[tex] \sf \: please \: answer \: and \: do \: not \: spam[/tex]
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It's based on integrals....
Hello Carousel!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve the integral.[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex]
First, let's take I as ⇨ [tex]\tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex].
[tex]\tt \:I = \int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x +1}} \: dx \\\tt \: I =\int \: \frac{ x + 2 }{( {x}^{2} + 2x + 1 + x + 2) \sqrt{x + 1}} \: dx \\ \tt \:I =\int \: \frac{ x + 2 }{( ({x + 1}^{2}) + x + 2) \sqrt{x + 1}}[/tex]
Let, x + 1 = m² => dx = 2mdm.
[tex]\tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: m} 2mdm \\ \tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: \bcancel{ m}} 2 \bcancel{m}dm \\ \tt \: I = \: \int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 } 2dm[/tex]
Now, divide the numerator & denominator by m²....we'll get it as...
[tex]\tt \:I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{ {m}^{2} + 1 + \frac{1}{ {m}^{2} } } \: dm \\\tt \: I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{( {m}^{2} + \frac{1}{ {m}^{2} } - 2) + 3} \: dm \\\tt \: I =2\int \: \frac{ (1 + \frac{1}{ {m}^{2} }) \: dm }{ ({m} - \frac{1}{ m } ) ^{2} + 3} [/tex]
Now, let m - 1/m be t => (1 + 1/m²) dm = dt
[tex]\tt \:I =2\int \: \frac{ dt}{ {t}^{2} + 3 } \\ \tt \:I = 2\int \: \frac{ dt}{ {t}^{2} + ( \sqrt{3}) ^{2} }[/tex]
We know, [tex]\tt \:\int \: \frac{dx}{ {x}^{2} + a ^{2} } = \frac{1}{a} tan ^{ - 1} (\frac{x}{a} ) + c[/tex]...therefore...
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{t}{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 1}[/tex]
Now, substitute the value of 't' in eq. 1..we'll get..
[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{m - \frac{1}{m} }{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 2}[/tex]
Now, substitute the value of 'm' in eq. 2...we'll get...
[tex] \tt \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{ \sqrt{x + 1} - \frac{1}{ \sqrt{x - 1} } }{ \sqrt{3} } ) + c \\ \tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x + 1 - 1}{ \sqrt{3} \sqrt{x - 1} } ) + c \\ \boxed{\boxed{ \bf \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x }{ \sqrt{3 (x - 1} )} ) + c }}[/tex]
The correct answer is Option B.__________________
The question is really long & tricky but once you get the hang of it you'll be good. Good luck!__________________
Hope it'll help you!
ℓu¢αzz ッ
A function f(x) is graphed on the coordinate plane at is the function rule in siope-intercept form? Enter your answer in the box f(x) =
9514 1404 393
Answer:
y = 2x +1
Step-by-step explanation:
The line rises 2 units for each 1 unit to the right, so its slope is ...
m = rise/run = 2/1 = 2
The line crosses the y-axis at y = 1, so the y-intercept is ...
b = 1
Then the slope-intercept form equation is ...
y = mx + b . . . . . . . for slope m and y-intercept b
y = 2x + 1 . . . . . . . . fill in the known values
what is the answer when you round 522 254 to the nearest 10
Answer:
522250
How to round to the nearest tenth:
Whenever you want to round a number to a particular digit, look only at the digit immediately to its right. For example, if you want to round to the nearest tenth, look to the right of the tenths place: This would be the hundredths place digit. Then, if it is 5 or higher, you get to add one to the tenths digit. If it is 4 or lower, the tenths digit remains the same.
For example, 3.58 can be rounded to 3.6 because the hundredths place digit, 8 is greater than or equal to 5.
3.32 would be rounded to 3.3, because the hundredths place digit, 2, is less than 5.
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2).
Use the graph to determine the input value for which f(x) = g(x) is true.
x = 0.5
x = 1
x = 1.5
x = 2
Answer:
1.5 Or C :)
Step-by-step explanation:
Write the number 1, 256 in expanded form.
0 10,000 + 200 + 50 + 6
0 1,000 + 200 + 50 + 6
0 100 + 200 + 50 + 6
O 100 + 20 + 5 + 6
Answer:
1,000 + 200 + 50 + 6
Question 1 (Essay Worth 10 points)
(03.03 MC)
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 4(1.08)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)
Answer: HEre finnaly this is right..
