Answer:
2.899
Step-by-step explanation:
Given that:
[tex]f' (x) =3 tan ^{-1} (x^2 -3x +2)[/tex]
[tex]\text{applying integration on both sides with respect to x}[/tex]
[tex]\int \limits ^{3}_{1}} f'(x) \ dx = \int ^3_1 3tan ^{-1} (x^2 -3x+2) \ dx[/tex]
[tex]f(3)-f(1)= 3 \int ^3_1 3tan ^{-1} (x^2 -3x+2) \ dx[/tex]
[tex]f(3) = \dfrac{\pi}{2}+3\int^{3}_{1} tan^{-1} (x^2 -3x+2)dx ---(1)[/tex]
[tex]\text{consider } \ \ 3\int^{3}_{1} tan^{-1} (x^2 -3x+2)dx[/tex]
[tex]h = \dfrac{b-a}{n}[/tex]
[tex]where; n = 10 , a =1, b= 3[/tex]
[tex]h = \dfrac{3-1}{10}[/tex]
[tex]h = \dfrac{2}{10}[/tex]
[tex]h = 0.2[/tex]
[tex]\text{The value of x and corresponding } y = 3tan^{-1}(x^2-3x+2) \ are:[/tex]
x 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
y f(0) f(1.2) f(1.4) f(1.6) f(1.8) f(2.0) f(2.2) f(2.4) f(2.6) f(2.8) f(3)
By simpson's rule:
[tex]\int \limits ^3_1 \ 3 tan^{-1} (x^2-3x+2) dx \simeq \dfrac{h}{3}(y_o+y_{10}) +4(y_1+y_3+y_5+y_7+y_9)+2(y_2+y_4+y_6+y_8)][/tex]
[tex]=\dfrac{0.2}{3}\Big[(0+3.3214)+(-1.9039+2.8265+1.4133+6.1259+11.5657)+2(-1.4133-0.9519+1.4133+4.5899)\Big][/tex]
[tex]= 1.32804[/tex]
[tex]\text{From}; f(3) = \dfrac{\pi}{2}+1.32804 \\ \\ f(3) = 2.89883633 \\ \\ \mathbf{f(3) \simeq 2.899}[/tex]
Trapezoidal rule is used to evaluate the area of the curve by using various strips of equal width which is in the form of trapezoids. The value of [tex]f(3)[/tex] is 2.8989.
Given information
In the given problem [tex]f[/tex] is the function such that,
[tex]f(1)=\dfrac{\pi}{2} \\[/tex]
The differentiated function is,
[tex]f'(x)=3\tan^-(x^2-3x+2)[/tex]
Integrate the above equation with respect to the x,
[tex]\int\limits^3_1 {f'(x)} \, dx =\int\limits^3_1 {3\tan^-(x^2-3x+2)} \, dx\\f(3)-f(1) =\int\limits^3_1 {3\tan^-(x^2-3x+2)} \, dx\\f(3) =3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx +f(1)\\f(3) =3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx +\dfrac{\pi}{2}[/tex] .........1
Let the above equation is the equation number 1.
Let the integrated function,
[tex]y=3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx[/tex]
Solve the above equation using the trapezoidal rule.
Trapezoidal rule-Trapezoidal rule is used to evaluate the area of the curve by using various strips of equal width which is in the form of trapezoids.
In the given problem,
[tex]h=\dfrac{b-a}{n}[/tex]
Use this formula for the integrated function,
[tex]h=\dfrac{3-1}{10}\\h=0.2[/tex]
Use the Simpson formula to solve the above equation,
[tex]=3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx[/tex]
[tex]=\dfrac{h}{3} (y_0+y_{10})+4(y_1+y_3+y_{5}+y_7+y_{9})+2(y_2+y_{4}+y_6+y_{8})[/tex]
Find the value of y by putting the values in the given formula. Thus,
[tex]=\dfrac{0.2}{3} (0+3.3214)+4(-1.9039+2.8266+1.4133+6.1259+11.5657)+2(-1.4133-0.9519+1.4133+4.5899)\\=1.32804[/tex]
Put this value in equation 1,
[tex]f(3) =1.30824 +\dfrac{\pi}{2}\\f(3)=2.8989[/tex]
Thus the value of [tex]f(3)[/tex] is 2.8989.
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Find the missing angle measurement of a triangle with these angles:
45°, 35.8°, x°
a = 45 b = 35.8 c = 57.503
Four siblings took turns babysitting their young cousin. If they divided the 5 hour shift evenly, how long did each one babysit for? Give the answer in hours and minutes.
