Answer:
[tex] \rm\displaystyle \frac{ {x}^{3} }{3} + 10 {x}^{2} + 100 x + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int (x + 10 {)}^{2} dx[/tex]
to do so simplify the integrand by using algebraic identity which yields:
[tex] \displaystyle \int {x}^{2} + 20x + 100 dx[/tex]
by sum integration we obtain:
[tex] \rm\displaystyle \int {x}^{2}dx + \int20x dx+ \int 100 dx[/tex]
remember that,
[tex] \displaystyle \int cxdx = c \int xdx[/tex]
so,we acquire:
[tex] \rm\displaystyle \int {x}^{2}dx + 20\int x dx+ \int 100 dx[/tex]
use exponent integration rule which yields:
[tex] \rm\displaystyle \frac{ {x}^{3} }{3} + 20 \frac{ {x}^{2} }{2} + \int 100 dx[/tex]
use constant integration rule which yields:
[tex] \rm\displaystyle \frac{ {x}^{3} }{3} + 20 \frac{ {x}^{2} }{2} + 100 x[/tex]
simplify:
[tex] \rm\displaystyle \frac{ {x}^{3} }{3} + 10 {x}^{2} + 100 x[/tex]
and we of course have to add the constant of integration:
[tex] \rm\displaystyle \frac{ {x}^{3} }{3} + 10 {x}^{2} + 100 x + \rm C[/tex]
Answer:
[tex]\displaystyle \int {(x + 10)^2} \, dx = \frac{(x + 10)^3}{3} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
U-Substitution
Step-by-step explanation:
*Note:
The answer below me is correct, but there is a simpler method to obtain the answer.
Step 1: Define
Identify
[tex]\displaystyle \int {(x + 10)^2} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = x + 10[/tex][u] Differentiate [Basic Power Rule]: [tex]\displaystyle du = dx[/tex]Step 3: Integrate Pt. 2
[Integral] U-Substitution: [tex]\displaystyle \int {(x + 10)^2} \, dx = \int {u^2} \, du[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int {(x + 10)^2} \, dx = \frac{u^3}{3} + C[/tex]Back-Substitute: [tex]\displaystyle \int {(x + 10)^2} \, dx = \frac{(x + 10)^3}{3} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
more help im dum lol
Answer:
32780
Step-by-step explanation:
Answer:
32,780
Step-by-step explanation:
It should be 30,000
Which word describes the slope of the line?
O Positive
O Negative
O Zero
O Undefined
Answer:
Option (1)
Step-by-step explanation:
Slope of a line is defined by the rule,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
Here, Rise and Run of the line are positive.
Therefore, sign of the slope of the line will be positive.
Option (1) will be the correct option.
What is the inverse fraction of f(x)=x/x-2
Answer:
[tex]inverse \ of \ f(x) : \frac{2x}{x-1}[/tex]
Step-by-step explanation:
[tex]y = \frac{x}{x-2}\\\\swap\ x\ and \ y\\\\x = \frac{y}{y-2}\\\\x(y -2) = y\\\\xy - 2x = y\\\\xy - y = 2x\\\\y(x-1)= 2x\\\\y = \frac{2x}{(x-1)}[/tex]
Step-by-step explanation:
Given two one-to-one functions f(x)f(x) and g(x)g(x) if
(f∘g)(x)=xAND(g∘f)(x)=x(f∘g)(x)=xAND(g∘f)(x)=x
then we say that f(x)f(x) and g(x)g(x) are inverses of each other. More specifically we will say that g(x)g(x) is the inverse of f(x)f(x) and
denote it by
g(x)=f−1(x)g(x)=f−1(x)
Likewise, we could also say that f(x)f(x) is the inverse of g(x)g(x) and denote it by
f(x)=g−1(x)
Given the function f(x)f(x) we want to find the inverse function, f−1(x)f−1(x).
First, replace f(x)f(x) with yy. This is done to make the rest of the process easier.
Replace every xx with a yy and replace every yy with an xx.
Solve the equation from Step 2 for yy. This is the step where mistakes are most often made so be careful with this step.
