2).
Answers
Answer:
6
Step-by-step explanation:
when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2
From the given figure prove that i) ΔABC and ΔDEF are congruent ii) A F = DC
Answers
Answer:
Proved
Step-by-step explanation:
Given:
We are first to prove that ΔABC and ΔDEF are congruent. That is they have same shape and size.
∆ABC≅∆DEF
AB = DE
BC = FE
See attachment for details