Can someone help me please thank you!
Answer:
135
Step-by-step explanation:
That's the answer.........
HELP PLS I GIVE BRAINLIEST
Answer:
1. $200
2. $65
3. $70
Step-by-step explanation:
1. 4x50=200
2. 200-135= 65
3. 135-65= 70
How do I do this please help me
Answer:
Answer of first one is. = angle 3
answer of second one is = angle 4
answer of third one is = angle 2
angle of fourth one is = 5
and last.one is angle 1
Can you guys help me? please
Answer:
3 square root 2.
Step-by-step explanation:
I think the answer is b (3 square root 2). the Pythagorean therom states that B^2+ B^2= C^2. we know that c squared is 36. 3 square root 2 is approximately 4.24. ( this squared is 17.98). 17.98 + 17.98 = 35.96. If i round this up, it is 36.
please help
travelling 14m to the right first and travelling 19m to the left . calculate the final position
Answer:
5 meters to the left
Step-by-step explanation:
Given that :
First travel : 14 meters to the right
Second travel : 19 m to the left
Final position :
First travel - Second travel.
(14 m - 19m)
Final position = - 5 m
-5m = 5 meters to the left.
Tacos from the taco truck or 60% off on Tuesdays Erica by the taco for 1.50 on Tuesday she wants to know the regular price of a taco quick answer
Answer:
3.75
Step-by-step explanation:
i did the lesson its correct :)
Answer:
Regular Price: 100%
$3.75
Sale price: 40%
$1.50
Discount:
60%
$2.25
Which equation can be used to find the regular price, r, of a taco?
1.5 = 0.4r
Step-by-step explanation:
Read the answers correctly, or you might be typing in the wrong answer.
Everything is all correct, Thank me later :)
HELP ASAP. pls ❤️ if u do this i’ll luv u 4ever
Answer:
A' ( 2,3)
B' ( 5,5)
C ( 7,3)
D'(5,2)
Which of the following expressions are equivalent to 0.7 * -4 * 0.4
Answer:
0.4
Step-by-step explanation:
Answer:
A and B
Step-by-step explanation: Khan
Jaxson drives 15 miles in 10 minutes. If he drove one hour in total at the same rate, how far did he go?
Answer:
90 miles
Step-by-step explanation:
15 miles/10 minutes = x miles/60 minutes
10*6=60 so 15*6=90
The point (2, 20) lies on the graph of y = kx'. Write the value of k.
Step-by-step explanation:
Y = 20 , X = 2
put in the equation
Y = KX ( given )
20 = K × 2
20/2 = K
10 = K
A number w increased by 6 is at least 24. Using an inequality
Answer:
x<24
Step-by-step explanation:
[tex]w + 6 \geqslant 24[/tex]
cube root(8+ 3 root 21)+ cube root (8-3 root 21)
plese give good answer with explanation or I will report
Answer:
[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex] = 1Step-by-step explanation:
Given[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex]To find The value of the expressionSolutionLet's rewrite the given as:
[tex]\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8}[/tex]Let the value is m and the expressions under 3rd roots are a and b, then we have
a = 3√21 + 8, b = 3√21 - 8m = ∛a - ∛bCube the both sides:
m³ = (∛a - ∛b)³m³ = a - b - 3[tex]\sqrt[3]{a^2b}[/tex] + 3[tex]\sqrt[3]{ab^2}[/tex]Simplify in bits:
a - b = 3√21 + 8 - 3√21 + 8 = 16ab = (3√21 + 8)(3√21 - 8) = 9*21 - 64 = 125∛ab = ∛125 = 5So the expression becomes:
m³ = 16 - 3[tex]\sqrt[3]{125a} + \sqrt[3]{125b}[/tex]m³ = 16 - 15∛a + 15∛bm³ = 16 - 15(∛a - ∛b)m³ = 16 - 15mSolve for m:
m³ + 15m - 16 = 0m³ - 1 + 15m - 15 = 0(m - 1)(m² + m + 1) + 15(m - 1) = 0(m - 1)(m² + m + 16) = 0m - 1 = 0, m² + m + 16 = 0m = 1 is the only real root, the quadratic equation has no real rootsThe answer is 1
My lil sister said she needs help with ALL of the questions..........if you help i will give you brainliest
Answer:
MONDAY: 2 hours
Tuesday: $34.65
Thursday: -54
Friday: 5 complete bags
Sorry that I did not do the question below wednesday but I still hope this helps.
Pls mark me brainliest.
