can you help me with this

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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Answer:

\(x\sqrt{3x}\)

Step-by-step explanation:

Since the insides of the quadratics are the same you can simply take 4x-x-2x which is 4x-3x which is just a single x

The conclusion is that since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.

A null hypothesis is a hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling error.

Here, the effect of a one-day SAT prep class at a 5% level of significance was assessed.  Since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.

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Answer:

O C. 0

Step-by-step explanation:

What is the sum of 15 and its additive inverse?

In Mathematics, the additive inverse of a number is defined as the number that when it is added to a specific number equals 0

From the above question, the additive of 15 = -15

Therefore, the sum of 15 and its additive inverse is calculated as:

15 + -15

= 15 - 15

= 0

Therefore, Option C is the correct option

Answer:

D. She multiplied p by 0.25 then subtracted that from p.

Step-by-step explanation:

p is the normal cost

discount is 25% so the total discount is 0.25p

the sale price = normal cost - discount = p - 0.25p = 0.75p

Answer:

3(2) + 15= 21; 3(3) +15= 24; 3(5) + 15= 30

Step-by-step explanation:

just plug in your x values and then solve

Answer:

52 years.

Step-by-step explanation:

Represent my current age by c.  Then 400 - 2c = 296, or

104 = 2c

Then c must be 104/2, or 52 years.

The Formula of Area of Obtuse Triangle is equal to ½ × b× h .

and by using Heron's formula,

A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2

A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.

Obtuse triangle: A type of triangle with the following properties:

Area formula of obtuse triangle :

Area of obtuse triangle = ½ × b × h

where b --> base of triangle

h ---> height of triangle.

The area of a triangle can also be found using Heron's formula.

A = √(S(S-a)(S-b)(S-c)),

where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.

the perimeter of the triangle = a + b + c cm then

S = (a + b + c)/2

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Answer:

60

Step-by-step explanation:

To check: half of 60 is 30, if 10 people leave that's 20, one third of 60 is 60/3  which = 20  

The room hold 60 people when it is full.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that room is 1/2 full of people. After 20 people leave, the room is 1/3 full.

The half of 60

60/2 =  30,

And if 10 people leave that's 20, one third of 60

60/3 = 20  

So, there are 60 people total.

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Answer:

y=2x+4

Step-by-step explanation:

From(0,4)

Equation in slope intercept form

Answer:

answer is a

Step-by-step explanation:

jus took the test <3

The advantage of renting from the given four options given is said to be; A: Financial Risk

Renting is defined as an agreement where a payment is made for the temporary use of a good, service or property owned by another.

Now, renting could also be callled Hiring or Letting but then a gross lease is when the tenant pays a flat rental amount with the landlord paying for all property charges regularly incurred by the ownership.

Thus, one advantage of renting is financial risk.

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Answer:

y = 18/5(11)

Step-by-step explanation:

If y varies directly as x, this is expressed as;

y∝x

y = kx

k is the constant of proportional constant

if y = 18 and x = 5

18 = 5k

k = 18/5

to get the expression that can be used to find the value of y when x is 11

y = kx

y = 18/5(11)

This gives the required expression

The correct values for the constants A and B are A = -3 and B = 25/2, satisfying the given initial conditions for the differential equation.

To find the constants A and B, we can use the given initial conditions.

Given: y(1) = 1 and y(2) = 2.

Substituting x = 1 into the general solution:

y(1) = A(x1​)+B(x3+x)

1 = A(1^4+6(1^2)+1) + B(1^3+1)

1 = A(8) + B(2)

Substituting x = 2 into the general solution:

y(2) = A(x1​)+B(x3+x)

2 = A(2^4+6(2^2)+1) + B(2^3+2)

2 = A(41) + B(10)

Now we have a system of equations:

A(8) + B(2) = 1    ---(1)

A(41) + B(10) = 2  ---(2)

Solving this system of equations, we can find the values of A and B.

Multiplying equation (1) by 5 and equation (2) by 3, we get:

5A(8) + 5B(2) = 5

3A(41) + 3B(10) = 6

40A + 10B = 5

123A + 30B = 6

Multiplying equation (1) by 6 and equation (2) by 2, we get:

6A(8) + 6B(2) = 6

2A(41) + 2B(10) = 4

48A + 12B = 6

82A + 20B = 4

Subtracting the equations, we get:

(82A + 20B) - (48A + 12B) = 4 - 6

34A + 8B = -2

Dividing both sides by 2:

17A + 4B = -1

Now we have a new equation:

17A + 4B = -1   ---(3)

From equations (1) and (2), we have:

40A + 10B = 5

123A + 30B = 6

Multiplying equation (1) by 3 and equation (2) by 1, we get:

120A + 30B = 15

123A + 30B = 6

Subtracting the equations, we get:

(123A + 30B) - (120A + 30B) = 6 - 15

3A = -9

A = -3

Substituting A = -3 into equation (3), we have:

17(-3) + 4B = -1

-51 + 4B = -1

4B = -1 + 51

4B = 50

B = 50/4

B = 25/2

Therefore, the correct answer is:

(B) A = -3 and B = 25/2.

