integrate (1-x³)² with respect to x
Answers
Answer:
Start off by expanding the square:
x^6 -2x³ + 1.
Now, we can integrate it in dx:
∫x^6 - 2x^3 + 1 dx = ∫x^6 dx - 2∫x^3 dx + ∫1 dx = (x^7)/7 - 2((x^4)/4) + x = (x^7)/7 - (x^4)/2 + x.
That's the result!
\(\\ \sf\longmapsto {\displaystyle{\int}}(1-x^3)^2dx\)
\(\\ \sf\longmapsto {\displaystyle{\int}}(1-x^6+2x^3)dx\)
\(\\ \sf\longmapsto x-\dfrac{x^{6+1}}{6+1}+2\dfrac{x^{3+1}}{3+1}\)
\(\\ \sf\longmapsto x-\dfrac{x^7}{7}+2\dfrac{x^4}{4}\)
\(\\ \sf\longmapsto x-\dfrac{x^7}{7}+\dfrac{x^4}{2}\)
Related Questions
if m<xyz = 58 and m<wxz = 51 find m<wzx
Answers
Answer:
m<wzx = 71
Step-by-step explanation:
Assuming these are interior angles of a triangle.
The sum of all three interior angles of a triangle is always 180 degrees, therefore:
m<xyz + m<wxz + m<wzx = 180
Substitute our values:
58 + 51 + m<wzx = 180
m<wzx = 180 - 58 - 51
m<wzx = 71
There is 12 inches in a whole hole how many inches is in a half of a hole?
Answers
Answer:
6 is hoing to be your answer
Answer:
6in
Step-by-step explanation:
log8(_)-log8 7 = log8 5/7
fill in the blank (_)
Answers
\(\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_8(x)-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\implies \log_8(\stackrel{x }{5})-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\)
(2a+3)²-2^(a-1)^(a+1)+a^(a-1)³
Answer = BRAINLIEST
Answers
Answer:
Just use algebra calculator
Step-by-step explanation:
ax2 + bx + c = y How is "a" connected to the 2nd difference sequence?
Answers
In the sequence given below,.
\(-4x^2+30x+74=y\)In relation to the general equation of a quadratic formula,
\(ax^2+bx+c=y\)Where, a, is the cofficient of x^2,
b is the coeffient of x and,
c is constant,
Relating the two equations,
\(\begin{gathered} a=-4 \\ b=30\text{ and,} \\ c=74 \\ ax^2+bx+c=y \\ -4x^2+30x+74=y^{}^{} \end{gathered}\)Hence, a = -4 in the sequence.
Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=
Answers
Answer:
Step-by-step explanation:
We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.
For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,
y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0
(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.
Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get
yp″=a1+2a2x....yp‴=2a2+3a3x+....
Substituting the general solution into the non-homogeneous equation, we get
a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)
So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:
a(n+1)=Y(n-2)/n^2
From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.
Please help I been stuck on this question for so long
Answers
Answer: 1/ 3 ^9
Step-by-step explanation:
Answer:
1/39
Step-by-step explanation:
3-9=1/39
The answer is 0ne over three exponent nine
solve the rational equation 8-6/x=5+12/x
Answers
Answer:
X = 6
Step-by-step explanation:
find the value of -3/8 x 8/15=
Answers
we have -3/8 x 8/15 = -3/8 x 8/ (3x5) = -1/5
ok done. thank to me :>
The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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A rectangle's area is 7 units larger than its perimeter. The width of the rectangle is 3 units. What is the length of the rectangle in units?
Answers
Answer:
length is 13 units
Step-by-step explanation:
case 1
l×b= 7+2(l+b)
lb = 7+2l+2b
given , b= 3
so,
l×3 = 7+ 2× l + 2× 3
3l -2l = 13
l = 13
Let length be x
Area
LB3xNow
area=2(L+B)+73x=2(3+x)+73x=13+2xx=13John plays basketball at the local gym. The gym charges a monthly membership fee of $15.00, plus each player pays $2.50 per game to pay for the cost of referees. John wants to spend less than $55 on basketball this month.
