Answer:
[tex]\int\limits {\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} \, dx = \frac{3}{2}\ln(x^2 + 1) + 4\sqrt{3}\tan^{-1}(\frac{x}{\sqrt 3} )+ c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} \, dx[/tex]
Required
Integrate
Using partial fraction, we have:
[tex]\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} = \frac{Ax+B}{x^2 + 1} + \frac{Cx + D}{x^2 + 3}[/tex]
Take LCM
[tex]\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} = \frac{(Ax+B)(x^2 + 3)+ (Cx + D)(x^2 + 1)}{(x^2 + 1)(x^2 + 3)}[/tex]
Cancel out the denominators
[tex]3x^3 + 4x^2 + 9x + 4} = (Ax+B)(x^2 + 3)+ (Cx + D)(x^2 + 1)[/tex]
Open brackets
[tex]3x^3 + 4x^2 + 9x + 4} = Ax^3+Bx^2 + 3Ax +3B+ Cx^3 + Dx^2 + Cx + D[/tex]
Collect like terms
[tex]3x^3 + 4x^2 + 9x + 4 = Ax^3+ Cx^3+Bx^2+ Dx^2 + 3Ax+ Cx +3B + D[/tex]
Compare like terms on opposite sides
[tex]Ax^3 + Cx^3 = 3x^3[/tex] [tex]A + C = 3[/tex]
[tex]Bx^2 + Dx^2 = 4x^2[/tex] [tex]B + D = 4[/tex]
[tex]3Ax + Cx = 9x[/tex] [tex]3A + C = 9[/tex]
[tex]3B + D = 4[/tex]
Subtract [tex]B + D = 4[/tex] from [tex]3B + D = 4[/tex]
[tex]3B - B + D - D = 4 - 4[/tex]
[tex]2B + 0 = 0[/tex]
[tex]2B = 0[/tex]
[tex]B = 0[/tex]
[tex]B + D = 4[/tex]
[tex]D =4 - B[/tex]
[tex]D =4 - 0[/tex]
[tex]D =4[/tex]
Subtract [tex]A + C = 3[/tex] from [tex]3A + C = 9[/tex]
[tex]3A - A + C - C = 9 - 3[/tex]
[tex]2A = 6[/tex]
[tex]A = 3[/tex]
[tex]A + C = 3[/tex]
[tex]C = 3 - A[/tex]
[tex]C = 3 - 3[/tex]
[tex]C = 0[/tex]
So, we have:
[tex]A = 3[/tex] [tex]B = 0[/tex] [tex]C = 0[/tex] [tex]D =4[/tex]
[tex]\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} = \frac{Ax+B}{x^2 + 1} + \frac{Cx + D}{x^2 + 3}[/tex]
[tex]\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} = \frac{3x+0}{x^2 + 1} + \frac{0*x + 4}{x^2 + 3}[/tex]
[tex]\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} = \frac{3x}{x^2 + 1} + \frac{4}{x^2 + 3}[/tex]
The integral becomes:
[tex]\int\limits {[\frac{3x}{x^2 + 1} + \frac{4}{x^2 + 3}]} \, dx[/tex]
Split:
[tex]\int\limits {\frac{3x}{x^2 + 1} \, dx + \int\limits {\frac{4}{x^2 + 3}} \, dx[/tex]
Split
[tex]\frac{3}{2} \int\limits {\frac{2x}{x^2 + 1} \, dx + 4\int\limits {\frac{1}{x^2 + 3}} \ dx[/tex]
Integrate
[tex]\frac{3}{2}\ln(x^2 + 1) + 4\sqrt{3}\tan^{-1}\frac{x}{\sqrt 3} + c[/tex]
Hence:
[tex]\int\limits {\frac{3x^3 + 4x^2 + 9x + 4}{(x^2 + 1)(x^2 +3)}} \, dx = \frac{3}{2}\ln(x^2 + 1) + 4\sqrt{3}\tan^{-1}(\frac{x}{\sqrt 3} )+ c[/tex]
HELPP PLEASEE TELL ME WHICH IS RIGHT AND WRONG AND HELP KE EXPLAIN I DONT WANNA FAIL SUMMER SCHOOL NO LINKS OR FILE WOULD BE DEEPLY APPRECIATED
Answer:
Orca Correct, Sea Star Wrong. Heart it if it was helpful :D
Step-by-step explanation:
11-4=7. Orca correct.
