Integrate [tex]e^{4x}\sqrt{1+e^{2x} } dx[/tex] please show work so i can learn
Answer:
[tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
Step-by-step explanation:
Step(i):-
Given that the function
f(x) = [tex]e^{4x} \sqrt{1+e^{2x} }[/tex]
Now integrating on both sides, we get
[tex]\int\limits{f(x)} \, dx = \int\limits{e^{4x} \sqrt{1+e^{2x} } dx[/tex]
= [tex]\int\limits{e^{2x} e^{2x} \sqrt{1+e^{2x} } dx[/tex]
Step(ii):-
Let [tex]1 + e^{2x} = t[/tex]
[tex]e^{2x} = t -1[/tex]
[tex]2e^{2x}dx = d t[/tex]
[tex]e^{2x}dx = \frac{1}{2} d t[/tex]
= [tex]\int\limits{( \sqrt{1+e^{2x} }) e^{2x} e^{2x} dx[/tex]
= [tex]\int\limits {\sqrt{t}(t-1)\frac{1}{2} dt }[/tex]
= [tex]\frac{1}{2} \int\limits {\sqrt{t} (t) -\sqrt{t} ) dt }[/tex]
= [tex]\frac{1}{2} \int\limits {(t^{\frac{1}{2} } t^{1} +t^{\frac{1}{2} } ) } \, dx[/tex]
[tex]= \frac{1}{2} \int\limits {(t^{\frac{3}{2} } +t^{\frac{1}{2} } ) } \, dx[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{3}{2}+1 } + \frac{t^{\frac{1}{2} +1} }{\frac{1}{2}+1 } )+C[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{5}{2} } + \frac{t^{\frac{1}{2} +1} }{\frac{3}{2} } )+C[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{5}{2} } }{\frac{5}{2} } + \frac{t^{\frac{3}{2} } }{\frac{3}{2} } )+C[/tex]
= [tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
Final answer:-
= [tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
The segments shown below could form a triangle.
А
C
8
11
A
9
9
C
B
O A. True
B. False
m^2+5=14
[tex] {x}^{2} [/tex]
x2+5=14
Answer:
okeed
Step-by-step explanation:
Y-21<85 help me pls
I don’t get this stuff lol
Answer:
it is y<106
Step-by-step explanation:
remember to add 85 and 21 together :)
What is an equation of the line that passes through the points (-7, -7)and (-7, 4)?
Answer:
It is 7 because it both has the same answer
Answer:
Hi! The correct answer is x= -7
Step-by-step explanation:
Use the slope formula and slope-intercept form y = mx + b to find the equation.
Write 34% as a fraction or mixed number in simplest form
17/50 = 34% Hope this helped
What is the value of the expression 6 +5. (8 = 2)2?
Answer:
The answer is 22
Step-by-step explanation:
might be wrong so I would wait for someone else to also answer.
How many milligrams of medication are in 500 mL of a 1% solution?
Help
Answer:
Step-by-step explanation:
5g. X% solution means there are Xg per 100mL. So 500mL at 1%: 5g
Find the radius, and the approximate circumference and area of the circle below. (Use 3 for \pi)
Answer:
Circ=37.704, Area= 112.112
Step-by-step explanation:
Circumference= pi *Diameter
Taking pi=3.142, Diameter=12
Circ=3.142*12=37.704
Area= pi * r^2
Area= 3.142*6*6=112.112
0.62 as a percent
(STEP BY STEP)
Answer:
0.62 = 0.62 × 100/100 = (0.62 × 100)/100 = 62/100 = 62%;
In other words:
1) Multiply that number by 100.
2) Add the percent sign % to it.
Answer:
62%
Step-by-step explanation:
You would take the decimal and move it to the right two spaces then add the percent sign in replace of the decimal.
.62 → 6.2 → 62. → 62%
Hope this helps!
Jermaine and Monica will usually both run 4.5 miles each time they go running. This month, Jermaine ran an additional 27 miles. Which answer choice shows an expression that represents the total distance Jermaine and Monica ran this month if j = the number of times that Jermaine ran and m = the number of times that Monica ran?
Answer:
4.5 (j + m) + 27
Step-by-step explanation:
Evaluate the expression when y = -6
Y2+5Y-3
Answer:
-45
Step-by-step explanation:
(-6)2+5(-6)-3=-45
Answer:
Solve the equation for Y by finding a , b , and c of the quadratic then applying the quadratic formula. Y = − 5 − √ 97 + 24 y 12 Y = − 5 + √ 24 y + 97 12
which values are solutions to the inequality below? check all that apply √x > 4
A.) 17
B.) 8
C.) 15
D.) 13
E.) 19
F.) 4
Which relationships describe angles 1 and 2?
