Answer:
2
Step-by-step explanation:
Evaluate the following integral:
[tex]\large\underline{\sf{Solution-}}[/tex]
Given integral is
[tex]\rm :\longmapsto\:\displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx[/tex]
To evaluate this integral, we use Method of Substitution.
So, Substitute
[tex]\rm :\longmapsto\: {x}^{e} + {e}^{x} = y[/tex]
[tex]\rm :\longmapsto\: \dfrac{d}{dx}({x}^{e} + {e}^{x}) = \dfrac{d}{dx}y[/tex]
[tex]\rm :\longmapsto\: {ex}^{e - 1} + {e}^{x} = \dfrac{dy}{dx}[/tex]
[tex]\rm :\longmapsto\:e( {x}^{e - 1} + {e}^{x - 1}) = \dfrac{dy}{dx}[/tex]
[tex]\rm :\longmapsto\:({x}^{e - 1} + {e}^{x - 1})dx = \dfrac{dy}{e}[/tex]
So, on substituting all these values in above integral, we get
[tex]\rm \: = \: \displaystyle\int\rm \frac{dy}{e \: y} [/tex]
[tex]\rm \: = \:\dfrac{1}{e} \displaystyle\int\rm \frac{dy}{ y} [/tex]
[tex]\rm \: = \:\dfrac{1}{e}log |y| + c[/tex]
[tex]\rm \: = \:\dfrac{1}{e}log \bigg| {x}^{e} + {e}^{x} \bigg| + c[/tex]
Hence,
[tex]\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx = \frac{1}{e}log \bigg| {x}^{e} + {e}^{x}\bigg| + c}}[/tex]
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LEARN MORE :-
[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f(x) & \bf \displaystyle \int \rm \:f(x) \: dx\\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf kx + c \\ \\ \sf sinx & \sf - \: cosx+ c \\ \\ \sf cosx & \sf \: sinx + c\\ \\ \sf {sec}^{2} x & \sf tanx + c\\ \\ \sf {cosec}^{2}x & \sf - cotx+ c \\ \\ \sf secx \: tanx & \sf secx + c\\ \\ \sf cosecx \: cotx& \sf - \: cosecx + c\\ \\ \sf tanx & \sf logsecx + c\\ \\ \sf \dfrac{1}{x} & \sf logx+ c\\ \\ \sf {e}^{x} & \sf {e}^{x} + c\end{array}} \\ \end{gathered}\end{gathered}[/tex]
What is the rule when you add a negative number and positive number?
Answer:
a negative plus positive equals a negative-
Answer:
"To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero."
Step-by-step explanation:
Simpler Explanation: If you add a positive number with a negative number, the sign (negative/positive) of the sum is the same as the integer (number) with the largest absolute value. For example;
1. 10 + -12 = -2
Here, the sum has the same sign (negative) as the largest number in the equation (-12).
2. 7 + -3 = 4
Here, the sum has the sign (positive) as the largest number in the equation (7).
Can someone please help me with these with step by step explanation. I also added a hint thing
Answer:
no i cant
Step-by-step explanation:
i just need points uwu
baka sussy
A new car is purchased for 20800 dollars. The value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 years.
Answer:
Step-by-step explanation: Exponential depreciation formula :-
y = A(1 - r)^t, where y is the value of good after t years , r is rate of depreciation and A is the initial value.
Given : A= $20800 ; r=10.75%=0.1075
The equation models this situation:
Then, the value of car after t=13 years :-
Hence, the value of car after 13 years = $4742.10
If I could get help
Answer:
4m, 6m, 7m, 5m
Step-by-step explanation:
To find perimeter you just add the side lengths togeather.
Please help!! Find the length of the third side. If necessary, write in simplest radical form.
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Work Shown:
[tex]a^2 + b^2 = c^2\ \text{ ... pythagorean theorem}\\\\4^2 + x^2 = \left(\sqrt{65}\right)^2\\\\16 + x^2 = 65\\\\x^2 = 65-16\\\\x^2 = 49\\\\x = \sqrt{49} \ \text{ ... only consider the positive root}\\\\x = 7\\\\[/tex]
If £2000 is placed into a bank account that pays 3% compound interest per year,
how much will be in the account after 2 years?