2(4x + 2) = 12
What is the first step?
Answer:
The first step is to distribute.
Step-by-step explanation:
2(4x + 2)= 12
8x + 4 = 12
You distribute the 2 to 4x and 2.
x + 2y < -2
How do I graph this
Answer:
Put
[tex]x < - 2 - 2y[/tex]
Then put some of value to y and get x then we can graph it
What is the answer to 2 1/3 ÷ (-3 2/3) ?
Answer:
2 1/3 / (-3 2/3) = -0.636363636 AKA 0.636
Step-by-step explanation:
Step-by-step explanation:
[tex]2 \frac{1}{3} \div ( - 3 \frac{2}{3} )[/tex]
[tex] \frac{7}{3} \div ( - \frac{11}{3} )[/tex]
[tex] \frac{7}{3} \times ( - \frac{3}{11} )[/tex]
=
[tex] - \frac{7}{11} [/tex]
. A and B are vertical angles. If mA = (5x – 28) and
mB = (3x + 4)º, find the measure of each angle.
Answer:
measure of both angles is 52°
x = 16
Step-by-step explanation:
5x - 28 = 3x + 4
2x - 28 = 4
2x = 32
x = 16
Plug in 16 for 'x': 3(16) + 4 = 48 + 4 = 52°
Answer:
Both are 56°
Step-by-step explanation:
5x-28=3x+4
x=16
5(16)-28= 56°
The cost to rent a raft is $7 per person. A raft can hold up to 6 people. There is a $3 launch fee per raft. What is the total cost for a group of 6?
Before you tell me the answer tell me how do I explain how I got my answer :{
Answer:
$42 [$7/person*6 people]+$6[$3 launch fee/raft*2 rafts]
Step-by-step explanation:
$48 total
PLEASE MARK BRAINLIEST
NEED IT FOR A NEW RANK
ty in advance:D
Find the length of side x in simplest radical from with a rational denominator.
Answer:
4
Step-by-step explanation:
The value of the hypotenuse x will be equal to √6.
What are trigonometric identities?Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities. The Pythagorean Theorem serves as the basis for some of the most popular trigonometric identities, including.
The study of correlations between triangles' side lengths and angles is known as trigonometry.
Given that the angles are 45 and the base is √3 the hypotenuse will be calculated as,
cosθ = Base / Hypotenuse
cos45 = √3 / x
x = √3 / ( 1 / √2)
x = √6
Therefore, the value of the hypotenuse x will be equal to √6.
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Solve the system.
3x + 2y + 4z = 11
2x – y + 3z = 4
5x – 3y + 5z = -1
Enter your answer as an ordered triple.
Someone help please!!
Answer: (x, y, z) = (-3, 2, 4)
In other words, x = -3, y = 2 and z = 4.
You'll enter the number only into each box.
===============================================================
Explanation:
There are a few routes we can take to solve this. I'll use substitution.
First let's isolate y in the second equation.
2x - y + 3z = 4
2x + 3z = 4+y
4+y = 2x+3z
y = 2x+3z-4
This is then plugged into the first equation
3x+2y+4z = 11
3x+2( y )+4z = 11
3x+2( 2x+3z-4)+4z = 11 .... replace y with 2x+3z-4; since y = 2x+3z-4
3x+4x+6z-8+4z =11
7x+10z-8 = 11
7x+10z = 11+8
7x+10z = 19 .... we'll call this equation (4) and come back to this later
--------------------------------------
Move onto the third equation (of the original equations given)
Plug in y = 2x+3z-4
5x - 3y + 5z = -1
5x - 3( y ) + 5z = -1
5x - 3( 2x+3z-4 ) + 5z = -1
5x - 6x - 9z + 12 + 5z = -1
-x - 4z + 12 = -1
-x - 4z = -1-12
-x - 4z = -13 ..... let's call this equation (5)
--------------------------------------
To recap, we found equation (4) and equation (5) to be
7x+10z = 19-x - 4z = -13We can then solve for x in equation (5) like so
-x - 4z = -13
-x = -13 + 4z
-x = 4z - 13
x = -(4z - 13)
x = -4z + 13
This is then plugged into equation (4)
7x+10z = 19
7(-4z+13)+10z = 19 .... note how we now have one variable
-28z+91+10z = 19
-18z+91 = 19
-18z = 19-91
-18z = -72
z = -72/(-18)
z = 4
We can use this value of z to find x
x = -4z+13
x = -4(4)+13
x = -16+13
x = -3
Use the values of x and z to find y. We'll revisit the first equation in which we isolated y
y = 2x+3z-4
y = 2(-3)+3(4)-4
y = -6+12-4
y = 6-4
y = 2
So overall, the solution to this system is (x, y, z) = (-3, 2, 4)
-------------------------------
Checking the answer:
We'll replace x,y,z with the values we found.