Replace yy with f−1(x)f−1(x). In other words, we’ve managed to find the inverse at this point!
Verify your work by checking that (f∘f−1)(x)=x(f∘f−1)(x)=x and (f−1∘f)(x)=x(f−1∘f)(x)=x are both true. This work can sometimes be messy making it easy to make mistakes so again be careful.
Explanation:
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is,
f−1(x)=2xx−1
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is, it is the inverse of function f(x).
That is,
f−1(x)=2xx−1
as required.
Answer my question please!! i will give brainlest!
Answer:
hello u so cool i admire you <3
A bag has 3 red marbles and 12 blue marbles. Half of the blue marbles are made of plastic. A marble is selected at random from the bag. What is the probability that it is a blue, plastic marble?
Answer: 2/5
Step-by-step explanation:
There are 15 total marbles in the bag. 12 are blue, with only 6 made from plastic. 6/15 reduced is 2/5
The following graphs have no scales assigned to them. Which of them could
not possibly be density curves for a continuous random variable if they were
provided with the right scale?
Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
E. Graph E
The graph A , graph C, could not possibly be density curves for a continuous random variable is they were provided with the right scale.
Given four graphs of different nature as options.
We are required to find the graph that is not continuous variable.
Continuous lines are those lines which when decreases, decreases with continuity and when increases,increases with continuity.
When we observe the graph A,graph C. In these graphs the value of function keeps increasing and decreasing a lot and not in continuity.
Hence graph A, graph C could not possibly be density curves for a continuous random variable is they were provided with the right scale.
Learn more about continuity at https://brainly.com/question/24637240
#SPJ1
Answer:
The answer is A, D, and E.
Step-by-step explanation:
can someone tell me how to do this? with steps?
Answer:
Step-by-step explanation:
In Δ AFB,
∠AFB + ∠ABF + ∠A = 180 {Angle sum property of triangle}
90 + 48 + ∠1 = 180
138 + ∠1 = 180
∠1 = 180 - 138
∠1 = 42°
FC // ED and FD is transversal
So, ∠CFD ≅∠EDF {Alternate interior angles are congruent}
∠2 = 39°
In ΔFCD,
∠2 + ∠3 + ∠FCD = 180
39 + ∠3 + 90 = 180
129 +∠3 = 180
∠3 = 180- 129
∠3 = 51°
Which is the most convenient placement of an isosceles triangle in the coordinate plane for finding the side lengths?
Answer:
The bottom left
Step-by-step explanation:
If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams
Answer:
750 is the answer..
Step-by-step explanation:
(12/40)*2500
Someone please ill mark you the brainliest! No cheating or else i’ll report you.
Answer:
............................
can i get the answer for this question would be verrryy much appreciated:)
Answer
The answer is EH= 50
What is the y-intercept of the function f(x) = -4.2^x
Answer:
[tex](0,-1)[/tex]
Step-by-step explanation:
The y-intercept always occurs when [tex]x=0[/tex]. To find the y-value of the y-intercept, substitute [tex]x=0[/tex] into your equation:
Given [tex]f(x)=-4.2^x[/tex], when [tex]x=0[/tex]:
[tex]f(x)=-4.2^0,\\f(x)=-(1)=-1[/tex]
Recall that [tex]n^0=1[/tex] for [tex]n\in \mathbb{R}[/tex]Therefore, the y-intercept of this function is [tex](0, -1)[/tex].
answer please? a girl needs help like right now:))
Answer:
No
Step-by-step explanation:
Which of the following is equivalent to (2x^3)(7x^4)?
Answer:
A: (2 times 7)x^3 plus 4
Step-by-step explanation:
2 times 7 is 14 so 14 in the parentheses and then add 3 plus 4 equals 7.
14x^7.
If a polynomial function f(x) has roots 3+ V5 and -6, what must be a factor of f(x)?
(X+(3-root5)
(X-(3-root5))
(X+(5+root3))
(X-(5-root3))
Answer:
Step-by-step explanation:
Radicals and imaginary numbers ALWAYS come in pairs when it comes to factors of polynomials. This is the called the conjugate theorem. If we are given a solution/root/zero that is
x = 3 + √5, then its conjugate is x = 3 - √5. Going backwards from the solution to the factor, we utilize the Zero Product Property and get
(x - (3 - √5)) which simplifies to (x - 3 + √5). if you are looking for the conjugate of the given zero, the choice you want is the second one down.
What is
4/11
as a decimal?
2.75
0.364
0.4
0.36
Maybe y’all don’t find the -
answer i got u guys its 0.36
Answer:
0.36
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
Hope it is helpful...Answer:
Yes, you are correct! 0.36363636... is the answer. 0.364 would be closest.
Happy learning!
--Applepi101
I need help with angles in a triangle to find x
I need help with these. please :(
Answer:
[tex]a. \: \: x = {60}^{o} [/tex]
[tex]b. \: \: x = {24}^{o} [/tex]
Step-by-step explanation:
Hint :Sum of angles = 180°
Simplify :[tex]a. \: \: {x}^{o} + {40}^{o} + {80}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} + {120}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} = {180}^{o} - {120}^{o} [/tex]
[tex] {x}^{o} = {60}^{o} [/tex]
[tex]b. \: 96+(x+12)+2x=180[/tex]
[tex]x+108+2x=180[/tex]
[tex]3x+108=180[/tex]
[tex]3x=180−108[/tex]
[tex]3x=72[/tex]
[tex]x = \frac{72}{3} [/tex][tex]x = 24[/tex]
Hope it is helpful...Two complementary angles have measures 4x and x + 50. Find x.
Answer:
x =17
Step-by-step explanation:
Complementary angles add to 90
4x+ x+5 = 90
Combine like terms
5x+5 = 90
Subtract 5 from each side
5x+5-5 = 90-5
5x = 85
Divide by 5
5x/5 = 85/5
x =17
select the right answer
Answer:
Blurry po
Step-by-step explanation:
Pwede kunan nyu ulit
What is the height of the pyramid ???
Answers:
A: 7cm
B: 5cm
C: 14 cm
D: 10 cm
Given:
[tex]m\angle ACD=45^\circ[/tex]
Point B is the center of the base.
Each side of the base = 10 cm
To find:
The height of the pyramid.
Solution:
It is given that the measure of each side of the base is 10 cm. It means the base is square. The length of the diagonal of a square is:
[tex]d=a\sqrt{2}[/tex]
Where, a is the side length of the square.
Putting [tex]a=10[/tex] in the above formula, we get
[tex]d=10\sqrt{2}[/tex]
It is given that point B is the center of the base. It means point B bisect each diagonal of a base. So,
[tex]BC=\dfrac{d}{2}[/tex]
[tex]BC=\dfrac{10\sqrt{2}}{2}[/tex]
[tex]BC=5\sqrt{2}[/tex]
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In triangle ABC,
[tex]\tan (45^\circ)=\dfrac{AB}{BC}[/tex]
[tex]1=\dfrac{h}{5\sqrt{2}}[/tex]
[tex]5\sqrt{2}=h[/tex]
[tex]7.0710678=h[/tex]
Round the value to the nearest integer.
[tex]h\approx 7[/tex]
The height of the pyramid is about 7 cm. Therefore, the correct option is A.
NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTS
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake?
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Explain her mistake. What is the correct formula?
Kelsey walked 1.7 miles to the park. Then she walked another 1.3 miles to a cafe. How far did Kelsey walk in all?
Answer:
3 miles
Step-by-step explanation:
1.7 carry a one because 3+7 is 10
+ 1.3
--------
3.0
Answer:
3 miles
Step-by-step explanation:
Kelsey first walked to the park which took 1.7 miles. Then she walked an additional 1.3 miles to get to the cafe.
If we are only counting the amount of miles that she walked without going back home then we can do this simply by doing
1.7+1.3
0.7+0.3 = 1.0 so we carry the one and in total we get 1.0+1.0+1.0 to get 3.0 miles or in other words 3 miles!
Como se encuentra la mediana?
Answer:
Para encontrar la mediana: Organice los puntos de datos de menor a mayor. Si el número de puntos de datos es impar, la mediana es el punto de datos intermedio de la lista. Si el número de puntos de datos es par, la mediana es el promedio de los dos puntos de datos intermedios de la lista.
