I'm guessing you mean
[tex]\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx[/tex]
First, compute the quotient:
[tex]\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}[/tex]
Split up the remainder term into partial fractions. Notice that
x ² + 4x + 3 = (x + 3) (x + 1)
Then
[tex]\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52[/tex]
So the integral becomes
[tex]\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}[/tex]
We can simplify the result somewhat:
[tex]\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}[/tex]
The perimeter of a rectangle is 332cm and the width is 76cm. Find the rectangle’s length
Which diagram shows an angle bisector
B
if it is not correct sory
Diagram B is a proper demonstration of an angle bisector.
Letter A is wrong because they are a set of intersecting ines.
Letter C is wrong because they are a set of parallel lines.
Letter D is wrong because they are also a set of perpendicular lines.
So, now, we know that Letter B is the correct answer. The reason for this is also because ∠ACD is bisected by line B.
I hope that this helped answer your question. Have a good day!
How many kilograms of tin will be required to make 250 kg of an alloy, if the alloy must contain 81% copper, 14% tin and 5% lead?
Answer:
35
Step-by-step explanation:
all are obeying a constant ratio
copper 81tin 14⇒?lead 5total 100 ⇒250?=250*14/100=35John's bank account was overdrawn. The status of his account was -$133. He did not realize the problem and wrote another check for $55. The bank charged him a $22 fee for being overdrawn.
What was the new status of John's account at this point?
Answer:
210
Step-by-step explanation:-133-55-22=210
Cuál es el valor de la siguiente expresión?
(6 + 27) / (5 - 2)
Answer: 11
Step-by-step explanation:
6+27=33
33/3 = 11
Find the number of steel ball bearings, each of diameter 0.7 cm, which can be made from 1 kg of steel, given that 1 cm' of steel has a mass of 7.85 g.
Answer:
707.7, or 707
Step-by-step explanation:
0.18 x 7.85 g = 1.413 g/one bearing. Total amount of bearings: 1kg = 1000 g/1.413
3 - 2 + 6 - 1 steps to please
Answer:
the answer is 6
hope this helps:)
Answer:
6
Step-by-step explanation:
3-2 = 1
6-1= 5
5+1= 6 this is the answer hope it is help for u
What’s x = in this equation
Answer:
5m
Step-by-step explanation:
Applying Pythagoras theorem:
a² + b² = c² (where a is base length, b is the height and c is the hypotenuse of the right triangle)
3² + 4² = c²
c² = 9 + 16 = 25
c = x = [tex]\sqrt{25}[/tex] = 5
∴ x = 5m
what is the population of nepal
How many different sets of answers are possible on a true-false test that has 11
questions?
X-18.6
_____=-0.326
15.3
Answer:
13.6122
Step-by-step explanation:
(x-18.6)/15.3=-0.326
x-18.6=-0.326*15.3
x-18.6=-4.9878
x=-4.9878+18.6
x=13.6122
Martina took a train to the bullfight. It traveled 544 km nonstop in 8.5 hours to get there. If the train moved at a steady speed, what was the rate of speed
Answer:
64 km per hour
Step-by-step explanation:
544/8.5=64
I want to know how to solve this.
Answer:
B
I just did it and got it right
5*213 is a 5 digit number replace the * number by smallest digit to make them divisible by 3
Answer:
1
Step-by-step explanation:
that is the answer
because 51213÷3=17071
Find the constant C such that x ^ 3 - 3x + 5 <= C where x in[0,3] 18 23 14 17 21
Plug in maximum value of x (3) and see what you get. The maximum value of the expression when plugged in is C.
[tex]3^3-3\cdot3+5=C[/tex]
[tex]27-9+5=C\implies 23=C[/tex]
Now that means,
[tex]x^3-3x+5\leq 23[/tex] for any x in [tex][0,3][/tex]
Hope this helps :)
a Find the sum of interior angle of the heptagon
Answer:
sum of the interior angles=900°
Answer:
900°
Step-by-step explanation:
To find any shape sum of interior angles ,
we use the formula,
(n-2)180°, where n is the number of sides
So for heptagon,
n=7
using formula,
(7-2)180°
=> 5(180)
=> 900°
Define bisector of a line
Answer:
The line that divides something into two equal parts. You can bisect line segments, angles, and more.
Step-by-step explanation:
A bisector is what divides a line into two equal parts.
Add -13 + 5. 8 -8 -18 18
Adult tickets for a movie cost six dollars and children's tickets cost three dollars if two adults and three children go to the movies how much will they pay?
Write a numerical or algebraic expression for each verbal phrase
Things did not go quite as planned. You invested $21360, part of it in a stock that paid 12% annual interest. However, the rest of the money suffered a 5% loss. If the total annual income from both investments was $, how much was invested at each rate? How much money was invested at 12% annual interest?
Answer:
1992
Step-by-step explanation:
Let x be the amount invested at 12%.
Then the rest amount is (21360-x) dollars.
