Answer:
-2x cos x + 2 sin x + C
Step-by-step explanation:
∫ (2x sin x) dx
If u = 2x, then du = 2 dx.
If dv = sin dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 2x (-cos x) − ∫ (-cos x) (2 dx)
= -2x cos x + 2 ∫ cos x dx
= -2x cos x + 2 sin x + C
Answer:
[tex]\displaystyle \large{2 \sin x - 2x \cos x + C}[/tex]
Step-by-step explanation:
We are given the indefinite integral:
[tex]\displaystyle \large{\int {2x \sin x} \ dx }[/tex]
Using by-part method, we have to substitute u-term and dv appropriately.
By-part is an integration of product rules, when integrated the product rules of differentiation, we’ll obtain:
[tex]\displaystyle \large{\int {u} \ dv = uv - \int {v} \ du}[/tex]
Above is by-part method/formula.
Where 4 terms are presented:
ududvvOur main terms to substitute are u and dv which mean u-term has to be a function that’s differentiatable and dv has to be a function that’s integratable.
The main concept of by-part is to understand how to substitute appropriately which you can simply follow below:
LIATE
Stands for Logarithm, Inverse (Trigonometry), Algebraic, Trigonometric and Exponential.
These are in orders from first to last on what to let u-term first. That means logarithm functions must be the first to substitute themselves as u-term, so if you encounter a logarithmic function and a polynomial function, you must let u = logarithmic function while dv = polynomial.
In this case, we have 2x which is polynomial and sin(x) which is trigonometric. According to LIATE, we have to let Algebraic or Polynomial 2x be first to substitute as u-term, that means our dv is trigonometric sin(x).
Therefore, we have:
u = 2xdu = 2dx dv = sin(x)dxv = -cos(x)Now, substitute these terms in accordingly to formula of by-part.
[tex]\displaystyle \large{\int {2x \sin x} \ dx = 2x \cdot (-\cos x) - \int {-\cos x \cdot 2 \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + \int {2 \cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \int {\cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \cdot \sin x + C}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \sin x + C}[/tex]
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Summary
Property
[tex]\displaystyle \large{ \int {k f(x)} \ dx = k \int{f(x)} \ dx \ \ \ \ \tt{(k \ \ \ is \ \ \ a \ \ \ constant.)}\\[/tex]
Only shown in explanation.
By-Part
[tex]\displaystyle \large{\int u \ dv = uv- \int v \ du}[/tex]
LIATE
The functions in order that should be u-term from first to last.
Logarithm Inverse TrigonometricThese functions above do not have integration formula by default.
Polynomial (Algebraic)TrigonometricExponential (Last since it’s the easiest to integrate, especially natural exponential)Indefinite Integral
Make sure to always add + C after evaluating the integral, regardless what multiplies or attempts to affect + C, we must always add + C.
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Find the value of using identities 996^2
Answer:
992,016
Step-by-step explanation:
[tex] {996}^{2} \\ = {(1000 - 4)}^{2} \\ = {1000}^{2} - 2 \times 1000 \times 4 + {4}^{2} \\ = 1000000 - 8000 + 16 \\ = 1000016 - 8000 \\ = 992,016 \\ [/tex]
which fraction equals a repeating decimal 3/10 1/3 6/12 3/4
First turn them all into decimals.
Divide the numerator (top) by the denominator (bottom).
3/10 is .3 and doesn’t repeat.
1/3 is .333333.....
6/12 is .5, doesn’t repeat.
3/4 is .75, also doesn’t repeat.
1/3 is the repeating decimal.
The sum of two numbers is 50. The first number is 18 less than the 2nd number. What are the
2 numbers?
Answer:
2y + 2 + y = 50 (combine like terms)
3y + 2 = 50
3y = 50 - 2
3y = 48
y = 16
Substitute 16 for y in either equation 1 or 2 and solve for x (I chose equation 1):
x + 16 = 50
x = 50 - 16
x = 34
Step-by-step explanation:
Which ratio is greater than 5/8 ? A. 12/24 B. 3/4 C. 15/24 D. 4/12
B is the 3/4 = .75 and 5/8 = .625
Find the slope, if it exists, of the line containing
(-8,-5) and (-19,- 13)
Answer: 8/11
Step-by-step explanation:
To find slope you can use this formula:
y2-y1/x2-x1
substitute the values with the ones from the 2 points
-13-(-5)= -8
-19-(-8)=-11
you then divide -8/-11
and you get 8/11
8/11 is the slope of those 2 points.
You intend to estimate a population mean μ with the following sample. 78.4, 85.3, 50, 68.4, 59.4, 73.7, 73.2, 47.4, 40.5
You believe the population is normally distributed.
Find the 99.5% confidence interval.
The answer must be done as an open-interval accurate to 2 decimal places.
Answer:
(17.75, 110.32)
Step-by-step explanation:
The sample mean is 64.03, and the standard deviation is 15.43.
The population is normally distributed, so 99.5% confidence is ±3 standard deviations.
The confidence interval is therefore:
(64.03 − 3 × 15.43, 64.03 + 3 × 15.43)
(17.75, 110.32)
The 99.5% confidence interval will be equal to (17.75, 110.32).
What is Probability?Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.
As per the given data provided by the question,
With a standard deviation of 15.43 and a sample mean of 64.03, respectively.
Since the population has normally distributed, 99.5% probability lies within a range of three standard deviations.
Consequently, the confidence interval is:
= (64.03 − 3 × 15.43, 64.03 + 3 × 15.43)
= (17.75, 110.32), this is up to 2 decimal places.
To know more about Probability:
https://brainly.com/question/11234923
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The area of a rectangular mirror is 11 11 16 square feet. The width of the mirror is 2 3 4 feet. If there is a 5 foot tall space on the wall to hang the mirror, will it fit
Meg skateboards One-fourth of a mile in One-half of an hour. At this rate, how far will she skateboard in an hour?
Answer: i'm pretty sure Meg would have skated 1/2 of a mile in an hour
Answer:
meg would have skated 1/2 of a mile in 1 hour.
Step-by-step explanation:
how to factorise 30+b-b²
Hey there!☺
[tex]Answer:\boxed{-(b-6)(b+5)}[/tex]
[tex]Explanation:[/tex]
[tex]30+b-b^2[/tex]
Factor 30+b-b^2 by grouping.
[tex]-(b-6)(b+5)[/tex]
Hope this helps!☺
If SE = 7 and EG = 20 , then SG =
Jerome has $28 in his pocket. He wants to buy as many candy bars as he can for $1.75 cach. Write an equation to show how many candy bars he can buy?
Answer:
16
Step-by-step explanation:
Take the total amount and divide by the amount per candy bar
28 /1.75
16
He can buy 16 candy bars
A car's rear windshield wiper rotates 140°. The total length of the wiper mechanism is 24 inches and the length of the wiper blade is 16 inches. Find the area wiped by the wiper blade. (Round your answer to one decimal place.)
Answer:
312.7 in^2Step-by-step explanation:
This problem is on the mensuration of flat shapes, sectors and arc.
we know that the area of a sector is given as
A=(∅/360)*πr^2
Given that the length of the wiper R=24 in
and the length of the blade r= 16in
To find the area of the wiped surface we only require the length of the blade as the radius
The area of the wiped surface is given as= (140/360)*3.142*16^2
A= 0.3888*3.142*256
A=312.7 in^2
6th grade math pls help
99 is 36% of what number?
Answer:
257
Step-by-step explanation:
36% of 275 is 99. 100% of 275 is 275, therefore 36 percent of 275 equals 99
Rhonda had $300 to buy supplies for the animal shelter. She bought 8 bags of dog food and 11 leashes. Each bag of food cost $25.19, and each leash cost $4.65. How much money did Rhonda have left after her purchases? $11.65 $14.29 $22.91 $47.33
Hey there! I'm happy to help!
We have 8 bags of dog food and each costs $25.19
8(25.19)=201.52
And we have 11 leashes each costing $4.65.
11(4.65)=51.15
We add these totals up.
201.52+51.15=252.67
We subtract this from 300 to see how much is left.
300-252.67=47.33
Rhonda had $47.33 left after her purchases.
Have a wonderful day! :D
Answer:
$47.33
Step-by-step explanation:
she bought 8 bags of dog food so: 8 x 25.19 = 201.52
she bought 11 leashes so: 4.65 x 11 = 51.15
201.52 + 51.15 = 252.67
300 - 252.67 = 47.33
An organism measures 2.9• 10-5 centimeters in diameter. What number in standard notation [ANSWERS PLEASE I’ll even cash app u 2$]
Use the tables above to compose the following functions.
A: f(g(2))
B: f(g(5))
C: g(f(-1))
D: g(f(5))
Answer:
A. 1
B. 2
C. 2
D. 0
Hope it helps :-)
Elaina wrote two correct variable expressions to represent the phrase “one-fourth of a number.”
Which variable expressions could Elaina have written?
Select each correct answer.
Answer:
C and D are both correct
hope that helps
here are the answer choices if anyone needs it :)
4 ÷ n
14n
n4
4n
Which situation can be represented by the inequality 3.35x + 25 < 6.75x + 5?
Answer:
x >100/17
plz mark brainliest
Solve -2a -5 > 3 Which graph shows the solutions?
Answer: a< -4 D
Step-by-step explanation:
Samantha is buying a bike for $290. If sales tax is 6.4%, how much will be added to the price of the bike?
Answer:
18.56
Step-by-step explanation:
6.4% of 290 is 18.56
you find this by multiplying 290 by 0.064 (which is the decimal form of 6.4%)
HELP!! Need Help With My Homework!
Answer:
x + 4 = 9 + 2x - 15
Step-by-step explanation:
Since, E is between F and G.
Therefore,
FG = EF + EG
x + 4 = 9 + 2x - 15
x + 4 = 2x - 6
4 + 6 = 2x - x
10 = x
or
x = 10
The temperature in Chicago was 12°F this
morning, while the temperature in Minneapolis
was -8°F. What is the difference between the
two temperatures?
Answer:
4 °F
Step-by-step explanation:
this is a segment addition practice. can someone please help me find the length indicated?
Answer:
3
Step-by-step explanation:
Points C, D, and E are collinear.
Segment CD = 8
Segment CE = 11
Segment DE = ?
According to the segment addition postulate:
[tex] CD + DE = CE [/tex]
[tex] 8 + DE = 11 [/tex] (substitution)
Subtract 8 from both sides
[tex] 8 + DE - 8 = 11 - 8 [/tex]
[tex] DE = 3 [/tex]
The missing lenght indicated = 3
Which interval for the graphed function has a local
minimum of 0?
[-3, -2]
[-2, 0]
[1, 2]
[2, 4]
Answer:
the answer is D i hope this help
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
A steel woodworking blade is created from a rectangular mold with vertices at (0, 0), (0, 1), (4, 0), and (4, 1). (All coordinates are in centimeters). At each point of the blade, the thickness, in milimeters, is equal to twice the y-coordinate. Find the height of the balance point of the blade.
Answer:
5.6 cm
Step-by-step explanation:
Given that a steel woodworking blade is created from a rectangular mold with vertices at (0, 0), (0, 1), (4, 0), and (4, 1). (All coordinates are in centimeters). At each point of the blade, the thickness, in milimeters, is equal to twice the y-coordinate.
The x axis or the horizontal length will be L = (1 - 0)^2 + ( 0 - 0 )^2
L = 1 cm
The y axis or the vertical length will be
L = sqrt ( [ 4-0]^2 + [0-0]^2)
L = Sqrt(16)
L = 4 cm
Given that at each point of the blade, the thickness, in milimeters, is equal to twice the y-coordinate.
That is,
Thickness = 2 × 4 = 8 mm
The height of the balance point of the blade will be;
Height = 8 mm + 4 cm + 8 mm
Height = 0.8 + 4 + 0.8
Height = 5.6 cm
Note that the thickness will be added to both the top and the bottom of the blade.
Evaluate 4-0.25g+0.5h when g=10 and h=5
Solve the problem.
A pendulum swinging through a central angle of 108° completes an arc of length 24 cm. What is the length of the
pendulum? Round to the nearest hundredth.
Answer:
Yes! I was looking to refresh my geometry skill!
Step-by-step explanation:
So, a 108* arc is 24 cm. How to solve it?
First, we need to find the Circumference, or perimeter of the circle. (That the swinging pendulum makes.
Second, use that in the formula for circumference, and find the radius.
Third, done! So, let's get to it!
All we have to do to find the circumference is divide 24 by 108, then multiply that by 360*(because a circle is 360*).
[tex]24/108*360=80[/tex]
So, our circumference is 80cm. Nice! Just need to input that into the circumference formula.
[tex]80=2\pi *r\\[/tex]
Now, to solve...
[tex]40=\pi *r\\40/\pi =r[/tex]
This rounds to about 12.73 cm.
Hope this helps!
Happy Geometry!
5. Susie has 24 bags of pretzels and 16 bags of chips. She wants to make snack
packs to sell at the carnival, and she wants each snack bag to have the same
number of pretzel bags and chip bags. ANSWER questions 5a, b and c
Step-by-step explanation:
Given that,
Susie has 24 bags of pretzels and 16 bags of chips.
She wants to make snack packs to sell at the carnival, and she wants each snack bag to have the same number of pretzel bags and chip bags.
To find the same no of pretzel bags and chip bags, we can take LCM of 24 and 16.
LCM of 24 and 16 = 48
It means she will need 48 pretzel bags and chip bags
please help, will give brainiest