Answer:
[tex]\displaystyle \int {\frac{1}{1+(2x)^2}} \, dx = \frac{artan(2x)}{2} + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Antiderivatives - Integrals
Indefinite Integrals
Integral Constant CU-Substitution
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Arctrig Integration [arctangent]: [tex]\displaystyle \int {\frac{1}{a^2 + u^2}} \, du = \frac{1}{a}arctan(\frac{u}{a}) + C[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{1}{1+(2x)^2}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite: [tex]\displaystyle \int {\frac{1}{1^2+(2x)^2}} \, dx[/tex]Step 3: Identify Variables
Identify variables for u-substitution of arctrig.
Set u: [tex]\displaystyle u = 2x[/tex]Differentiate [Basic Power Rule]: [tex]\displaystyle \frac{du}{dx} = 1 \cdot 2x^{1 - 1}[/tex][Derivative] Simplify: [tex]\displaystyle \frac{du}{dx} = 2[/tex][Derivative] Rewrite: [tex]\displaystyle du = 2dx[/tex]Set a: [tex]\displaystyle a = 1[/tex]Step 4: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \frac{1}{2}\int {\frac{2}{1^2+(2x)^2}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \frac{1}{2}\int {\frac{du}{a +u^2}}[/tex][Integral] Arctrig Integration [arctangent]: [tex]\displaystyle \frac{1}{2}[\frac{1}{a}arctan(\frac{u}{a})] + C[/tex][Integral] Back-Substitute: [tex]\displaystyle \frac{1}{2}[\frac{1}{1}arctan(\frac{2x}{1})] + C[/tex][Integral] Divide: [tex]\displaystyle \frac{1}{2}[arctan(2x)] + C[/tex][Integral] Multiply: [tex]\displaystyle \frac{arctan(2x)}{2} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration of Arctrig
Book: College Calculus 10e
A picture is mounted on a frame measuring 25 centimeters by
15 centimeters. It has a border of 3 centimeters round it. Find the area
and perimeter of the picture.
25 cm
13 cm
A=kW
P-HIWAW
3 cm
picture 3 cm
115 cm
13 cm
cm
Answer:
I think it's 1,125 and 4485
Step-by-step explanation:
25x13x3
115x13x3
What is the next number in the sequence -16, -6, 4, 14
Answer
24
Step-by-step explanation:
you are adding by 10
-16+10=-6
-6+10=4
4+10=14
14+10=24
EI Sr. López necesita una escalera para podar sus árboles de naranjas. Le dice al herrero que necesita alcanzar una altura de 3 m sin estirar los brazos. El herrero sabe que el Sr. López mide 1.70 m, y sabe que por seguridad, una persona no debe subir más arriba del penúltimo peldaño de la escalera. El herrero le vende una escalera como la que se muestra.
la escalera tiene que ser de 2.30mts
AD is the perpendicular bisector of BC.
BD = 5x – 10 and DC = 3x + 10.
Determine the value of x.
5x-10= 3x+10
5x-3x= 10+10
2x÷2= 20÷2
x= 10
Step-by-step explanation:
as AD bisects them they will be two equal parts so
5x-10=3x+10
5x-3x=10+10
2x=20
divide both sides by 2 and
x=10
Sam wants to buy a watch that cost $188. This is $48 more than 4 times
he sved last month. How much dia he save last month? *
Answer:
$35
Step-by-step explanation:
188-48 gives you the 4x what he saved
140/4 gives you the total which is 35.
Caroline saves money in an arithmetic sequence: $350 the first year, another $550
the second, and so on. How much money does she save after 31 years?
Calculate the size of angle x.
Give your answer to 1 decimal place.
8 cm
11 cm
х
15 cm
Given:
Consider the below figure attaches with this question.
To find:
The size of angle x.
Solution:
Law of Cosines:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
Three sides of the triangle are 11 cm, 8 cm, 15 cm. Since 11 cm is the opposite side of the angle x, therefore [tex]a=11[/tex].
Let [tex]A=x,a=11,b=8,c=15[/tex]. Substitute these values in the above formula.
[tex]\cos x=\dfrac{8^2+15^2-11^2}{2(8)(15)}[/tex]
[tex]\cos x=\dfrac{64+225-121}{240}[/tex]
[tex]\cos x=\dfrac{168}{240}[/tex]
[tex]\cos x=0.7[/tex]
Taking cos inverse on both sides, we get
[tex]x=\cos^{-1} 0.7[/tex]
[tex]x=45.572996^\circ[/tex]
[tex]x\approx 45.6^\circ[/tex]
Therefore, the measure of angle x is 45.6°.
The map of a trail is shown below. Find the value of x.
16+23=39
180-39=151
Answer:
151
I need to do this class soon, please help me
Answer:
Step-by-step explanation:
18. x + 25 = 55
x = 30
19. 2x - 5 = 95
2x = 100
x = 50
20. 3x - 22 = 2x + 26
x - 22 = 26
x = 48
21. 3x - 18 + 105 = 180
3x + 87 = 180
3x = 93
x = 31
22. 19x + 17x = 180
36x = 180
x = 5
27(5) = 135
23. 5x + 40 + 2x = 180
7x + 40 = 140
7x = 140
x = 20
5(20) = 100
2(20) = 40
5(20) + 40 = 100 + 40 = 140
Use special right triangles.
Find the exact value of x and y.
18
30°
X = ?
y = ?