Answers
Step-by-step explanation:
Assuming that for each option, you play the same number of games,x
Let y represent the cost of playing x games using option A
Option A is to buy a membership card and pay $2 every time you go to the gym. The membership card costs $20. It means that
y = 20 + 2x
Let z represent the cost of playing x games using option B
Option B is to pay $4 each time you go. It means that
z = 4x
To determine how many games will be played before cost of option A equal to the cost of option B, we would equate y to z. It becomes
20 + 2x = 4x
4x - 2x = 20
2x = 20
x = 20/2 = 10
It will take 10 games for both to be the same
15+2.5x <55
Decimal:1.15
This holiday season, Ms. Bastarache organized to give each 9th grader a $10 Dunkin Donuts gift card. Because she bought a lot of cards, Ms. Bastarache tipped the Dunkin Donuts employee $20.
This function represents the relationship between the number of gift cards, c, and T(c), the total cost of the cards.
T(c) = 10c + 20
Be sure to answer BOTH questions below.
1. Determine the total cost, in dollars, for Ms. Bastarache to give out 93 gift cards.
2. Last year, Ms. Bastarache spent $820, how many cards did she purchase?
need help asap plzzzzzz
Answers
Answer:
1. $950
2. 80
Step-by-step explanation:
Rudd Clothiers is a small company that manufactures tall-men’s suits. The company has used a standard cost accounting system. In May 2020, 10,500 suits were produced. The following standard and actual cost data applied to the month of May when normal capacity was 15,500 direct labor hours. All materials purchased were used.
Answers
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
What
Is
Happening
Help
Write the equation of the line that has a slope of 2 and passes through the point (-5, 1).
y = 2x - 5
y = 2x + 11
y = 2x + 1
y = 2x + 9
Answers
Step-by-step explanation:
= 2x +b
Use the given point (2, 5)
5 = 2(2) +b
b = 5 -4 = 1
The equation of the line is
y = 2x +1
Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept
find the approximate area of the shaded region, given that the area of the sector is approximately 13.08 square units.
Answers
The area of the shaded region is 3915 units².
We have,
Area of the sector.
= 13.08 units²
Now,
To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.
Area = √[s(s - a)(s - b)(s - c)]
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case,
The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:
Calculate the semi-perimeter:
s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units
Use Heron's formula to find the area:
Area = √[7(7 - 5)(7 - 5)(7 - 4)]
= √[7(2)(2)(3)]
= √[84]
≈ 9.165 units (rounded to three decimal places)
Now,
Area of the shaded region.
= Area of the sector - Area of the isosceles triangle
= 13.08 - 9.165
= 3.915 units²
Thus,
The area of the shaded region is 3915 units².
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PLEASE WILL MARK IF YOU HELP!!
Answers
Answer:
22°
63°
m<H=22°
m<G=63°
Problem 1
Answer: 79--------------------------
Work Shown:
For any triangle, the three angles always add to 180
For any isosceles triangle, the base angles are congruent. The base angles are opposite the congruent sides. We see that angle O = angle H.
O+H+T = 180
H+H+T = 180
2H+T = 180
2H+22 = 180
2H = 180 - 22
2H = 158
H = 158/2
H = 79
=======================================================
Problem 2
Answer: 54--------------------------
Work Shown:
We'll use the same ideas as problem 1.
In this case, angle O = angle D = 63 since they are the base angles opposite the congruent sides.
D+G+O = 180
63+G+63 = 180
G+126 = 180
G = 180-126
G = 54
The probability of randomly selecting a white flower from a garden that has green, pink, yellow, and white flowers is 6%.
Which of the following describes the likelihood of selecting a white flower?
A.
likely
B.
unlikely
C.
neither unlikely nor likely
Answers
Answer:
b. unlikely
Step-by-step explanation:
I don't really know a step by step explanation :( sry
write an algebraic equation for the followingn problem and then solve for it. Hilltop dormitory just purchased a new soft drink machine on sale for $480. The sale price was 75% of the original price. What was the original price of the soft drink machine?
Answers
Answer:
Step-by-step explanation:480 x o.75=360
and now you add this amount on payed
360 + 480=840 was original price
¿De qué número 64 es el 80%?
