Need answers with explanation

[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:

This transformation is known as a vertical stretch. This is the graph of a transformation of \begin{align*}y=x^2\end{align*}. The points are plotted from the vertex as right and left one and down one-half, right and left 2 and down two, right and left three and down four and one-half

Answer:

x = 11

Step-by-step explanation:

1. Because this is a straight angle, (11x + 7)° and (5x - 3)° add up to 180°.

2. (Solving)

Step 1: Simplify both sides of the equation.

Step 2: Subtract 4 from both sides.

Step 3: Divide both sides by 16.

Therefore, x = 11! I hope this helped you.

32 kilometers + 35 kilometers + 17 kilometers

= 67 kilometers + 17 kilometers

= 84 kilometers

#LearnWithEXO

Answer:

84 kilometers

I hope it will help you po

Answer: Jose incorrectly rounded $2.85 down to $2. The estimate should $18.

Step-by-step explanation:

lol i had this question

Answer:

I think its 10 and ethier 11 or 12

Answer:

299,792,460

Step-by-step explanation:

just round to the nearest 10th

Answer:

The speed of light is exactly 299,792,458 m/s because that is how a meter is defined. A meter is defined as the distance light travels in 1/299792458 seconds in vacuum. Why was this particular number chosen? To keep the definition of meter consistent with the old standard which was an actual physical bar. The length of this bar was arbitrary though.

Step-by-step explanation:

Your welcome :)

A ratio will just be trying to find whole number versions of these decimals and then compare them side by side (always divide the larger number by the smaller number).

Therefore:

[tex]\frac{0.0000275}{0.000005}=5.5=\frac{5.5}{1}[/tex]

However, this isn't a proper ratio. Generally, ratios are whole numbers. Since it's 5.5, we can easily make this a whole number by multiplying it by 2. Keep in mind though, what we do to one number we do to the other! So:

[tex]\frac{2}{2}(\frac{5.5}{1})=\frac{2*5.5}{2*1}=\frac{11}{2}[/tex], technically this is a better format since it's whole numbers, but it gives you the ratio (11:2) which is a bit tougher to interpret than (5.5:1)

Therefore, the ratio we'll use is 5.5:1 for simplicity's sake:

From this ratio, we can see that the red tablet is 5.5x the size of the white tablet.

Hope this helps! :)

Answer:  x3+y3+z3=k

Step-by-step explanation:

x3+y3+z3=k                                    

You're welcome mr/ms

Answer:

15, 16, 17

Step-by-step explanation:

let the consecutive numbers be n , n + 1 , n+ 2 , then

n + n + 2 = 32 ( sum of first and third )

2n + 2 = 32 ( subtract 2 from both sides )

2n = 30 ( divide both sides by 2 )

n = 15

n + 1 = 15 + 1 = 16

n + 2 = 15 + 2 = 17

The 3 numbers are 15, 16, 17

Step-by-step explanation:

let the 1st and 2nd consecutive number be

x , x + 1 , x + 2

their sum = 32

so, x + x + 2 = 32

→ 2x + 2 = 32

→ 2x = 32 - 2 = 30

→ x = 30/2 = 15

so,

1st and 3rd consecutive number is

x = 15

x + 2 = 15 + 2 = 17

as they are consecutive number so 2nd number is 16

and a/q sum of 1st and 3rd number is 32

15 + 17 = 32

hope this answer helps you dear...take care and may u have a great day ahead!

Answer D.

Step-by-step explanation:

D.

Line segment L'M' has a slope of 6 and passes through point H.

Given that line segment LM is dilated by a scale factor of to form L'M'. Statement D). is true.

The dilation of a line segment is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than 1 (k > 1), the image will be larger than the pre-image, making the segments (sides) of the image longer than the corresponding sides of its pre-image (an enlargement).

When a line segment gets dilated, it gets longer or shorter. But, the slope does not change. Also, the center of dilation which lies on the line segment, stays on the line only. Thus, D). is true.

Learn more about dilation of a line segment here

https://brainly.com/question/21426541

#SPJ2

Answer:

y = -x- 5

Step-by-step explanation:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-2=-1(x-(-7))[/tex]

[tex]y-2=-(x+7)[/tex]

[tex]y=-x-7+2[/tex]

[tex]y=-x-5[/tex]

I hope this help you

Answer:

6/13

Step-by-step explanation:

because if you do 10-4=6

Answer:  y = -(9/5)x - 1

Step-by-step explanation:

Rewrite the equation in standard form:  y = (5/9)x+(8/9).  [y=mx+b]

A line perpendicular to this would have a slope that is the negative inverse of the original slope (5/9), which would make it -(9/5).  The y-intercept would also change, but we don't know the value, yet.  For now, we'll use "b" for the y-intercept.  This results in a perpendicular line:

y = -(9/5)x + b

We can calculate b, the y-intercept, by using the point (-5,8) and solving for b.

8 = -(9/5)*(-5) + b

8 = (9) + b

b = -1

The line perpendicular to 5x−9y=−8 that passes through the point ​(−5​,8​) is

y = -(9/5)x - 1

Answer: I think it's 32.8

Step-by-step explanation:

Step-by-step explanation:

7^2+8^2=113

Then square root 113 which is 10.63 to 2.d.p

So x=10.63

Answer:

68.48

Step-by-step explanation:

12.45*5.5=68.48

Answer:

19xyz

Step-by-step explanation:

First, let us just forget about the xyz at the end of each number. Now, we just have the simple addition problem 3 + 7 + 9. First. let us do 3 + 7, which gives us 10. Now, let us take our 10 and add the 9 to it. 10 + 9 is 19. Now, we can add our xyz back to the equation. Now, we have 19xyz. As we do not know anything about what x, y, or z equals, nothing further can be done with this equation. Therefore, the answer is 19xyz.

Hope this helps! :D

Answer: 19xyz

Step-by-step explanation:

I literally just learned this right now bc i'm in school

Answer:

C=3/2

Step-by-step explanation:

C4-1=5

Add 1 onto both sides

C4=6

Divide each side by 4

C=6/4

Simplify (Divide by 2)

C=3/2

Answer:

first 7 then 3  5  4  6

Step-by-step explanation:hope it helps

Answer:

A. 5/7 x

D. 7/9x

Step-by-step explanation:

I hope this helped ♡ sorry if im wrong

Answer:

18 cards

Step-by-step explanation:

TO solve subtract:

130-4= 126

Then divide:

126/7 =18

Check your work:

18*7= 126

126+4= 130

Hope this helps!

Answer:

The 2nd answer is the correct

Step-by-step explanation:

Hope this helps:)

Answer

A) Morning: 2:45am. / afternoon: 2:45pm

B) Morning: 6:05am / afternoon: 6:05pm

c) Morning: 9:15am. / afternoon: 9:15pm

d) Morning: 11:35am. / afternoon: 11:35pm

Step-by-step explanation:

Answer: They answer is A (-1,0)

Step-by-step explanation:

I plotted (-3,2) and (1,-2) and found they midpoint of it.

Answer:

9(413)2= 7434 and 6(593)=3558

Step-by-step explanation:

Hope this helps