I need help with this right now before it’s due
Grapes
Answer:
21, 6, 12
Step-by-step explanation:
your welcome:)
You randomly choose one game piece. Find the theoretical probability of each event. Reduce the fraction in lowest terms and
indicate the percentage rounded to the nearest hundredth, if necessary.
Answer:
Yellow= 1/2 or 50%chance
Red= 1/5 or 20% chance
Blue= 1/5 or 20% chance
Green= 1/10 or 10% chance
Step-by-step explanation:
There are 10 game pieces
5 are yellow
2 are red
2 are blue
And 1 is green
5/10=1/2=50%
2/10=1/5=20%
2/10=1/5=20%
1/10=10%
Add these up and you get 10/10 or 100%
Hope this helps and don't forget to follow!
Mr. Tuyen uses
7/8
of a tank of gas each week to drive to and from his job.
How many tanks of gas does Mr. Tuyen use in 7 weeks? Enter your answer as a fraction and as a mixed number.
Answer:
Mr.Tuyen uses 3 1/8 tanks of gas in 5 weeks. The improper fraction version would be 25/8 if that is what you're looking for
Find the range of the data.
6, 8, 14, 4, 26, 24, 2, 4, 18, 9
A rectangular garden plot has an area of 36 ft. 2. If the width of the plot is 4ft, what is the length?
9ft
12ft
18ft
4ft
Answer:
I think it should be 9 because 9x4 is 36
(-3, 3), (1, 1), (0 -2), (1, -4), (5, -1) domain and range
is it a function plz help i aint no good at math
Answer:
not it is not aa function
Step-by-step explanation:
Factorise the expressions and divide them as directed.
Ok. These are the answers. Tell me if you didm't understand my writing.
8k + 4 - 11k + 9 show work please
Answer:
8+4−11+9
8+13−11
8+13−11
−3+13
^^^
Step-by-step explanation:
Alternate exterior angles are congruent
Which angle forms a pair of alterhate
exterior angles with angle 3?
f
<3 = 41?)
Answer:
Angle 6
Step-by-step explanation:
The opposite exterior angle to angle 3 is angle 6.
For another example, the opposite exterior to angle 1 is angle 8.
If you were to cut them out and put them over each other, they're congruent. Hope that helped you out :)
Answer:
<3=<6 forms a pair of alternate
exterior angles with angle 3.
Factorise the following.
Answer:
1:(x-6)²
2:(9-8x)²
Step-by-step explanation:
1: (x-6)(x-6)=(x²-36)
2:(9-8x)(9-8x) = (81 - 64x²)
How do you Solve 20/3=10/9x
Answer:
200
Step-by-step explanation:
100✓9283+374+_+38_+_+_("#9#9_+
Answer:
x = 6
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Plz help me!
Plz we’ll mark brainliest if correct!
Answer:
Seems like 7 of them failed
Step-by-step explanation:
The chart pretty much tells you
Answer:
7 students
Step-by-step explanation:
Find the slope of the line that passes through (3, 7) and (1, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Giving everything. Plzz help.
The answer in this picture is B(143)
Answer:
A
Step-by-step explanation:
180 _80 =100
180_65= 115
180_72 = 108
Then :
108 + 115 + 100 = 323
Then :
360 _ 323 = 37
Then :
180 _37 = 143
X _7 =143
X =150
The polygons are similar. but they are not necessarily drawn to scale. Find the value of x
Answer:
x=9
Step-by-step explanation:
Since the polygons are similar, the ratios of their respective sides are equal.
32/24=(x-1)/6
x-1=8
x=9
need help horribly geometry question
Answer:
23.31 ft
Step-by-step explanation:
Reference angle = 47°
Opp = 25 ft
Adj = x
Apply trigonometry ratio TOA:
Tan 47 = Opp/Adj
Tan 47 = 25/x
x*Tan 47 = 25
x = 25/Tan 47
x = 23.3128772 ≈ 23.31 ft (to 2 d.p)
is going to plant y vegetable seeds in one garden and 3y+8 vegetable seeds in another. How many seeds is Frank going to plant?
Answer:
4y + 8 vegetable seeds
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
We know that Frank has 2 gardens, one with y vegetable seeds and another with 3y + 8 vegetable seeds. If we are trying to find the total amount of seeds planted, we must add the 2 gardens together:
Garden 1: y
Garden 2: 3y + 8
Garden 1 + Garden 2 = Total veggie seeds
y + 3y + 8 = Total veggie seeds
Total veggie seeds = 4y + 8
(Please Help) ASAP!
POINT:30
Answer:
We have 4 triangles with base 3 and height 4 and a square with side length 3 so:
Triangles:
The area for a triangle is calculated by [tex]\frac{bh}{2}[/tex] where b is the base and h is the height so we have [tex]\frac{12}{2}\cdot 4[/tex] so we have a total area of 24.
[b]Square:[/b]
The area of a square is calculated by [tex]s^{2}[/tex] where s is the side length so we have the area is 9.
Now we put them together for the surface area so we get 24 + 9 = [tex]\boxed{33}[/tex]
Hope this helped!
(sorry for taking so long, TeX takes so long to type out(Math typesetting software))
classify the segment in each part below. only use the information given in the figure do not assume measures are equal unless the markings indicate they are
Answer:
i dont know i just need points for more questions sorry
Step-by-step explanation:
Meng conducted a survey to determine the favorite flavor of ice cream in
his hometown. Fifteen of the fifty people he surveyed like strawberry best.
How many of the 3,500 residents in the town would you expect to like
strawberry ice cream? *
Answer:
1,050
Step-by-step explanation:
It’s in my notebook, so I can’t show