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]
In the equation y = mx + b, the "b" is the y-intercept
True
False
Answer:
False
Hope my answer helps you pls mark me as brainiest :)
A 270 inch board is cut into two pieces one piece is 4 times the length of the other, find the length of the shorter piece
Answer:
54 inches
Step-by-step explanation:
let 4x = the bigger piece
let x = the smaller one
4x + x = 270
5x = 270
x = 54
Answer:
54 inches
Step-by-step explanation:
x + 4x = 270
5x = 270
x = 54 (shorter piece)
4x = 216 (longer piece)
Patrick drives from P to Q at an average speed of 40 mph . His drive back from Q to P is at an average speed of 45 mph and takes two minutes less. How far, in miles, is it from P to Q?
QUICK ASAP PLS
Answer:
Step-by-step explanation:
66
A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other.name the type of triangle asd formed
Find the length of AM
Find the length of OM
Find the length of the string of each person
Answer:
The triangle formed is Equilateral triangle.
I have taken Perpendicular = P ( you can say M)
√400 - x² = OP (OM)
√3 x = AP (AM)
The length of the string of each person = 20√3 m
Step-by-step explanation:
As given , circular park with radius 20m
Let , Ankur sit on boundary point A
Syed sit on boundary point S
David sit on boundary point D
As given,
Ankur, Syed and David are sitting at equal distance on its boundary
⇒AS = AD = SD
Let AS = AD = SD = 2x
As the sides are equal
⇒ The triangle formed is Equilateral triangle.
Now,
Draw a perpendicular on the side SD
Let OP be the perpendicular
⇒SP = PD = [tex]\frac{1}{2}[/tex]SD = [tex]\frac{1}{2}. 2x = x[/tex]
So, we get
SP = x , PD = x
Now, Draw the line OS and OA
AS , we can see that ,
ΔOPS and ΔAPS are right angle triangle ,
So , apply Pythagoras theorem to ΔOPS and ΔAPS
In ΔOPS
OS² = OP² + PS²
⇒20² = OP² + x²
⇒400 - x² = OP²
⇒√400 - x² = OP
Now,
In ΔAPS
AS² = AP² + PS²
⇒(2x)² = AP² + x²
⇒4x² - x² = AP²
⇒√3x² = AP
⇒√3 x = AP
Now,
We can see that,
AP = AO + OP
⇒√3 x = 20 + √400 - x²
⇒√3 x - 20 + = √400 - x²
Squaring both side
⇒(√3 x - 20 )²= (√400 - x²)²
⇒3x² + 400 - 40√3 x = 400 - x²
⇒3x² + x² = 40√3 x
⇒4x² = 40√3 x
⇒x = 10√3
∴ we get
AS = SD = AD = 2(10√3) = 20√3 m
⇒The length of the string of each person = 20√3 m
Wyatt’s class is having pizza party. Each group of 3 students eats 1 1/2 pizzas.
whats it the anwser for this 27 + y < 10
Answer:
Simplifying
27 + y = 10
Solving
27 + y = 10
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-27' to each side of the equation.
27 + -27 + y = 10 + -27
Combine like terms: 27 + -27 = 0
0 + y = 10 + -27
y = 10 + -27
Combine like terms: 10 + -27 = -17
y = -17
Simplifying
y = -17
Step-by-step explanation:
X Squared - 2x - 24 = 0
Answer:
x=−4 or x=6
Step-by-step explanation:
what percent of 157 is 119.3
Answer:
75.8 is your answer
Step-by-step explanation:
119:157*100 =
(119*100):157 =
11900:157 = 75.8
Answer:
187.301 is 157% of 119.3
Step-by-step explanation:
write the equation of the line that is parallel to y = 4x -7 and passes through the point (-2, -5). show your work.
Answer:
y = 4x + 3
Step-by-step explanation:
To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.
When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.
So far, the equation is y = 4x + b.
Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.
This would be:
-5 = 4 * -2 + b
-5 = -8 + b
3 = b
This means the equation is y = 4x + 3.
9. Put these numbers in greatest to least order: 2/3, 60%, 0.06, 3/4
Step-by-step explanation:
0.0660%2/33/4hope it's right :)
The temperature in fargo was -28 degrees on monday afternoon. by the evening it dropped an additional 15 degrees. what was the temperature in the evening
Please this is due in 5 minutes do it quick with step by step
Answer:
-43 degrees
Step-by-step explanation:
Start: -28 degrees
-28 degrees - 15 (dropped means subtract)
-28 - 15 = -43
Answer:
-43
Step-by-step explanation:
On Monday, a local hamburger shop sold a combined total of 276 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Monday?
Estimate the value of 50.
O A. between 5 and 6
O B. between 6 and 7
C. between 7 and 8
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D. between 8 and 9
PLEASE HELPP
Answer: c
Step-by-step explanation: because 7 squared is 49 and 8 squared is 64
nvm i read the question wrong
Step-by-step explanation:
the person above is correct
Haley draws a picture to show 8 / 2 which picture could be Haley's
Answer:
.. ..
.. ..
Step-by-step explanation:
8/2=4
please help me, yall :))))
help me pls someone?
2.) Prime fact of 80 ?
Step by step please
(+12) - (-12) =
Resultado, porque, operación completa, 10 puntos
You do not need to show all of your work for this one. But be sure that you can prove your answer is correct!
[tex]\color{plum}m∠ABC = 71° [/tex]
Steps to derive the correct answer :Opposite angles of a parallelogram are equal.Angles on the same side are supplementary.Which means :
m∠ABC = ∠ADC (opposite angles of a parallelogram)
m∠ABC :
= 37° + 34°
= 71°
Thus, the measure of ∠ABC = 71°
Let us find the measures of the other angles as well :
m∠BCD + m∠ADC = 180°
m∠BCD + 71 = 180°
m∠BCD = 180 - 71
m∠BCD = 109°
Thus, the measure of∠BCD = 109°
m∠BCD = ∠BAD (opposite angles of a parallelogram)
m∠BAD = 109°
Thus, the measure of ∠BAD = 109°
Therefore, m∠ABC = 71°
Answer:
109°Step-by-step explanation:
Given isosceles trapezoid AB = CD
Angles B and C are congruent and angles A and D are congruent.
A and B, as well as C and D sum to 180 as supplementary angles, therefore:
m∠ABC = 180° - ∠A = 180 - ∠D = 180° - (34°+37°) = 180° - 71° = 109°Tell whether x and y show direct variation. Explain your reasoning. 2x = 3y
Answer:
YES: direct variation
Step-by-step explanation:
2x = 3y is equivalent to y = (2/3)x, which has the form of a proportional relationship (direct variation) y = kx. YES
Please help, will make brainliest
Answer/Step-by-step explanation:
1. Sin A = opp/hyp
Opp = 3
Hyp = 5
[tex] sin(A) = \frac{3}{5} [/tex] (substitution)
[tex] sin(A) = 0.6 [/tex]
2. Sin B = opp/hyp
Opp = 4
Hyp = 5
[tex] sin(B) = \frac{4}{5} [/tex] (substitution)
[tex] sin(B) = 0.8 [/tex]
3. Cos Q = adjacent/hypotenuse
Adjacent = 12
Hypotenuse = 13
[tex] cos(Q) = \frac{12}{13} [/tex] (substitution)
[tex] cos(Q) = 0.9231 [/tex] (4 decimal places)
4. Cos S = adjacent/hypotenuse
Adjacent = 5
Hypotenuse = 13
[tex] cos(S) = \frac{5}{13} [/tex] (substitution)
[tex] cos(S) = 0.3846 [/tex] (4 decimal places)
plz help me I dont know
geometery plz help
9514 1404 393
Answer:
all are No
Step-by-step explanation:
The given triangle is ΔABE, where AB is the hypotenuse and BE is the long side.