In the first equation, 3x+2y+4z = 11 becomes 3(-3)+2(2)+4(4) = 11 and that simplifies to 11 = 11. In other words, the expression 3(-3)+2(2)+4(4) turns into 11. This confirms the first equation.Repeat the same idea for the second equation. We have 2x-y+3z=4 turn into 2(-3)-2+3(4) = 4 and that simplifies to 4 = 4. The answer is verified here. The third equation 5x-3y+5z = -1 becomes 5(-3)-3(2)+5(4) = -1 which simplifies to -1 = -1. We get a true equation here as well.Since all three equations are true when (x, y, z) = (-3, 2, 4), this verifies the answer completely. This is the only solution to the system. The system is independent and consistent.
please help!! i really need it.
ill give brainilest!!
Answer:
14
Step-by-step explanation:
i think it's 14. i hope i helped :)
p is an odd number
explain why p^2 + 1 is always an odd number
Will give brainliest if your right
A scientist conducts an experiment to observe the half-life period of the radioactive element barium. He starts the experiment with 200 grams of barium and records the mass at the end of every thirteen day. After how many days is the mass of barium closest to 1.5 grams?
Answer:
It would be 91 days
Step-by-step explanation:
Hope this helps :)
Tera can jog 5.5 miles in 1
hour. At the same rate, how face can she jog in 2 hours
Answer:
11 miles
Step-by-step explanation:
if she can jog 5.5 miles in 1 hour, than in 2, she can jog 11 miles, because 5.5(miles) x 2 (hours) = 11
hope this helps :)
a brainliest would be appreciated
help would be great during these troubling times
Answer:
117 - 120 < -3
-3 < -3
False no
because it is not above -3
Step-by-step explanation:
Answer: No
Step-by-step explanation:
x = 9
y = 6
13x - 20y < -3?
Substitute the values of x and y
13(9) - 20(6) < - 3?
117 - 120 < -3?
-3 </ -3
-3 = -3
(9, 6) is not a solution
I JUST DOD THE IMPOSSIBLE AND SOLVED A RUBIX CUBE IN 19 MOVES
Answer: see what you gotta do is/right/left/up/turn left/ down/up/down/down/ right up/ 2nd row turn left/ then do it all over again in you got it
Step-by-step explanation:
/right/left/up/turn left/ down/up/down/down/ right up/ ALSO CAN I BRAINLIEST IF I HELPED.
Find how many years it takes for money to triple when invested at an annual interest rate of 4.3% compounded continuously. That’s the entire question and I’m not quite sure what to do?
9514 1404 393
Answer:
25.5 years
Step-by-step explanation:
The multiplier for continuous compounding at annual rate r for t years is ...
e^(rt)
You want the value of t when that is 3 and r=0.043.
3 = e^(0.043t)
ln(3) = 0.043t
t = ln(3)/0.043 ≈ 25.549 . . . . years
Which relation is a function?
A. (1, 0), (3.0), (1.1), (3, 1) (1.3)
B. (1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7), (6,5), (4.4), (3, 3), (2, 1)
D. (9. -3), (19, 3) (4, -2), (4, 2), (0, 0)
Answer:
A
Step-by-step explanation:
A function is a relationship between inputs where each input is related to exactly one output.
A function can be one-to-one and many-to-one but can not be one-to-many.
The relation that is a function is
(1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7),
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can be one-to-one and many-to-one but can not be one-to-many.
A. (1, 0), (3.0), (1.1), (3, 1) (1.3)
This is not a function because we have one-to-many.
(1, 0) and (1, 1) are one-to-many.
B. (1, 1), (2, 2), (3, 3), (4, 4). (5, 8).
This is a function because it satisfies the function.
The given relation are one-to-one.
C. ( 2, 7), (6,5), (4.4), (3, 3), (2, 1)
This is not a function because we have one-to-many.
(2, 7) and (2, 1) are one-to-many relations.
D. (9. -3), (19, 3) (4, -2), (4, 2), (0, 0)
This is not a function because we have one-to-many relations.
(4, -2) and (4, 2) are one-to-many relations.
Thus,
The relation that is a function is
(1, 1), (2, 2), (3, 3), (4, 4). (5, 8). C. ( 2, 7),
Option B is the correct answer.
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