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Answer:

10^n   means to multiply by 10

10^-n means to divide by 10 or multiply by 1 / 10

So .0009763 means 9.763 / 10000 = 9.763 * 10-4

can also write as 9.763E-4

If multiplying then the power of 10 would have to be negative

Answer:

y = -6x -8

Step-by-step explanation:

4 = -6(-2) -8

4 = 12-8

4 = 4

The explaination above shows how to verify your answer.

Hope this helps u!

Answer:

D. BC = 12cm, <B = 45, AC = 12cm

Step-by-step explanation:

Edge 2021

The measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm

A right triangle is a triangle that has one of its angle measure to be 90 degrees.

From the question, we have:

Angle B = 45 degrees

Since angle B is 45 degrees, then the legs of the triangle are equal (i.e. 12 cm)

Hence, the measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm

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We want to compare two linear equations and answer some things in regards to these.

So we have two sets of data:

A) First we want to compare the steepness of the lines, it will represent how much money you and your friend gets per week, a more steep line means a larger weekly income.

By the given points, you can see that you have an increase of $60 in 3 weeks, while your friend has an increase of $60 in 4 weeks, thus, your line should be steeper.

B)  We know that for a line that passes through points (x₁, y₁) and (x₂, y₂) the slope is given by:

\(s = \frac{y_2 - y_1}{x_2 - x_1}\)

So, for you, the slope is:

\(s_y = \frac{\$100 - \$40}{5 weeks - 2 weeks} = \$20\ per \ week\)

For your friend the slope is:

\(s_f = \frac{\$120 - \$60}{8 weeks - 4 weeks} = \$15 \ per \ week\)

C) Your friend saves $5 less than you per week.

D) You, by week 5, have $100

So you need to save another $65

And you save $20 per week, so we need to solve:

$20*x = $65

x = $65/$20 = 3.25

Rounding to the next whole number, x = 4

And this is 4 weeks after the 5th week, so you need to save for a total of 9 weeks.

For your friend, he has $120 at the 8th week, then he must save another $45, and he saves $15 per week, so we need to solve:

$15*x = $45

x = $45/$15 = 3

He must save for another 3 weeks, for a total of 11 weeks.

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Answer:

A) A cylinder with a height of 2 and a diameter of 8.

Step-by-step explanation:

The height of the cylinder is half the radius. Therefore.

Height of the cylinder = (half of the radius)/2

Answer choice A) A cylinder with a height of 2 and a diameter of 8.

Note that a diameter is found using the following formula:

d (diameter) = 2r (radius).

First, divide 2 from the diameter to find the radius:

8/2 = 4

Next, divide by 2 again to find the height of the cylinder:

4/2 = 2

In this case, the height of the cylinder is 2, ∴ the choice is correct.

~

Answer:

a

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

-6*(-4)

The negative signs cancel:

6*4

24

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Step-by-step explanation:

a) The range at which the internal temperature can rise is from 2°F to 6°F, which means that in order fo the final temperature of the turkey to fall within the range of 165-170°F, we need to pull remove the turkey when the internal temperature is at a minimum of 164°F or a maximum of 168°F.

b) I'd rather err on the higher side of the internal temperature. After all, no one eats poultry cooked medium rare due to the high probability of salmonella poisoning and the 165-170°F is meant to destroy the microbes that causes food poisoning. Not only that, poultry meat gets sufficiently cooked at that range.

Answer:

72 sweets

Step-by-step explanation:

72 / 6 =12

72 / 8 = 9

72 / 9 = 8  

a) g^(-1)({0}) = [0, 1)
b) g^(-1)({-1, 0, 1}) = (-1, 0) ∪ [0, 1) ∪ [1, 2)
c) g^(-1)({x | 0 < x < 1}) = (0, 1).

the inverse of g(x) = ⌊x⌋ for the set {x | 0 < x < 1} is g^(-1)({x | 0 < x < 1}) = (0, 1).

a) The inverse of g(x) = ⌊x⌋ is the set of values x for which ⌊x⌋ = 0. Since the greatest integer less than or equal to 0 is 0 itself, the inverse of g(x) = ⌊x⌋ for the set {0} is g^(-1)({0}) = [0, 1).

b) To find the inverse of g(x) = ⌊x⌋ for the set {-1, 0, 1}, we need to determine the values of x for which ⌊x⌋ takes on these values. For ⌊x⌋ = -1, x must be in the range (-1, 0). For ⌊x⌋ = 0, x must be in the range [0, 1). For ⌊x⌋ = 1, x must be in the range [1, 2). Therefore, the inverse of g(x) = ⌊x⌋ for the set {-1, 0, 1} is g^(-1)({-1, 0, 1}) = (-1, 0) ∪ [0, 1) ∪ [1, 2).

c) The inverse of g(x) = ⌊x⌋ for the set {x | 0 < x < 1} can be found by determining the values of x that satisfy this condition. Since g(x) rounds down to the nearest integer, the values of x for which 0 < x < 1 are in the interval (0, 1). Therefore, the inverse of g(x) = ⌊x⌋ for the set {x | 0 < x < 1} is g^(-1)({x | 0 < x < 1}) = (0, 1).

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An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.

Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.

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1. To transform from standard form to vertex form you need to complete the square.

To transform from vertex form to standard form multiply the equation out and combine all the like terms.

2. The attributes from vertex form would be the roots ( zeros)

From standard form the attribute would be the lowest point, also known as the vertex.