60%
Answer:
There would be 2,120 dollars in that account
Answer:
Step-by-step explanation:
A=P(1 - r/n)^nt
A = 5,000 (1 - 0.03/1)^(1)12)
A = 5,000 (1 - 0.03)^2
A = 5,000 (0.9)^2
A = $5,314.06
Can anyone help me and if u don’t know how to do it don’t comment on my stuff
Answer:
Step-by-step explanation:
(5x +x^4) -((3x^4 )+4x), open the parenthesis and distribute the negative sign
5x+(x^4) -(3x^4) -4x, combine like terms
(-2x^4) +x
A airplane flies 3 hours. The distance is 1200 miles. What is the speed?
Answer:
400 mph
Step-by-step explanation:
1200/3 = 400 miles per hour
write the equation (y=kx)
= kx. where k is the constant of variation. Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3.
Simply so, which graph represents an equation in the form y KX?
Slope of y = kx Theorem The graph of the direct-variation function with equation y = kx has constant slope k. Now solve this system of equations for k. So by the definition of slope, k is the slope of the line through these points. Thus, k is the slope of the line with equation y = kx.
Also, which statement is always true about the graph of an equation in the form y KX Y KX? The equation y = kx is a proportional graph. It means that you multiply x by a number and you have k. The point (0, 0) will always be on the graph, because no matter what K is, if you are multiplying by 0 for x, you will get 0 for y.
Secondly, what is Y KX called?
In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation. In this function, m (or k) is called the constant of proportionality or the constant of variation.
What is direct variation?
Direct Variation. Directly Proportional. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).
i need help on math please solve this
Answer:
6/13
Step-by-step explanation:
because if you do 10-4=6
Solve the equation :
7:x=2:3
Answer:
x=8
Step-by-step explanation:
Since 7-2 is 5, that means that both sides are increasing by 5.
3+5 = 8 so therefore 8 =x
Select all the statements that best describe the graph below.
The Correct choices are :
The Rate of change is not constant The dependent variable is number of book salesThe independent variable is dayThe relationship is non - linear This is a negative relationship8. Bir doğru parçasının yuvarlak uzunluğu 7 cm dir. a) Doğru parçasının en küçük uzunluğu kaç cm olabilir? b) Doğru parçasının en büyük uzunlugu kaç cm olabilir?Aciillll
Answer:
yfyffyfyfyg
Step-by-step explanation:
xgsxfuftuxfyfjfyfyfyffyfyfygyfdtdtdhfgjhtuydxfyyxff
4 digit number that is not divisoble by 2,3,5 or 10
Answer:
isiiqywyysyu the first one the first time in a even if it well y eh I just saw your message garako thiya na na hey I k h I just got home from a ko xa ki xaina the morning to get well soon dd ko we
Step-by-step explanation:
eheuieiriieu to be ei ufuirijwjjeuuwuw to jnndhejfjitNeed HEELPPPP Did you know that chickens sometimes eat vegetables and fruits? A farmer likes to give the chickens apples to share. The farmer observes that 5 chickens eat 8 apples. What is the ratio of the number of chickens to apples?
3:8
5:8
8:3
8:5
Answer:
It would be 5:8
Step-by-step explanation:
Set up a proportion and solve round to the nearest tenth. 45 is what percent of 80?
Answer:
the answer: 56.25 percent of 80
Antonio works as a furniture salesman and earns a bace salasry of 450$ per week plus 6% commision on sales. What was antonios weekly commission if his total sales was 3750?
Answer:
$ 198
Step-by-step explanation:
450 + 0.06x = 3750
0.06x = 3750 - 450
x = (3300 * 0.06) = 198
x = 198
In the auditorium there are 13 red chairs and 37 blue chairs. What is the ratio of the number
of blue chairs to the number of red chairs?
Each number in a list of numbers is 3 more than the number before it. The first number in the list is −4. What is the fifth number?
Answer:
- 16
Step-by-step explanation:
-4 - 3 = -7 (1st and 2nd)
3rd) - 7 - 3 = - 10
4th) -10 - 3 = -13
5th) -13 - 3 = -16
Answer:
a. -8
Step-by-step explanation:
help asap please!! :(( I need help
Answer:
m1= 43
m2=17
m3=120
m4=m5=m6=60
m7=17
m8=120
m9=43
Step-by-step explanation:
"Given ABC is an isosceles triangle and DBE is an equilateral triangle. we have to find each missing measure.
In triangle ABC,
∠1=∠9 (∵isosceles triangle)
⇒ 4x+3=9x-47
⇒ 9x-4x=3+47 ⇒ 5x=50 ⇒ x=10
Hence, ∠9=∠1=(4x+3)°=4(10)+3=43°
Also, given ΔBDE is an equilateral triangle, and all angle of equilateral triangle are equal.
∴ ∠4+∠5+∠6=180°
⇒ ∠4+∠4+∠4=180° ⇒ 3∠4 = 180° ⇒ ∠4 = 60°
∴ ∠4=∠5=∠6=60°
By exterior angle property, ∠3=∠5+∠6=60°+60°=120°
∠8=∠5+∠4=60°+60°=120°
In ΔABD, ∠1+∠2+∠3=180°
⇒ 43°+120°+∠2=180°⇒ ∠2 = 17°
In ΔABD, ∠9+∠8+∠7=180°
⇒ 43°+120°+∠7=180°⇒ ∠7= 17°"
by SerenaBochenek
The Peyton family stayed in a hotel room for 5 nights while on vacation. The total cost before tax was $1,075. If the hotel room tax rate in the city is 14%, what was the total cost for the hotel room?
Answer:
1225.50
Step-by-step explanation:
14% of 1075 =0.14 x 1075=150.5
1075 +150.5 = 1225.5
The 14% of $1075 is $150.5 thus the total cost for the hotel room overall 5 nights including tax will be $1225.50.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
The total cost before tax was $1,075.
The tax rate is 14%
14% of $1075 will be,
(14/100)1075 = $150.5
Total cost includes tax = $1075 + $150.5 = $1225.50
Hence "The 14% of $1075 is $150.5 thus the total cost for the hotel room overall 5 nights including tax will be $1225.50".
For more about the percentage,
brainly.com/question/13450942
#SPJ2
OMG please help me! Please!
Answer:
(2,4)
X always comes before Y. So the X is 2 and the Y is 4, so (2,4).
how can you tell that a website is valid and reliable?
A. Make sure it sounds valid and reliable when you read it?
B. Use the CARS checklist
C. If it is written using scholarly terms, then it must be written by an expert
D. if there are no grammar or spelling errors then it probably is good
Answer: the CORRECT answer is B
Why B?:
The CARS Checklist (Credibility, Accuracy, Reasonableness, Support), created by Dr. Robert Harris, is a system for evaluating the quality of research information.
At the beginning of the year, Grayson had $45 in savings and saved an additional $19 each week thereafter. Jacob started the year with $90 and saved $16 every week. Let GG represent the amount of money Grayson has saved tt weeks after the beginning of the year and let JJ represent the amount of money Jacob has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the who has more money saved after 18 weeks.
Answer:
The will have the same amount $ 387
Step-by-step explanation:
Grayson: y = 19x + 45
Jacob: y = 16x + 90
Grayson: y = 19(18) + 45
342 + 45 = $387
Jacob: y = 16(18) + 90
288 + 90 = $378
two companies listed a revenue for the year in their respective websites. Company a has revenue in the amount of 1.6×10^6 and company b has revenue in the amount of 7.2x10^8. how many Times greater is the revenue for company b?
guys pls help me!!!!!!!
Answer:
40
Step-by-step explanation:
alternate interior
Answer:
its 40 degrees
Step-by-step explanation:
its said by the top person :)
| -5 -(-8) | i need help with algabraic expression
Solve for m < DBC.......
Answer:
∠ DBC = 34°
Step-by-step explanation:
∠ DBC = ∠ ABC - ∠ ABD = 64° - 30° = 34°
what is the answer to 1/4 - (-1/6)
Answer:
5/12
Step-by-step explanation:
1/4 + 1/6 = (6+4)/24 = 10/24 = 5/12
why +1/6?
because: - (-) = +