Sea star...11-4=7
Wrong its 7, not -7
Answer:
The orca is right and the sea star is wrong.
If you were to add 11 to -4, it would no longer be a negative number.
You take four out of 11 which would bring it to a zero. There would be 7 left, therefore the answer being a positive 7.
A regular hexagon of side 8 cm is given. the hexagon is devided into 6 congruent triangles . calculate the area of the hexagonal
Answer:
96√3 cm^2
Step-by-step explanation:
half base = 4 cm
height of each triangle = 4√3 cm
Area of each triangle
(8 * 4√3)/2 = 16√3 cm^2
area of the hexagonal = 16√3 * 6 = 96√3 cm^2
Use the diagram below to match the ratios below. B a A b sin B COS B tan B tan A COS A sin A
Answer:
See explanation
Step-by-step explanation:
Given
The attached triangle
Required
Complete the ratios
(a) sin B
[tex]\sin(B)[/tex] is calculated as:
[tex]\sin(B) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(B) = \frac{b}{c}[/tex]
(b) cos B
[tex]\cos(B)[/tex] is calculated as:
[tex]\cos(B) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(B) = \frac{a}{c}[/tex]
(c) tan B
[tex]\tan(B)[/tex] is calculated as:
[tex]\tan(B) = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan(B) = \frac{b}{a}[/tex]
(d) tan A
[tex]\tan(A)[/tex] is calculated as:
[tex]\tan(A)= \frac{Opposite}{Adjacent}[/tex]
[tex]\tan(A) = \frac{a}{b}[/tex]
(e) cos A
[tex]\cos(A)[/tex] is calculated as:
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(A) = \frac{b}{c}[/tex]
(f) sin A
[tex]\ain(B)[/tex] is calculated as:
[tex]\sin(B) = \frac{Opposite}{Adjacent}[/tex]
[tex]\sin(B) = \frac{a}{c}[/tex]
True or false: Is 8.4 equal to 8 hours and 40min? Moreover, What would be the hour and min for 8.9? Explain thoroughly
Answer: I only have an answer for the first question, but I think its true .
I'm not sure though so I would clarify it .
Step-by-step explanation:
The reason why I think its true because, 8.4 is also equal to 8.40 . Also, if 8.4 was the answer to something and you put: 8.40 you would still be right .
Hope you get this right!
Find the area of the triangle.
8 in.
14 in.
Area: 18
square inches
Write an equation for the nth term of each geometric sequence:
5, 10, 20, 40,
Answer:
a(n) = 5*2^(n-1)
Step-by-step explanation:
The nth term of a geometric series is given by the relation :
a(n) = ar^(n-1)
Where, a = first term ; r = common ratio ; a(n) = nth term of the series.
Given the series : 5, 10, 20, 40,
First term, a = 5
Common ratio = a2/ a1 = a3/a2
Common ratio = 10/5 = 20/10
Common ratio = 2 = 2
Hence, nth term =
a(n) = 5*2^(n-1)
Which number line shows the solution set for |a|= 6
Answer:
O the first number line
Step-by-step explanation:
|a| = 6
|?| = absolute value
to find absolute value of a number, it must be a opposite number from the origina number
|a| = 6
|-6| = 6
6 = 6
Answer:
A)
Step-by-step explanation:
find the nonpermissible replacement for b in this expression b-7/b-1
Answer:
1
Step-by-step explanation:
b cannot equal 1 as that would be dividing by zero
If you help me and explain to me how you got you’re answer you get Brainly
Answer:
KRM = 44 degrees, MRD = 46 degrees
Step-by-step explanation:
This angle is a right angle so it equals 90 degrees. That means that equations 3g + 29 and 7g + 11 will amount to 90 degrees.
(3g + 29) + (7g + 11) = 90
Combine like terms:
10g + 40 = 90
10g = 50
g = 5
Plug in 5 to both equals (in this case the question only asks for 3g + 29 or KRM):
3(5) + 29 =
15 + 29 =
44 =
7(5) + 11 =
35 + 11 =
46 =
Please help me!! I will try to give brainliest!!!