The 12% stock earning is 0.12x dollars.
The rest amount loss is 0.05*(21360-x) dollars.
Your equation is
interest - loss = total interest, or
0.12x - 0.05*(21360-x) = 1992 dollars.
Simplify and solve for x.
determine the area and perimeter
Answer:
Area is the total surface covered by the shape and perimeter is the total length of the shape.
the perimeter of a rectangular field is 342 yards. if the width of the field is 77 yards, what is its length
Anyone know the answer to this?
Quick response
Help me please!!!٩(๑꒦ິȏ꒦ິ๑)۶
the 1st one
9514 1404 393
Explanation:
Add sin(θ)
cos(θ) = sin(θ)
Divide by cos(θ)
1 = sin(θ)/cos(θ) = tan(θ)
Square both sides
1 = tan²(θ)
Add 1
2 = tan²(θ) = sec²(θ)
Take the square root
√2 = sec(θ) . . . . for 0 < θ < π
_____
Additional comment
The equation cos(θ) -sin(θ) = 0 has two solutions: θ = π/4 and θ = 5π/4. For the first-quadrant solution, sec(θ) = √2. For the third-quadrant solution, sec(θ) = -√2.
What is the volume of the right rectangular prism?
a) 21cm^3
b) 42cm^3
c) 120cm^3
d) 240cm^3
Answer:
c part is correct answer
Answer: D) 240 cm^3
Step-by-step explanation:
On edge
16. Simplify: look at picture
please give detailed steps!!
Answer:
[tex] 2\sqrt{3} [/tex]
Step-by-step explanation:
1. Expand the expression
[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]
2. To multiply the fractions, multiply the numerators and denominators seperately
[tex] = \frac{6 \sqrt{3} }{ \sqrt{3} \sqrt{3} } [/tex]
3. Calculate the product : when a square root of an expression is multiplied by itself, the result is that expression.
[tex] \frac{6 \sqrt{3} }{3} [/tex]
4. Reduce the fraction with 3 and the solution is :
[tex] = 2 \sqrt{ 3} [/tex]
need the answer as soon as possible
Answer:
soln
Step-by-step explanation:
=21÷x-2s
=21÷7-2×9
=3-18
=-15
Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets of information and the number of bits. Be sure to define your variables.
Answer: 8b
Step-by-step explanation:
Equation:
Let b equal the number of bytes
byte = 8b
a continuous random variable is uniformly distributed in the interval a<X<b the Lower quartile is 5 and upper quartile is 9 find
a. the values of a and b
b. p(6<X<7)
c. the cumulative distributive function
راز
(a) X has a probabiliity density of
[tex]f_X(x) = \begin{cases}\dfrac1{b-a}&\text{if }a<x<b\\0&\text{otherwise}\end{cases}[/tex]
If the lower quartile is 5 and the upper quartile is 9, then
[tex]\displaystyle \int_a^5 f_X(x)\,\mathrm dx = 0.25 \text{ and } \int_9^b f_X(x)\,\mathrm dx = 0.25[/tex]
Computing the integrals gives the following system of equations:
[tex]\displaystyle \int_a^5\frac{\mathrm dx}{b-a} = \frac{5-a}{b-a} = 0.25 \\\\ \int_9^b \frac{\mathrm dx}{b-a} = \frac{b-9}{b-a} = 0.25[/tex]
5 - a = 0.25 (b - a) ==> 0.75a + 0.25b = 5 ==> 3a + b = 20
b - 9 = 0.25 (b - a) ==> 0.25a + 0.75b = 9 ==> a + 3b = 36
Eliminate a :
(3a + b) - 3 (a + 3b) = 20 - 3×36
-8b = -88
==> b = 11 ==> a = 3
and so P(X = x) = 1/(11 - 3) = 1/8 for all 3 < x < 11.
(b)
[tex]\displaystyle P(6<X<7) = \int_6^7f_X(x)\,\mathrm dx = \int_6^7\frac{\mathrm dx}8 = \boxed{\frac18}[/tex]
(c) The distribution function is then
[tex]\displaystyle F_X(x) = \int_{-\infty}^x f_X(t)\,\mathrm dt = \begin{cases}0&\text{if }x\le3 \\ \dfrac x8 &\text{if }3<x<11 \\ 1&\text{if }x\ge11\end{cases}[/tex]
2 Why does it make sense to add 8 + 2 to make a ten and make new problem, 10 + 4?
Step-by-step explanation:
Hahahaha this is math.lol
X:3/2+1/2x=2x
I need to solve for x
Answer: x = 1
Step-by-step explanation:
Given
3/2 + (1/2)x = 2x
Multiply 2 on both sides to cancel out the denominator
2 · [3/2 + (1/2)x] = 2 · 2x
3 + x = 4x
Subtract x on both sides
3 + x - x = 4x - x
3 = 3x
Divide 3 on both sides
3 / 3 = 3x / 3
[tex]\boxed {x=1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions