Three children's tickets to the circus cost
$53.85. Two adult tickets to the circus
cost $63.90. How much more does
1 adult ticket cost than 1 children's ticket?

[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]

Answer:

5/12

Step-by-step explanation:

1/4 + 1/6 = (6+4)/24 = 10/24 = 5/12

why +1/6?

because: - (-) = +

Answer:

4m, 6m, 7m, 5m

Step-by-step explanation:

To find perimeter you just add the side lengths togeather.

Answer:

10% = 0.1 x 400 = 40

400 - 40 = 360$

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

Answer:

6/13

Step-by-step explanation:

because if you do 10-4=6

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:

Answer:

B is the correct answer, The first choice (which you chose) is the incorrect answer.

Step-by-step explanation:

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.

Answer:

no i cant

Step-by-step explanation:

i just need points uwu

baka sussy

Answer:

40

Step-by-step explanation:

alternate interior

Answer:

its 40 degrees

Step-by-step explanation:

its said by the top person :)

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.

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

Answer:

0.315

Step-by-step explanation:

act like the fraction is a division problem divide 6 by 19.

this decimal is a repeating decimal so it will never end rounded to the thousandth place it is 0.315

Answer:

(2,4)

X always comes before Y. So the X is 2 and the Y is 4, so (2,4).

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).

Answer:

400 mph

Step-by-step explanation:

1200/3 = 400 miles per hour

============================================================

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]

Answer:

Step-by-step explanation:

Required function is:

The matching option is C

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:

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

Answer:

∠ DBC = 34°

Step-by-step explanation:

∠ DBC = ∠ ABC - ∠ ABD = 64° - 30° = 34°

Answer:

x=3 or C

Step-by-step explanation:

I just did the math and got it correct on my FLVS quiz

Answer:

BC = 20

Step-by-step explanation:

Since B is the midpoint of AC , then

AB = BC = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 40 = 20

Answer:

$ 198

Step-by-step explanation:

450 + 0.06x = 3750

0.06x = 3750 - 450

x = (3300 * 0.06) = 198

x = 198

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

The Correct choices are :

Answer:

yfyffyfyfyg

Step-by-step explanation:

xgsxfuftuxfyfjfyfyfyffyfyfygyfdtdtdhfgjhtuydxfyyxff