In each of the other triangles listed, The first two letters are not the name of the hypotenuse, so none are similar.
_____
Additional comment
The similar triangles would be ΔADB, ΔEDC, ΔBEC, and ΔBDE.
Answer:
all of them are
Step-by-step explanation:
Poor Milhouse is hopelessly in love with Lisa. Unfortunately for Milhouse, Lisa does not feel the same way. However, Milhouse remains hopeful, since on any given day independently there is a 6% chance that Lisa smiles at him. (Assume a month has 30 days for this problem.) What is the probability that Milhouse goes longer than a month without a smile from Lisa
Answer:
15.6%
Step-by-step explanation:
Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...
94% / 100 = 0.94
[tex]0.94^{30}[/tex] = 0.156
Now we can turn this decimal into a percentage by multiplying by 100
0.156 * 100 = 15.6%
Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%
Using the binomial distribution, it is found that there is a 0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.
For each day, there are only two possible outcomes, either Lisa smiles at him, or she does not. The probability that she smiles at him on day is independent of any other day, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
On any given day independently there is a 6% chance that Lisa smiles at him, hence, [tex]p = 0.06[/tex].Considering a 30 day month, we have that [tex]n = 30[/tex].The probability that Milhouse goes longer than a month without a smile from Lisa is the probability of no smiles during 30 days, that is, P(X = 0), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.06)^{0}.(0.94)^{30} = 0.1563[/tex]
0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
To have $25,000 to spend on a new car in five years, how much money should Jill invest today at 8% compounded monthly?
Answer:
The answer is C. $16,780
Step-by-step explanation:
Answer:
c, 16,780
Step-by-step explanation:
plato
2) Add 1/3n + 2/3 and -1/6n + 1/6m
Answer:
m/6+ n/3 +1/2
Step-by-step explanation:
Please please please help ill do anything
Answer:
Anything??
Step-by-step explanation: (Im joing btw didnt want to offend anyone lol)
x=40
Help please I will reward you
Answer:
Add each side of the rectangle together to get the perimeter.
Step-by-step explanation:
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mr chowdhary purchased a house for rs 6.1 lakh and spent 30000 on its repairs. he then sold it rs 8 lakh. find his gain percent
Given:
Purchasing price = 6.1 lakh
Amount spent of repair = 30000
Selling price = 8 lakh
To find:
The gain percentage.
Solution:
We have,
Purchasing price = 6.1 lakh
Amount spent of repair = 30000 = 0.3 lakh
So, total cost price is
[tex]C.P.=6.1+0.3[/tex]
[tex]C.P.=6.4[/tex]
The total cost price is 6.4.
Selling price(S.P.) = 8 lakh
Now,
[tex]Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100[/tex]
[tex]Gain\%=\dfrac{8.0-6.4}{6.4}\times 100[/tex]
[tex]Gain\%=\dfrac{1.6}{6.4}\times 100[/tex]
[tex]Gain\%=\dfrac{1}{4}\times 100[/tex]
[tex]Gain\%=25\%[/tex]
Therefore, the gain percent is 25%.
Enter an equation in point-slope form for the line.
Slope is 8 and (-7, -1) is on the line.
The equation of the line in point slope form is:
Answer:
y + 1 = 8 (x + 7)
Step-by-step explanation:
point slope form is
y - y1 = m (x - x1)
So replace the y1 with the y point, and the x1 with the x point
y - (-1) = m (x - (-7) )
then replace the m with the slope
y - (-1) = 8 (x - (-7) )
now solve
y + 1 = 8 (x + 7)
Simon makes a model of a boat, using a scale of 1:30
If the model has a height of 40 cm, find the height of the real boat.
give your answers in metres
Answer:
12 meters
Step-by-step explanation:
30 times 40 = 1200
100 cm in a meter
1200/100= 12