find the general solution for x^2y'' - 5xy' 13y=0

Answer:

4k+2 (when k=6)

5k+6 (when k=4)

Step-by-step explanation:

Answer:

14

12

Step-by-step explanation:

Just run through possible even numbers up till 26.

14 + 12 = 26 and they are two consecutive even numbers

We are here given that the slope of line A is -4 and line B is perpendicular to line A . As we know that the product of slopes of two perpendicular lines is -1 . Therefore ,

\(\longrightarrow m_Am_B =-1\\\)

\(\longrightarrow m_B =-\dfrac{1}{-4}=\boxed{\dfrac{1}{4}}\)

From the given graph we can see that the line B intersects y axis at (0,6) . Therefore this is the coordinate of the y intercept of line B .

Now we can use the slope intercept form of the line to find the equation of line B,

\(\longrightarrow y = m_Bx + c \\ \)

\(\longrightarrow \underline{\underline{y =\dfrac{1}{4}x +6}}\)

And we are done!

Answer:

-27/64p^3  

Tell me if you want a step by step. :)

Answer:

3

Step-by-step explanation:

The actual prime factors of 60 are 2, 3, and 5.

Answer:

3

Step-by-step explanation:

prime fatorizations are 2, 3, and 5

Using Tap working problem solving,

when faucet and drain working together, the time to fill up the tub is 60 minutes.

We have the following information about question,

The time taken by faucet to fill up the tub

= 15 minutes

The time taken by drain to empty the tub

= 20 minutes

we have to calculate the time in which the tub is fully fill the tube with drain open.

Rate of fill up the tub by faucet = 1/15 i.e 1/15 th of tub in one minute .

Rate of empty the tub by drain = 1/20 i.e 1/20 th of tub in one minute.

In one minute both are working together and will fill the tub = 1/15 - 1/20 = 1/60 i.e 1/60 th of tub

Since, it takes one minute to fill 1/60th of the tub and it will take 60 minutes to fill the tub.

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Answer:

300

Step-by-step explanation:

I think its 300 but if I'm wrong then XD I Don't know

Answer:

  5.48 lb

Step-by-step explanation:

12 inches is 1 foot.

12.8 times that length will have 12.8 times that weight:

  12.8 · 0.428 lb = 5.4784 lb ≈ 5.48 lb

__

The given values have 3 significant figures, so the answer needs to be rounded to 3 significant figures.

The sum of three consecutive number is 63, hence the number is 20.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Let x represent the number. The sum of three consecutive number is 63, hence:

x + (x + 1) + (x + 2) = 63

x = 20

The sum of three consecutive number is 63, hence the number is 20.

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470 = 29x+35

(x is number of birthday cakes)

subtract 35 from both sides,

435 = 29x

divide both sides by 29 to get x by itself,

15 = x

15 birthday cakes were made!

Answer:

35+29x=470 x=15 cakes

Step-by-step explanation:

3 35 represents rate for the oven and then 29 dollars per cake is the 29. 470 is the total amount of money you spent you just have to solve the equation from then to get x equals 15

Answer:

(6f - 6.1)

Step-by-step explanation:

Since you are multiplying DIFFERENT signs, the signs change. SO the "-" turns into a "+" and the "+" turns into a "-".

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.

A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.

We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.

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The solutions to the equation tan(x) = 0 within the interval [0, 2π) are x = 0 and x = 2π. To solve the equation tan(x) = 0 within the interval [0, 2π), we can consider the properties of the tangent function and its periodicity.

The tangent function is defined as the ratio of the sine and cosine functions: tan(x) = sin(x)/cos(x).

First, we note that tan(x) is equal to 0 when sin(x) = 0 and cos(x) ≠ 0. This occurs when x is an integer multiple of π.

In the given interval [0, 2π), the solutions for tan(x) = 0 are x = 0, π, and 2π.

