On a morning in December, Carl wakes up and checks the thermometer. He reads that it is -10°F. In two hours he checks and the temperature has risen 4°F. In another three hours the temperature has risen 7°F. At the last time, he checks the thermometer, what is the temperature? Also writes an addition equation that models this situation​

Answer:

a = a

b = b

c = c

Step-by-step explanation:

Formula: [tex]a^2+b^2=c^2[/tex]

C is always the largest number

a times a + b times b = c times c

[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:

2% of 1kg

Step-by-step explanation:

20g/1kg x 100

= 20g/1000g x 100

1/50 x 100

=2

Therefore, 20g is 2% of 1kg

Hope it helps you

Answer:

2%

Step-by-step explanation:

1kg=1000g

=20/1000×100%

=2%

Answer:

Sidney made $20 less than three times Caseys weekly salary. If x represents Caseys weekly salary, write an expression for Sidney's weekly salary.

Step-by-step explanation:

x = Caseys weekly salar

3x = three times Caseys weekly salary

'3x - 20' is the expression for Sidney's weekly salary

I hope this helps :)

2

Step-by-step explanation:

:) hope its correct lol

Answer:

x=5

Step-by-step explanation:

Since the angle with the expession and the one that has a measure of 58 and corresponding, they have equal measure. This helps us write an equation-

12x-2=58

now, solve

-2+2=0, 58+2=60

12x=60

12x/12=60/12

x=5

hope this helps:)

please crown me brainliest!!!

Answer:

12x-2°=58°

12x=58°+2°

=60°

x=60÷12

=5

Answer:

apollo 1

Step-by-step explanation:

Answer: The input is 5.

Step-by-step explanation: Since both are functions of f(x), you can set 9x-27 equal to 18 and then solve the equation. 9x-27=18, add 27 to both sides to get 9x=45, divide both sides by 9, x=5.

:)

Answer:

A, 38cm

Step-by-step explanation:

since u have to take 15cm (the length) then multiply by 2 to take both the sides of the rectangle

then you have to take the width 2 times to take the perimeter and add it up. so 15x2 and 4x2 added is 38. there!

Answer:

immm go with A

Step-by-step explanation:

if im wrong plz tell me

Answer:

5/8

Step-by-step explanation:

1/4 (2/2)=2/8

3/8 (already simplified)

2/8+3/8=5/8

Answer:

5

Step-by-step explanation:

(8+4+5+4+9+0) /6 = 5

Answer:

true its true ..

Step-by-step explanation:

we can know our profit or loss by our selling price

Answer:

hi baby its me nick this is my new account

Step-by-step explanation:

Answer:

the answer is 6.8 litres

Step-by-step explanation:

3.4 × 2 = 6.8

Answer:

559.41 miles/hour

Step-by-step explanation:

Just use a calculator

Answer:

HF for shoo

Step-by-step explanation:

Answer: there are two variations to the answer depends how you solve it    

Answer: (-9,-8) and (5,-4)

Step-by-step explanation:

I'm not 100% sure but i think this is the answer

Answer:

-3 < x < -1/2

Step-by-step explanation:

4<-2x+3<9

1<-2x<6

-1/2 > x > -3

so

-3 < x < -1/2

x = 36

Answer:

Step-by-step explanation:

Q

(

2

,

1

)

and

R

(

8

,

13

)

is partitioned from

Q

to

R

into a

1

:

2

ratio at point

Z

. What are the coordinates of

Z

?

Answer:

Mean = 90, Median = 93, Mode = 90, Range = 6

Step-by-step explanation:

Mean:

96 + 90 + 94 + 93 + 90 = 463

463 ÷ 5 = 92.5

92.5 to nearest tenth = 90

Mean = 90

Median:

90, 90, 93, 94 ,96

Median = 93

Mode

96, 90, 94, 93, 90

Mode = 90

Range:

96 - 90 = 6

Range = 6

Answer:

234567

Step-by-step explanation:

Answer:

AP equation:

Based on the first two terms, we have:

The equation is:

Next two terms are:

Answer:

the desired element lies in the 3rd row and 1st column, and is 25.

Step-by-step explanation:

We are given a 3 by 3 matrix:  There are 3 rows and 3 columns.

The symbol a       represents the element of this matrix that lines in row m and column 1.  Thus, the desired element lies in the 3rd row and 1st column, and is 25.

                      mn