Select each correct answer.
supplementary angles
complementary angles
adjacent angles
vertical angles
result for Which relationships describe angles 1 and 2?
Answer. Answer: They are supplementary angles, because angle 1 + angle 2 = 180° , i.e. they form a line.
Hope you enjoy! :)
help me with this question
Answer:
-3
Step-by-step explanation:
Rise over run is slope or rate of change
-6/2=-3
What is the real part of 6 plus 3i
Answer:
63
hope it's 9 lol ❤❤❤❤❤❤
THANK YOU. ^O^ :)
Answer: 6
Step-by-step explanation: A complex number is written as a+bi where a is the real part(whole number) and b is the imaginary part.
Brainiest if right so pls solve down below!
9514 1404 393
Answer:
D) 54
Step-by-step explanation:
Put the numbers where the variables are and do the arithmetic.
2[(x -1) +2xy]
= 2[(4 -1) +2(4)(3)]
= 2[3 +24]
= 2(27) = 54 . . . . matches choice D
Answer:
54Step-by-step explanation:
We know that:
Given expression: 2[(x - 1) + 2xy]x = 4y = 3Solution:
2[(x - 1) + 2xy]=> 2[(4 - 1) + 2(4)(3)]=> 2[3 + 2(4)(3)]=> 2[3 + 24]=> 2[27]=> 54Hence, Option D is correct.
Sales tax is 7% What will be the sales tax on a purchase of 28.95
Answer:
7%=$2.03
$28.95+$2.03=$30.98
I am not 100% sure but it is better than nothing.
A circle has a diameter of 4 meters.
What is its perimeter (to the nearest hundredth)?
What is its area (to the nearest hundredth)?
m^2
Answer:
Step-by-step explanation:
r = d/2
r = 4/2
r = 2
pi = 3.14
Circumference = 2 * pi * r
Circumference = 2 * 3.14 * 2
Circumference = 12.56
Area = pi r^2
Area = 3.14 * 2^2
Area = 4 * 3.14
Area = 12.56
The answer is 132 ft
Answer:
Lol, thank you for telling me this information..
cual es el resultado de simplificar. Adjunto foto
Answer:
⣿⣯⣿⣟⣟⡼⣿⡼⡿⣷⣿⣿⣿⠽⡟⢋⣿⣿⠘⣼⣷⡟⠻⡿⣷⡼⣝⡿⡾⣿ ⣿⣿⣿⣿⢁⣵⡇⡟⠀⣿⣿⣿⠇⠀⡇⣴⣿⣿⣧⣿⣿⡇⠀⢣⣿⣷⣀⡏⢻⣿ ⣿⣿⠿⣿⣿⣿⠷⠁⠀⠛⠛⠋⠀⠂⠹⠿⠿⠿⠿⠿⠉⠁⠀⠘⠛⠛⠛⠃⢸⣯ ⣿⡇⠀⣄⣀⣀⣈⣁⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠈⠀⣀⣁⣀⣀⡠⠈⠉ ⣿⣯⣽⡿⢟⡿⠿⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠈⢠⣴⣾⠛⠛⠿⠻⠛⠿⣷⣶ ⣿⣿⣿⠀⠀⠀⣿⡿⣶⣿⣫⠉⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⠿⠾⣿⡇⠀⠀⢺⣿ ⣿⣿⠻⡀⠀⠀⠙⠏⠒⡻⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⡓⢚⠟⠁⠀⠀⡾⢫ ⣿⣿⠀⠀⡀⠀⠀⡈⣉⡀⡠⣐⣅⣽⣺⣿⣯⡡⣴⣴⣔⣠⣀⣀⡀⢀⡀⡀⠀⣸ ⣿⣿⣷⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢾⣷⣿ ⣿⣿⣟⠫⡾⠟⠫⢾⠯⡻⢟⡽⢶⢿⣿⣿⡛⠕⠎⠻⠝⠪⢖⠝⠟⢫⠾⠜⢿⣿ ⣿⣿⣿⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⣋⣀⣈⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢸⣿ ⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⣿⣿⣿⣿⣦⡔⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⣿⢽⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠘⠛⢅⣙⣙⠿⠉⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣅⠀⠓⠀⠀⣀⣠⣴⣺⣿⣿⣿⣿⣿⣿⣿⣿
Step-by-step explanation:
i nu speak that language
Estimate the diameter of a circle with a circumference of 80 feet
1. 12.74 feet
2. 25.48 feet
3. 40 feet
4. 50.96 feet
Answer:
2) 25.48
The diameter of the circle d = 25.48
Step-by-step explanation:
Step(i):-
we know that the diameter of a circle d = 2 r
The circumference of the circle = 2π r
Given that the circumference of the circle = 80 feet
Step(ii):-
The circumference of the circle = 2π r = 80
⇒ π (2r )= 80
⇒ πd = 80
⇒ [tex]d = \frac{80}{3.14}[/tex]
d = 25.477
Final answer:-
The diameter of the circle d = 25.477
Please show all of your work for this!
Answer:
17 unitsStep-by-step explanation:
BE is midsegment of ACDF
BE = 1/2(CD + FA)2(3x + 3) = 6x - 16 + 4x - 106x + 6 = 10x - 2610x - 6x = 6 + 264x = 32x = 8Similarly, FA is midsegment of BEZW
FA = 1/2(BE + WZ)WZ = 2FA - BEWZ = 2(4x - 10) - (3x + 3)WZ = 8x - 20 - 3x - 3WZ = 5x - 23Substitute x with 8:
WZ = 5*8 - 23 = 40 - 23 = 175x5x5x5= ______ to the power of _____
Answer:
5 4
Step-by-step explanation:
its fristly 5
ok then bb
Answer:
5x5x5x5=625
Step-by-step explanation:
Mia went to the art store and bought 2 poster boards and 3 markers. She spent A total of $6.50. The total tax was $1.25. How much did each marker cost? *
In the proportion x/5= 15/3 which number is equal to x in the proportion?
Please help! Algebra hw! Hrw
Answer:
x^9 -20x^7 -6x^3 3x^2 13
Step-by-step explanation:
Standard form for polynomials is to order the degrees of the number from highest to lowest, left to right. So, knowing this, we can infer that it goes x^9 - 20x^7 - 6x^3 + 3x^2 + 13. The degree is 9 (highest exponent), and the leading coefficent (number in front of/multiplying highest degree var) is 1.
Answer: (x^9)+(-20x^7)+(-6x^3)+(3x^2)+13
Step-by-step explanation:
Standard form would just be to organize the polynomial in descending order of the degree (..._^3+_^2+_^1+constant)
(a) What is wrong with the following equation? x2 + x − 42 x − 6 = x + 7 (x − 6)(x + 7) ≠ x2 + x − 42 The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 6, but the right-hand side is. None of these — the equation is correct. (b) In view of part (a), explain why the equation lim x → 6 x2 + x − 42 x − 6 = lim x → 6 (x + 7) is correct. Since x2 + x − 42 x − 6 and x + 7 are both continuous, the equation follows. Since the equation holds for all x ≠ 6, it follows that both sides of the equation approach the same limit as x → 6. This equation follows from the fact that the equation in part (a) is correct. None of these — the equation is not correct.
Answer:
Attached please find answer
Step-by-step explanation:
= (x² + x - 42) / (x - 6)
= [x² + (7x - 6x) - 42] / (x - 6)
= [x² + 7x - 6x - 42] / (x - 6)
= [(x² + 7x) - (6x + 42)] / (x - 6)
= [x(x + 7) - 6(x + 7)] / (x - 6)
= [(x + 7)(x - 6)] / (x - 6)
= x + 7 → when x approches 6
= 6 + 7
= 13
Other method:
Lim (x² + x - 42) / (x - 6)
x→ 6
When x → 6, there is an indeterminate expression because: 6 - 6 = 0
Do you know the l'Hôpital's rule, when x → a:
Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]
f(x) = x² + x - 42
f'(x) = 2x + 1
g(x) = x - 6
g'(x) = 1
= f'(x) / g'(x)
= (2x + 1)/1
= 2x + 1 → when x approches 6
= 12 + 1
= 13
After a 65% reduction, you purchase a new clothes dryer on sale for $189. What was the original price of the clothes dryer ?
Answer:
$122.85
Step-by-step explanation:
65/100 x 189 = $122.85
Given that V, W, and X are the midp oints of ASTU, what is the relationship between TX and XU?
A 2TX = XU
B. TX = 1/2XU
C. TX || XU
D. TX=XU
Please select the best answer from the choices provided
Answer:
the answer is D
Step-by-step explanation:
got it right on edg