Answers
PLEASE hELP!!!!!!
which number best represents the location of point E on the number line below?
A: 1.8
B: 1.6
C: 1.5
D: 1.3
Answers
Answer:
It would be -1.8 but i dont see that so probably a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
HELP ME please. i dont understand this.
Answers
Answer:
Step-by-step explanation:
Perimeter add all the sides.
so let's walk around and combine like terms:
starting on the bottom moving to the left.
3x^2 + x^2= 4x^2 (there are no other squared terms)
back to the bottom moving left again:
-11x-3x+3x+x = -10x (-3x + 3x =0)
so -11x + x = -10x
now add all of the constants
-1 + 2 = 1
so your answer is
4x^2 -10x + 1
9 - 4x + 3y; x = 8 and y =3
Answers
We have the following expression given:
\(9-4x\text{ +3y}\)We have some conditions given:
\(x=8,\text{ y= 3}\)Then we just need to replace these conditions into the equation and we got:
\(9-(4\cdot8)+\text{ (3}\cdot3\text{)= 9}-32+9=18-32=\text{ }-14\)Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.
Answers
The volume of the cone is approximately 211.06 cubic meters.
Why is that?
Well, the formula for the volume of a cone is:
V = (1/3)πr^2h
where:
Substituting the given values, we get:V = (1/3)π(4.5m)^2(10m)
V = (1/3)π(20.25m^2)(10m)
V = (1/3)π(202.5m^3)
V = 67.5π
Using a calculator, we get:
V ≈ 211.06 cubic meters
Therefore, the volume of the cone is approximately 211.06 cubic meters.
Look at ZV SW and ZTSW in the image below.
Which of the following is the best description for this pair of angles?
O acute
O complementary
O straight
supplementary
Answers
Answer:
Supplementary is your answer
0.2 is 10 times as 2
Answers
Answer:
5 times
Step-by-step explanation:
please follow me
1. What is the Importance of Finance in a Business?
2. What is the impact of Business in our economy?
Answers
Answer:
1) Finance is very important in a business as to meet the expenses from manufacturing a product to solding it capital is required. without finance one cannot run a business . even a small scale business requires some finance.
2) Business has a great impact in our economy. it increases the overall economy and contributes somewhere between 70 to 72% to the GDP.
NEED A RESPONSE ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:c
Step-by-step explanation:
what ace attorney game is this from
Answers
Answer:
it looks like the pc version since the quality is nice
there are n given points (numbered from 0 to n-1) on a plane maximum number of points inside the circle
Answers
Circle Detection Algorithm is a highly efficient and effective solution to finding the most number of points that lie on any one circle in a 2D real plane.
The algorithm to solve this problem is known as the "Circle Detection Algorithm." This algorithm starts by considering three points randomly selected from the given N points.
Next, the algorithm checks the number of points that lie on this circle. If this number is greater than the current maximum, then this circle becomes the new candidate for the circle that contains the most number of points.
To ensure that the algorithm is efficient, it is important to choose the points randomly, as this reduces the chances of getting stuck in a local maximum.
The mathematical formula to calculate the center and radius of the circle that passes through three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:
x = ( (y₂ - y₁)(y₃² - y₁² + x₃² - x₁²) - (y₃ - y₁)(y₂² - y₁² + x₂² - x₁²) ) / (2 * (x₃ - x₁)(y₂ -y₁) - 2 * (x₂ - x₁)(y₃ - y₁) )
y = ( (x₂ - x₁)(x₃² - x₁² + y₃² - y₁²) - (x₃ - x₁)(x₂² - x₁² + y₂² - y₁²) ) / (2 * (y₃ - y₁)(x₂ -x₁) - 2 * (y₂ - y₁)(x₃ - x₁) )
r = √(x₁ - x)² + (y₁ - y)²
Once the center and radius have been calculated, the algorithm can easily check the number of points that lie on the circle by calculating the distance of each point from the center and checking if it is equal to the radius.
Complete Question:
Given N points on the 2D real plane, what is the most efficient algorithm to find the most number of points that lie on any one circle?
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