If differential equation is 3(1+x^2)dy/dx = 2xy(y^3-1) then exponential is |y^3-1| = Ce^(x^2).
To solve the given differential equation, we can begin by separating the variables. We divide both sides of the equation by 2xy(y^3-1) to get:
3(1+x^2)dy/dx = 2xy(y^3-1)
(3(1+x^2))/(2xy(y^3-1)) dy = dx
Next, we integrate both sides with respect to their respective variables. On the left side, we integrate with respect to y, and on the right side, we integrate with respect to x:
∫(3(1+x^2))/(2xy(y^3-1)) dy = ∫dx
After evaluating the integrals, we obtain:
ln|y^3-1| = x^2 + C
Where C is the constant of integration. Finally, we can exponentiate both sides of the equation:
|y^3-1| = e^(x^2+C)
|y^3-1| = Ce^(x^2)
Here, Ce^(x^2) represents the constant of integration. Since the absolute value can be positive or negative, we consider both cases and solve for y to obtain the general solution.
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What is the greatest common factor of 12 and 30?
A 2
B 3
C 6
D 12
Answer:
6 is the answer
Step-by-step explanation:
6
Answer:
C- 6
Step-by-step explanation:
12=
1,2,3,4,6,12
30=
1,2,3,5,6,10,15,30
hope this helps :) also, brainliest?? :)
My brothers hw is 3x +(-6 + 3y)
Answer:
3x + 3y - 6
Step-by-step explanation:
3x - 6 + 3y =
3x + 3y - 6
What is the measure of this angle?
Answer:
25
Step-by-step explanation:
Answer:
? = 25°
Step-by-step explanation:
all triangle interior angles added together = 180°, so:
? = 180° - 119° - 36°
? = 25°
Solve the inequality.
2x-5<9
The solution is:
Answer:
x < 7
Step-by-step explanation:
Given
2x - 5 < 9 ( add 5 to both sides )
2x < 14 ( divide both sides by 2 )
x < 7
No período: \"Quando analisaram o desempenho da economia brasileira, os empresários afirmaram sua satisfação\". As orações presentes são, respectivamente
a) principal, coordenada.
b) subordinada, subordinada.
c) subordinada, principal.
d) subordinada, coordenada.
Answer:
a
Step-by-step explanation:
Select all the true sentences!!!
Answer:
only the 1st is true
Step-by-step explanation:
the rest are wronf
Help me please I give points thank you
NO FAKE ANSWER PLS
Answer:it is #4
7:4
so 7 suv and 4 trucks
The answer would be the Third option
Priya has 5 pencils, each x inches in length. When she lines up the pencils end to end, they measure 34.5 inches. Select ALL the equations that represent this situation. *
Answer:
Equation b and c represent the situation.
Which statement is true about Angle C P B?
Lines C D and A B intersect at point P.
It is supplementary to Angle A P C.
It is complementary to Angle A P C.
It is congruent to Angle A P C.
It is linear to Angle A P D.
Answer:
A. It is supplementary to angle APC
Step-by-step explanation:
Vocabulary:
Supplementary Angle - Two angles that when added together equal 180 degrees.
If we look at the graph provided which is attached below we can see that if we add angles CPB and APC it forms a straight line (a straight line always = 180 degrees) Making the answer A. It is supplementary to angle APC
Answer:
Step-by-step explanation:
Which statement is true about Angle C P B?
It is supplementary to Angle A P C.
It is complementary to Angle A P C.
It is congruent to Angle A P C.
It is linear to Angle A P D.
Identify a1 and r for the geometric sequence
a1 =
r =
Answer:
a₁ = - 256 , r = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
Given
[tex]a_{n}[/tex] = - 256 [tex](-\frac{1}{4}) ^{n-1}[/tex] , then by comparison
a₁ = - 256 and r = - [tex]\frac{1}{4}[/tex]
PLEASE HELP!!!!!
Find the volume and surface area of the composite figure. Give your answer in terms of π.
Answer Options
V ≈ 661.3π cm3; S = 264π cm2
V = 328π cm3; S ≈ 1045.3π cm2
V ≈ 1045.3π cm3; S = 328π cm2
V = 400π cm3; S ≈ 661.3π cm2
Answer:
V ≈ 661.3π cm3; S = 264π cm2
Step-by-step explanation:
Explain the steps taken to write an equation from a description given in words.
Answer:
Step-by-step explanation:
10+10+20
5+5=10
6+4=10
10+10=20
Answer:
the person above me is incorrect
To write an equation from a description given in words, you first have to identify and define the variable. Then you would identify the coefficient, constants, and operations between the terms. Finally, you can translate to write the equation.
What is the range of the function f(x) = -4|x + 1| − 5?
A. (-∞, -5]
B. [-5, ∞)
C. [-4, ∞)
D. (-∞, -4]
Answer:
answer is A
Step-by-step explanation:
hope that helps
The range of the function f(x) = -4|x + 1| − 5 is (-∞, -5). The correct option is A.
What are a domain and range?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.
The given function is f(x) = -4|x + 1| − 5. Plot the function on the graph and it is observed that the range of the function varies from -∞ tp 5.
The graph of the function is attached with the answer below. The absolute function has the vertex at (-1,-5).
Therefore, the range of the function f(x) = -4|x + 1| − 5 is (-∞, -5). The correct option is A.
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Consider the equation: −34=x^2−14x+10 1) Rewrite the equation by completing the square. 2) What are the solutions to the equation?
Answer:
1) x^2 - 14x + 44 = 0
(x^2 - 14x + 49) - 5 = 0
(x-7)^2 - 5 = 0
2)Assuming no complex number x...
(x-7)^2 = 5
x-7 = 5
x-7 = -5
x= 12, x=2
==============
Please give brainliest, I really want to rank up, thank you!
The answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2What are equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.So, the equation is:
−34 = x² −14x+10(A) Rewrite the equation by completing the square:
−34 = x² −14x+10x² - 14x + 44 = 0(x² - 14x + 49) - 5 = 0(x-7)² - 5 = 0(B) The solutions of the equation:
(x-7)² = 5x-7 = 5x-7 = -5x= 12, x=2Therefore, the answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2Know more about equations here:
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4. Find the circumference of a circle with a
diameter of 20 centimeters.
Answer:
circumference = π(diameter) = 3.14(20) =62.8 cm
Step-by-step explanation:
HELP! Ill vote brainliest and 60 pts is on the line!
The Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, was used to solve the equation. 2x2 − 8x + 7 = 0. Fill in the missing denominator of the solution.
4 plus or minus the square root of 2, all over blank
−16
2
4
14
Answer:
2
Step-by-step explanation:
[tex]2x^2-8x+7=0\\\\[/tex]
a=2
b=-8
c=7
[tex]\frac{8+ \sqrt{16-4(2)(7)} }{4}[/tex]
4±[tex]\sqrt{2}[/tex] /2
Answer:
The answer is 2 hope this helps :3
Step-by-step explanation:
Identify the zero(s) of this function (Desmos)
Answer:
x=2, -6
Step-by-step explanation:
[tex]3x^{2} +12x-36=0[/tex]
[tex]x^{2} +4x-12=0[/tex] (Divided by 3)
[tex](x-2)(x+6)=0\\x_{1} =2, x_{2} =-6[/tex]
What is the standard deviation for a portfolio that has $3,500 invested in a risk-free asset with 5 percent rate of return, and $6,500 invested in a risky asset with a 15 percent rate of return and a 22 percent standard deviation?
The standard deviation for the portfolio is 7.65%. This value is calculated by considering the weights and standard deviations of the assets in the portfolio.
To calculate the standard deviation of a portfolio, we need to consider the weights and the standard deviation of each asset in the portfolio. In this case, we have $3,500 invested in a risk-free asset and $6,500 invested in a risky asset.
First, let's calculate the standard deviation of the risky asset:
Standard Deviation = 22%
Next, we need to calculate the weighted average of the standard deviations of the assets in the portfolio:
Weighted Standard Deviation = (Weight of Risky Asset * Standard Deviation of Risky Asset)
Weighted Standard Deviation = (0.65 * 22%)
Now, we can calculate the standard deviation of the portfolio using the weighted standard deviation:
Portfolio Standard Deviation = [tex]\sqrt{(Weighted Standard Deviation^2)}[/tex]
= [tex]\sqrt{(0.65 * 22\%)^2}[/tex] = [tex]\sqrt{(0.65^2 * (22\%)^2}[/tex] = [tex]\sqrt{(0.4225 * 0.484)}[/tex] = [tex]\sqrt{0.204}[/tex]
Portfolio Standard Deviation = 0.452 = 7.65%
Therefore, the standard deviation for the portfolio is approximately 7.65%.
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P(A)=0.30 P(B)=0.58 P(A and B)=0.25 Find P(BIA). Round your answer to two decimal places.
The conditional probability P(B|A) is approximately 0.83.
To find the conditional probability P(B|A), we can use the formula:
P(B|A) = P(A and B) / P(A)
Given that P(A and B) = 0.25 and P(A) = 0.30, we can substitute these values into the formula:
P(B|A) = 0.25 / 0.30
Performing the calculation:
P(B|A) = 0.8333...
Rounding the answer to two decimal places:
P(B|A) ≈ 0.83
Therefore, P(B|A) is approximately 0.83.
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Write in terms of i
Simplify your answer as much as possible.
square root of -48
Given Galois field GF(2^4) with modulus IP= x^4+x^3+1: (4) How
many generators do the multiplicative group have? (5) List all the
generators of the multiplicative group.
In Galois field GF(2^4) with modulus IP = x^4 + x^3 + 1, there are eight generators in the multiplicative group, namely {x, x^3, x^5, x^6, x^7, x^9, x^11, x^12}, which have multiplicative orders equal to the order of the group (15) and generate all non-zero elements in the field.
To determine the generators of the multiplicative group in Galois field GF(2^4) with modulus IP = x^4 + x^3 + 1, we need to find elements that have multiplicative orders equal to the order of the group, which is 15.
The multiplicative group in a Galois field consists of all the non-zero elements. In this case, the elements of the field are polynomials of degree 3 or less with coefficients in GF(2) (the field with two elements, 0 and 1).
To find the generators, we can start by selecting an element from the field and compute its powers until we find an element whose power equals 1. The smallest power that gives 1 is the order of the element.
We can start with x, which represents the polynomial x^1. We compute its powers modulo the modulus IP:
x^2 = x * x = x^1 * x^1 = x^1
x^3 = x * x^2 = x^1 * x^1 = x^1
x^4 = x * x^3 = x^1 * x^1 = x^1
Since x^4 = x^1, the order of x is 4, which is not equal to the order of the multiplicative group (15). Therefore, x is not a generator.
We continue this process with other elements until we find generators. Let's try x^2:
(x^2)^2 = x^4 = x^1
(x^2)^3 = x^6 = x^2
(x^2)^4 = x^8 = x^4 = x^1
Since (x^2)^4 = x^1, the order of x^2 is 4, which is not equal to 15. Therefore, x^2 is not a generator.
We repeat this process with other elements until we find an element whose order is 15. Let's try x^3:
(x^3)^2 = x^6 = x^2
(x^3)^3 = x^9 = x^3
(x^3)^4 = x^12 = x^8 = x^4 = x^1
Since (x^3)^4 = x^1, the order of x^3 is 4, which is not equal to 15. Therefore, x^3 is not a generator.
We continue this process with x^4, x^5, and so on until we find a generator. After checking all possible elements, we find the following generators of the multiplicative group in GF(2^4) with modulus IP: {x, x^3, x^5, x^6, x^7, x^9, x^11, x^12}.
These eight elements have multiplicative orders equal to 15 and generate all the non-zero elements in the field under multiplication.
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10. Identify the property illustrated by the following equations a. 3+ [6+(-3)] = 3 +(-3+6) b. [3+(-3)] + 6 = 0 +6
The property illustrated by the given equations is the commutative property of addition.
The commutative property of addition states that changing the order of the numbers being added does not affect the sum. In equation (a), we can see that the numbers inside the parentheses are being added first, and then the sum is added to the number outside the parentheses. Similarly, in equation (b), the numbers inside the parentheses are added first, and then the sum is added to the number outside the parentheses.
In both cases, regardless of the order in which the numbers are added, the final sum remains the same. This demonstrates the commutative property of addition. The property holds true for any real numbers, and it allows us to rearrange the terms without changing the result.
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Evaluate the following expression will give branliest
256 to the power of 5/8
Answer:
32
Step-by-step explanation:
The formula needed to solve this question by hand is:
[tex]x^{\frac{m}{n}} =\sqrt[n]{x^{m}}[/tex]
256^(5/8) = 8th root of 256^5
256^(5/8) = 8th root of 1280
256^(5/8) = 32
Please answer I will make brainlest:)
Answer:
(3,-4)
Step-by-step explanation:
find the zeros of the following equation using the quadratic formula y = x2 + 13x – 48
Who can describe and correct the error in finding volume of the cone
I need help with (G)
Answer:
[tex]2^{5}[/tex]
Step-by-step explanation:
jack has a square flower bed in his garden with perimeter 120 m, he wants to deconstruct this flower bed and turn it into a triangular flower bed with maximum area. if he wants the triangular flower bed to have the same perimeter as the square flower bed, then what would be the area of such a triangular flower bed(rounded off to the nearest integer)?
To find the maximum area for the triangular flower bed with the same perimeter as the square flower bed, we can use the concept of an equilateral triangle.
Let's denote the side length of the square flower bed as 's'. Since the perimeter of the square is 120 m, each side of the square will be s = 120 m / 4 = 30 m.
Now, for the triangular flower bed to have the same perimeter as the square flower bed, it should also have a perimeter of 120 m. In an equilateral triangle, all three sides are equal in length.
Let's denote the side length of the equilateral triangle as 't'. Since the perimeter of the equilateral triangle is 120 m, each side of the triangle will be t = 120 m / 3 = 40 m.
The formula for the area of an equilateral triangle is given by:
Area = (sqrt(3) / 4) * t^2
Substituting the value of t, we get:
Area = (sqrt(3) / 4) * (40 m)^2
Area ≈ 346.41 m^2
Rounded off to the nearest integer, the area of the triangular flower bed would be 346 m^2.
£864.00 to be accrued
after £800 is invested with
2% pa simple interest.
Answer: 4 years
Step-by-step explanation:
Your question isn't complete but I believe that you want to calculate the number of years. This will be:
Simple Interest = PRT/100
where,
Interest = 864 - 800 = 64
Principal = 800
Rate = 2%
Therefore, 64 = 800 × 2 × T /100
Cross multiply
64 × 100 = 1600T
6400 = 1600T
T = 6400/1600
T = 4
Therefore, time will be 4 years
Given a A PQR with vertices P (2, 3), Q 1-3, 7) and R(-1, -3): The equation of median PM is :
The equation of the median PM in triangle PQR with vertices P(2, 3), Q(-3, 7), and R(-1, -3) is y = (1/3)x + 7/3.
To find the midpoint of QR, we calculate the average of the x-coordinates and the average of the y-coordinates. The x-coordinate of point M is (-3 + (-1))/2 = -2/2 = -1, and the y-coordinate of point M is (7 + (-3))/2 = 4/2 = 2.
Therefore, the coordinates of point M are (-1, 2). Now, we have two points, P (2, 3) and M (-1, 2), and we can find the equation of the line passing through these points using the point-slope form.
The slope of the line passing through P and M is (2 - 3)/(-1 - 2) = -1/-3 = 1/3. Using the point-slope form, we have:
y - 3 = (1/3)(x - 2)
Expanding and rearranging the equation, we get:
y = (1/3)x + 7/3
Therefore, the equation of the median PM in triangle PQR is y = (1/3)x + 7/3.
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