Answer:
If you round it the 30. If not round 29.7
Step-by-step explanation:
Branliest plz :)
It takes Max 9 minutes to read 10 pages of his book. Which equation represents the
relationship between the number of pages, p, that Max can read and the number of
minutes, m?
Answer:
y represents the pages, while x represents the minutes. for every y, there is 9/10 x, therefore the equation is y=9/10x
What is the name of part B in the sphere below? A sphere. The great circle is labeled B. radius diameter center great circle
Answer: I'm pretty sure that it is D. Great circle
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
El lado mas largo de un triangulo rectangulo es 5 mas que 4 veces el laso mas corto. El tercer lado es 10metros que la suma de los otros dos. sea 8 cm la longitud del lado mas corto.
Answer:
the answer is that yoy need to learn how to speak english
4 time 4
equals 16
For Cinco de Mayo last week, Anna's Taqueria was having a deal on tacos. You could order 6 tacos for $8.94 or get 10 tacos for $14.50. Which is the better deal?
Answer:
the best one is 10 tacos for 14.50
Step-by-step explanation:
first u have to find unit rate for 6 tacos is 1.49 and for 10 tacos is 1.45 the difference is 4 cents but the best deal is the ten tacos
Which polynomial is in standard form? o 4 + 3xy - 5xy3 + y4 o –x4 + x3y2 + 7xy3 - 2y4x2 0893 + 10ab2 - 12a2b3
Answer:
46
Step-by-step explanation:
What is the GCF of 162? SHOW ALL YOUR WORK AND EXPLAIN
Answer:
162
Step-by-step explanation:
Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162. There are 10 integers that are factors of 162. The greatest factor of 162 is 162.
Find the greatest common divisor (gcd):
gcd(162)
Hint: | What is the largest divisor of a positive integer?
A positive integer's largest divisor is the integer itself:
Answer: gcd(162) = 162
The volume of a sphere is 2400 cm³, What is the approximate diameter of the sphere?
A) 16.6 cm
B) 10.1 cm
C) 8.3 cm
D) 4.2 cm
Answer:
Option A is the correct answer, since it is the closest answer.
Step-by-step explanation:
volume: V = 4/3 πr³
Try replacing r with half number of the options
A) 4/3 x π x 8.3 ^3 = 2395.09
B) 4/3 x π x 5.05 ^3 = 539.46
C) 4/3 x π x 4.15 ^3 = 299.38
D) 4/3 x π x 2.1 ^3 = 38.79
What is the radius of a sphere with a volume of 384\text{ ft}^3,384 ft
3
, to the nearest tenth of a foot?
Answer:
r≈4.5 ft
Step-by-step explanation:
r≈4.5 ft
\text{Volume of a Sphere:}
Volume of a Sphere:
V=\frac{4}{3}\pi r^3
V=
3
4
πr
3
384=
384=
\,\,\left(\frac{4}{3}\pi\right) r^3
(
3
4
π)r
3
384=
384=
\,\,(4.1887902)r^3
(4.1887902)r
3
Evaluate 4/3pi in calc
\frac{384}{4.1887902}=
4.1887902
384
=
\,\,\frac{(4.1887902)r^3}{4.1887902}
4.1887902
(4.1887902)r
3
Evaluate \frac{4}{3}\pi
3
4
π in calc
91.6732472=
91.6732472=
\,\,r^3
r
3
\sqrt[3]{91.6732472}=
3
91.6732472
=
\,\,\sqrt[3]{r^3}
3
r
3
Cube root both sides
4.5090066=
4.5090066=
\,\,r
r
\text{Final Answer:}
Final Answer:
r\approx 4.5\text{ ft}
r≈4.5 ft
Round to nearest tenth
The radius of the sphere is approximately 4.2 feet.
What is the volume of the sphere?To find the volume of a specific sphere, we need to know its radius. Once we have the radius, we can plug it into the formula and calculate the volume.
The formula for the volume of a sphere is:
V = (4/3) x π x r^3
where V is the volume of the sphere, r is its radius, and π is a mathematical constant approximately equal to 3.14.