Step-by-step explanation:
que tenga un lindo día
can someone please help me with this i dont have much time left
Answer:
Step-by-step explanation:
sin A = opposite/hypotenuse
=5/13
cos A =adjacent/hypotenuse
=12/13
tan A =opposite/adjacent
=5/12
cosec A = hypotenuse/opposite
=13/5
sec A = hypotenuse/adjacent
=12/5
cot A = adjacent/opposite
=12/5
A boy spends 3/8 of his journey in playing games on his mobile.Then 4/5 of the remaining time talking to his sister.If he has 5 min to complete his journey,what is the total time of the journey
Answer:
40 mins
Step-by-step explanation:
time spent talking to his sister = (1 - 3/8) x 4/5 =
5/8 x 4/5 = 1/2
total fraction of time spent playing games and talking to his sister :
[tex]\frac{3}{8} + \frac{1}{2}[/tex]
[tex]\frac{ 3 + 4}{8}[/tex] = [tex]\frac{7}{8}[/tex]
fraction of time remaining to complete the journey = 1 - 7/8 = 1/8
let t = total journey time
1/8 x t = 5
multiply both sides of the equation by 8
t = 5 x 8 = 40 minutes
The mean sustained wind velocity, v, can be determined by the equation v = 6.3 StartRoot 1013 minus p EndRoot, where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second? 103 millibars 194 millibars 363 millibars 910 millibars
Answer:
910 millibars
Step-by-step explanation:
According to the Question,
Given That, The mean sustained wind velocity equation [tex]v=6.3*\sqrt{1013-p}[/tex] And The mean sustained wind velocity is 64m/s (v=64) . where, p is the air pressure(in millibars).Now, the air pressure at the center of a hurricane when the mean sustained wind velocity is 64 m/s is
[tex]64=6.3*\sqrt{1013-p}\\\frac{64}{6.3} = \sqrt{1013-p}\\[/tex]
on squaring both sides we get,
(10.1587)² = 1012 - p ⇒ p = 908.80≈910millibar
p = 910millibars air pressure .
Answer: 910
Step-by-step explanation: Did the review and got it right
Determine the value of x in the diagram,
108°
72
1080
Answer:
72
Step-by-step explanation:
parallel sides= same angle.
also alternate angles theorem shows that if angles that alternate are the same. 72,108,72,108
Any help on this please ?
Answer:
x=35
Step-by-step explanation:
because the angles are next to each other they are supplementary, which makes the total of the angle 180 degrees.
the equation would be:
180=x+14 +4x -9
add the like terms
180=5x =5
then subtract 5 from both sides
175=5x
then divide five from both sides
x=35
Solve for xx. Round to the nearest tenth of a degree, if necessary.
Answer:
50.8Step-by-step explanation:
sin x = 6.2/8
sin x = 0.775
x = 50. 8
Bye , have a nice day ! :-)
Applying the sine ratio, sin ∅ = opposite/hypotenuse, the value of x, to the nearest tenth of a degree, is: 50.8°.
Hpw to Use the Sine Ratio?When solving a right triangle involving the opposite side and hypotenuse, the sine ratio can be used which is, sin ∅ = opposite/hypotenuse.
Apply the sine ratio to find x
sin x = opp/hyp = 6.2/8
x = sin^(-1)(6.2/8)
x = 50.8°
Learn more about the sine ratio on:
https://brainly.com/question/2920412
#SPJ2
PLEASE HELP!!! If the quadratic equation has the form y = ax 2and y = ax 2+ c, then their axis of symmetry must always be?
Answer:
axis of symmetry , x = 0
Step-by-step explanation:
For the quadratic equation of the form [tex]ax^2 + bx + c[/tex],
the axis of symmetry is the straight line [tex]x =- \frac{b}{2a}[/tex]
( i) Given equation y = ax² + 0x + 0
b = 0, therefore axis of symmetry is x = 0
( ii ) Second equation y = ax² + 0x + c
b = 0, therefore axis of symmetry is x = 0