Part A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function?
0≤x≤8
Part B: What does the y-intercept of the graph of the function f(m) represent?
the length at the start of the study
Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent?
6.86−5.047−3=1.82
it represents the average growth in length of the fish from the 3rd month to the 7th month of the study
Step-by-step explanation:
whats the y intercept
Answer:(0,4)
Step-by-step explanation:
BEST ANSWER WILL GET BRAINLIEST. Consider the table below. For what value of x does f(x)=-1f(x)=−1 ?
The correct answer would be 3. f(x) = -1, so you got to find the -1 in the y row of the table and just say that x =3 if y =-1.
Answer:
x = 3
Step-by-step explanation:
The question is asking for which value of x gives -1
You don't have an equation, however you do have a table of values
Y is similar to f(x) in the sense that it is the output, while x is the input.
All you must do is see where y = -1, this is the same for when f(x) = -1
So, there is only one moment where y = -1, which is when x = 3
With this, we can conclude that for the value of x = 3, f(x) = -1
The U.S. population in 1910 was 92 million people. In 1990, the population was 280 million. This could either be a linear or exponential model. You will create both and then look at the true population increase and decide which model is closer the the true growth.
The actual U.S. population data (in millions) was:
Which model provides a better forecast for the U.S. population for the year 2030, linear or exponential or neither?
Question 5 options:
Linear model
Exponential model
Neither
Answer:
The linear model means that there is a uniform increase and in this case of US population from 92 million people in 1910 to 250 million people in 1990 .
This means an increase of 250 − 92 = 158 million in 1990 -1910 = 80 years or 158 80 = 1.975 million per year and in x years it will become 92 + 1.975 x million people. This can be graphed using the linear function 1.975 ( x − 1910 ) + 92 ,
graph{1.975(x-1910)+92 [1890, 2000, 85, 260]}
The exponential model means that there is a uniform proportional increase i.e. say p % every year and in this case of US population from 92 million people in 1910 to 250 million people in 1990 .
This means an increase of 250 − 92 = 158 million in 1990 − 1910 = 80 years or
p % given by 92 ( 1 + p ) 80 = 250 which gives us ( 1 +p ) 80 = 250 92 which simplifies to p = ( 250 92 ) 0.0125 − 1 = 0.0125743 or 1.25743 % .
This can be graphed as an exponential function 92 × 1.0125743 ( x − 1910 ) , which gives population in a year y and this appears as graph{92(1.0125743^(x-1910)) [1900, 2000, 85, 260]}
Step-by-step explanation:
Hope this helps
Please answer correctly !!!!!!!!!!!!!! Will mark brainliest answer !!!!!!!!!!!!!!!
Answer:
where is your Question??????
Help me please!! i beg
Eat the Legendry Fruit: And play King legcy
Step-by-step explanation:
please solve the equation and describe what mistake asif did
Answer:
1/2
Step-by-step explanation:
8×+1=5
8×=5-1
8×=4
×=4/8=1/2
estaba previsto destinar 3/14 de partes de una finca a plazas de aparcamiento pero finalmente han destinado 3/4 de lo previsto a zonas ajardinadas que fraccion de la finca se ha destinado a plazas de aparcamiento
Queremos ver que fracción de la finca se ha destinado a plazas de aparcamiento.
La solución es:
La fracción de la finca que se destina a plaas de aparcamiento es 3/56
Sabemos que originalmente se iba a destinar 3/14 del total de la finca a plazas de aparcamiento, pero finalmente se destino 3/4 de lo previsto a zonas ajardinadas.
Es decir, se destino 3/4 de los 3/14 del total de la finca a zonas ajardinadas, entonces el 1/4 restante se dedico a plazas de aparcamiento, esto da:
(1/4)*3/14 = 3/56
La fracción de la finca que se destina a plaas de aparcamiento es 3/56
Sí quieres aprender más, puedes leer:
https://brainly.com/question/16649102
Solve the following quadratic equation.
d²-5d+6=0
Answer:
[tex]d=2[/tex] and [tex]d=3[/tex]
Step-by-step explanation:
[tex]d^2-5d+6=0[/tex]
[tex](d-2)(d-3)=0[/tex]
[tex]d=2[/tex] and [tex]d=3[/tex]
PLEASEEEEEE HELPPPPPPPPP
[tex]5x + 3 = - 9 \\ = > 5x = - 9 - 3 \\ = > 5x = - 12 \\ = > x = \frac{ - 12}{5} \\ = > x = - 2 \frac{2}{5} [/tex]
Answer:Option A .
[tex] - 2 \frac{2}{5} [/tex]
hello can anyone help?
Harry drives 182 miles.
His average speed is 35 miles per hour.
How long does the journey take?
Give your answer in hours and minutes.
Answer:
5 hours 12 minutes
Step-by-step explanation:
Amount of time the journey took = 182 miles ÷ 35 miles/h
= 5.2h
= 5h 12mins
is 513 a composite number?
Answer:
yes, since 513 has more than two factors
have a spook-tastic day
Step-by-step explanation:
why is 3/8 bigger than 3/12
Answer:
3/8 is is bigger then 3/12
Step-by-step explanation:
The reason is that 3/12 is equivalent to 2/8 and 3/8 is equivalent to 6/16
Sorry if its wrong! ^^""
As, 0.375> 0.25, so, 3/8 is greater than 3/12.
Here, we have,
To get the answer, we first convert each fraction into decimal numbers.
We do this by dividing the numerator by the denominator for each fraction as illustrated below:
3/8 = 0.375
3/12 = 0.25
Then, we compare the two decimal numbers to get the answer.
0.375 is greater than 0.25.
i.e. 0.375> 0.25, as 0.375 - 0.25 = 0.125
Therefore, 3/8 is greater than 3/12.
Hence, As, 0.375> 0.25, so, 3/8 is greater than 3/12.
To learn more on subtraction click:
brainly.com/question/2346316
#SPJ6
3. The difference of two-thirds of a number x and
6 is at least -24. Which inequality represents all
possible values for x?
The inequality that represents all possible values for x is x ≥ -27.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The given statement can be written in terms of inequality as,
2/3x - 6 ≥ -24
=> 2/3x ≥ -24 + 6
=> 2/3x ≥ -18
=> x ≥ -27
Hence, the inequality expression for the given problem can be written as x ≥ -27.
To know more about linear inequality click on,
https://brainly.com/question/11897796
#SPJ2
m/5=3(2m+1) verbal expression
Answer:
m = -15/29
Step-by-step explanation:
1) Distribute
[tex]\frac{m}{5} =6m+3[/tex]
2) Subtract 6m from both sides of the equation
[tex]\frac{m}{5} -6m=6m+3-6m[/tex]
3) Simplify
a. Find common denominator
[tex]\frac{m}{5} +\frac{5(-6)m}{5} =6m+3-6m[/tex]
b. Combine fractions with common denominator
[tex]\frac{m+5(-6)m}{5} =6m+3-6m[/tex]
c. Multiply the numbers
[tex]\frac{m-30m}{5} =6m+3-6m[/tex]
d. Combine like terms
[tex]\frac{-29m}{5} =6m+3-6m[/tex]
e. Combine like terms
[tex]\frac{-29m}{5} =3[/tex]
4) Multiply all terms by the same value to eliminate fraction denominators
[tex]5 *\frac{-29m}{5} =5*3[/tex]
5) Cancel multiplied terms that are in the denominator
[tex]-29m=5*3[/tex]
6) Multiply the numbers
[tex]-29m=15[/tex]
7) Divide both sides of the equation by the same term
[tex]\frac{-29m}{29} =\frac{15}{-29}[/tex]
8) Simplify
a. Cancel terms that are in both the numerator and denominator
[tex]m=\frac{15}{-29}[/tex]
b. Divide the numbers
[tex]m=-\frac{15}{29}[/tex]
HELP PLEASE ASAP!!! PLEASE AND THANKS
Answer:
x >= 12
Step-by-step explanation:
2x + 7 <= 3x - 5
7 + 5 <= 3x - 2x
12 <= X
Based on what you've read, answer the following questions.
1. Laura bought a rectangular rug for her living room. It measures 9 feet long and 8 feet wide. What is the area of her rug?