We are given the volume of the sphere, so we can plug it into the formula and solve for the radius:
384 = (4/3) x π x r^3
Dividing both sides by (4/3) x π, we get:
r³ = 384 / ((4/3) x π)
r³ = 72.825
Taking the cube root of both sides, we get:
r ≈ 4.243
The radius of the sphere is approximately 4.2 feet.
To know more about volume follow
https://brainly.com/question/29091596
#SPJ2
Which linear inequality is graphed In the figures
Which is the lower rate?
44 people in 4 theaters or 100 people in 10 theaters
Answer:
100 in 10 theaters. 100÷10=10 44÷4=11
Find cos0, where 0 is the angle shown. Give an exact value, not a decimal approximation. (listing BRAINLEST)
Step-by-step explanation:
everything can be found in the picture
simon has a quarter, dime, nickel, and penny in his pocket. He wants to buy a snack at the canteen that costs 40¢. If he pulls out one coin at a time, what is the probability that the first 3 coins that are equal to $0.40?
Answer:
1/4
Step-by-step explanation:
Q=event of pulling a quarter (25 cents)
D=event of pulling a dime (10 cents)
N=event of pulling a nickel (5 cents)
P=event of pulling a penny (1 cent)
Simon needs to pull out the penny last, so that the first three coins add up to $0.40.
We assume the coins are wrapped so it is a random choice.
For the first coin, probability of NOT pulling a penny is 3/4,
similarly, for the second coin, probability of NOT pulling a penny is 2/3,
for the third coin, probability of NOT pulling a penny is 1/2,
For all this to happen, we use the multiplication rule
P(3 coins but no penny) = (3/4*2/3*1/2) = 1/4
answer please I’m dying from math
Step-by-step explanation:
It's C
I hope it helped:)
what is the length if the baseedge labeled X? Will mark brainliest if correct.
Answer:
Answer is 18
Step-by-step explanation:
[tex]w = 3 \frac{v}{hl} [/tex]
w = 3(108 ÷ 18)
=3(6)
=18
Jacob and Shawna are selling shirts and hats for a
school fundraiser. Jacob sold 1 hat and 7 shirts for a
total of $68. Shawna sold 4 hats and 14 shirts for a total
of $146. Find the cost of one hat and one shirt.
answer:
$9 for a shirt
$5 for a hat
what is a secant of a circle
In geometry, a secant of a curve is a line that intersects the curve at a minimum of two distinct points. In the case of a circle, a secant will intersect the circle at exactly two points.
Which step is the same in the construction of a perpendicular line through a point on a line and the construction of a perpendicular line through a point off a line?
Create only one arc on the original line.
Create two arcs on the original line.
Place the compass on only one point off the original line.
Place the compass on only one point on the original line.
Step-by-step explanation:
Create two arcs on the original line.
Place the compass on two points on the original line, one after another for marking a point.
make a line from the original point on the line to the marked point (MP)
the sketch as attached
For making a perpendicular line through a point open the compass to a radius that is less than half of the segment and draw an arc intersecting line and then draw arcs using the intersection points. In the last construct a line that joins the two points.
The steps that involve the same drawing of a perpendicular line by a Point on s line and perpendicular to the point off a line is to put the compass on a point off the original line.Hence the option C is correct.
Learn more about the in the construction of a perpendicular.
brainly.com/question/24508203.
Rosa budgets her allowance so she uses equal amounts for spending,saving, and gifts. Her weekly allowance is $6.75. How much does Rosa save each week?
Answer:
29.54
Step-by-step explanation:
29.54. is your answer to this problem
A kite is flying 99 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 62º. Find the length of the string. Round your answer to the nearest tenth. (plz help)
Can someone help me? Question attached, 20 points.
Answer:
6
Step-by-step explanation:
[tex]V = A * b = 5A[/tex]
[tex]5A = 141.3[/tex]
[tex]A = 28.26[/tex]
[tex]\pi r^2 = 28.26[/tex]
[tex]3.14 r^2 = 28.26[/tex]
[tex]r^2 = 9[/tex]
[tex]r = 3[/tex]
[tex]D = 2r = 2 * 3 = 6[/tex]