2. One can of paint will cover an area of 400 square feet. Will one can of paint be enough to cover an exterior brick wall that is 48 feet long and 9 feet high?
3. Roger owns a one-acre piece of land. The length of the land is 484 feet. What is the width of his property? (Hint: One acre = 43,560 square feet)
4. The Animal World Safari Park is a rectangular piece of land with an area of 323 square miles. The length of the park is 17 miles. What is its width?
5. Penny is making a square tablecloth that has an area of 49 square feet. What is the length of one of its sides?
Answer:
1. The area is 72 ft².
2. No, one can of paint will not be enough.
3. The width of his property is 90 ft.
4. The width of the park is 19 miles.
5. The length of a side is 7.
Step-by-step explanation:
We will use the formula Area = length x width to answer the questions.
1. 9 x 8 = 72
2. 48 x 9 = 432, 432 > 400
3. 43560/484 = 90
4. 323/17 = 19
5. √49 = 7
Hope this helps!
Answer:
1. The area is 72 ft².
2. No, one can of paint will not be enough.
3. The width of his property is 90 ft.
4. The width of the park is 19 miles.
5. The length of a side is 7.
Step-by-step explanation:
3(x − 5) − 5x = −25 + 6x
x=5/4
the explantion would be to long lol
Answer:
x = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
3(x - 5) - 5x = - 25 + 6x ← distribute parenthesis and simplify left side
3x - 15 - 5x = - 25 + 6x
- 2x - 15 = - 25 + 6x ( subtract 6x from both sides )
- 8x - 15 = - 25 ( add 15 to both sides )
- 8x = - 10 ( divide both sides by - 8 )
x = [tex]\frac{-10}{-8}[/tex] = [tex]\frac{5}{4}[/tex]
Saved
Question 11 (5 points)
What's 21-91 - 1-21?
O A) -20
B) 16
C) 20
D) -18
Any one know the answer I don’t know it
Danica and Irma are flying kites. Danica's kite is 7 times as high as Irma's kite. Danica's kite is 273 feet high. How high is Irma's kite?
A .280 feet
B. 39 feet
C. 1,911 feet
D. 40 feet
Answer:
39
Step-by-step explanation:
273/7=39
Answer:
What is 39 feet
273 Divided By 7= 39 Feet
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Have a happy day!
By which rule are these triangles congruent
A. AAS
B. ASA
C. SAS
D. SSS
Answer:
option D
Step-by-step explanation:
this trianle will be congurent by SSS method easily
Answer:
Option D.SSS These triangles congruent with SSS property
Find (i) x ,y ,z and w (ii) x + y + z + w
Please lemme know with explanation
Answer:
x = 60°, y = 100°, z = 120°, w = 80°
Step-by-step explanation:
x and 120° are adjacent angles on a straight line and sum to 180°
x + 120° = 180° ( subtract 120° from both sides )
x = 60°
Similarly
y + 80° = 180° ( subtract 80° from both sides )
y = 100°
and
z + 60° = 180° ( subtract 60° from both sides )
z = 120°
--------------------------------------------------------------------
The sum of the interior angles in a quadrilateral = 360°
sum the interior angles of the quadrilateral and equate to 360°
60° + 80° + 120° + 4th angle = 360°
260° + 4th angle = 360° ( subtract 260° from both sides )
4th angle = 100°
w and 100° are adjacent angles on a straight line and sum to 180° , so
w + 100° = 180° ( subtract 100° from both sides )
w = 80°
helppppppppppppppppppppppppppppppppppp
Answer:
24 kilograms of catfish
Step-by-step explanation:
Take the percentage of catfish as a decimal or fraction and multiply it by the total amount of fish caught. The percent of catfish is 40% which is the same thing as 0.4. Multiply that by the total 60 kg of fish to get 24 kg of catfish.
A real root of X3 – 3x2 + x + 7 = 0 lies between two consecutive integers.
Find these two integers.
Answer:
B. between -2 and -1
Step-by-step explanation:
Brainlyist please
find the square root of 20 upon 121
Answer:
heres the square root of 20 4.47214 but i dont know what else to do for this answer. (sorry)
Step-by-step explanation:
√20 = √(4 * 5) = √4 * √5 = 2√5 ≈ 4.47214