However, we need to consider that the tangent function has vertical asymptotes at x = π/2 and 3π/2, where the cosine function is equal to zero. Therefore, the values x = π/2 and 3π/2 are not solutions within the given interval [0, 2π).

So, the solutions that lie within the interval [0, 2π) and satisfy tan(x) = 0 are x = 0 and x = 2π.

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Answer:

B. 3/5 is correct.

Step-by-step explanation:

P(A or B) is the number of students within either set (circle) divided by the total number of students (10).

There are 6 students (3+1+2)  in the sets, so

P(A or B) = 6/10 = 3/5

Answer B. 3/5 is correct.

The value of P(A or B) from the Venn diagram is 2/5.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

Event A = Students that play basketball

Event B = Students that play Soccer

Now,

From the Venn diagram,

P(A) = 3/10

P(B) = 2/10

P(A ∩ B ) = 1/10

Now,

P(A or B) = P(A U B ) = P(A) + P(B) - P (A ∩ B)

So,

P(A U B )

= P(A) + P(B) - P (A ∩ B)

= 3/10 + 2/10 - 1/10

= (3 + 2 - 1) / 10

= 4/10

= 2/5

Thus,

The value of P(A or B) is 2/5.

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The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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Answer:

B.)

Step-by-step explanation:

B.) Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations.

When you multiply the top by 3 you'd get 6x+24y=-9 and when you multiply the bottom equation by -2 you'd get -6x-12y=8

6x and -6x would cancel each other out eliminating the x variable.

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Answer: -5, -7, and -9

Step-by-step explanation:

checking the pattern they are subtracting by two by the next term, so subtracting 2 from -3 would be -5 and so on.

Answer:

it rose by 0.45

Step-by-step explanation:

In sigma notation, the sum is represented as follows: ∑ (k^2 + 1), k = 1 to 2.

The given sum is: 12 + 22 + 32 + 132.

To write this sum using sigma notation, we can observe the pattern in the terms. The first term is 12, the second term is 22 (which is 12 + 1), the third term is 32 (which is 22 + 1), and the fourth term is 132 (which is 32 + 1 + 2).

We can see that each term is obtained by adding the square of the position number (k^2) to the previous term, along with an additional constant value of 1 or 2 depending on the position.

So, let's write the sum using sigma notation:

∑ [(k^2 + c(k-1))], where k starts from 1 and goes up to 4.

In this notation, k represents the position of the term, k^2 represents the square of the position number, and c represents the constant value added to the previous term.

For the given sum, the constant value c changes depending on the position of the term:

For the first term (k = 1), c is 1.

For the second term (k = 2), c is 1.

For the third term (k = 3), c is 1.

For the fourth term (k = 4), c is 2.

So, the corrected sigma notation for the given sum is:

∑ [(k^2 + c(k-1))], k = 1 to 4.

This indicates that we sum the terms (k^2 + c(k-1)) as k takes values from 1 to 4, where c changes based on the position of the term.

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The growth factor in the function is 5.

An exponential function with the form A(t) = \(C a^t\), where a > 0

When t = 0, the function's initial value is represented by the number C, and the growth (or decay) factor is represented by the number a.

If a > 1, the function represents growth; If 0 < a < 1, the function represents decay.

Given:

y = 4 x \(5^7\\\)

we know the general form of Exponential function

g(x) = \(ab^x\)

where a is the initial amount

b is the growth or decay factor

and, x is the time

Now, comparing to the given function

Initial amount= 4

Growth factor = 5

time = 7

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Multiple bits of data can be processed simultaneously by "neural networks," which can also pick up on patterns.

The neural network is a collection of algorithms that aims to identify underlying links in a set of data using a method that imitates how the human brain functions.

Thus, "Neutral networks" have the capacity to analyze a large amount of data concurrently while picking up trends.

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Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.

2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.

3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.

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The pairs that are included in the set of solutions for y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

If a point is located on a line of an equation, then the ordered pair of that point is defined as belonging to the set of solutions for the equation.

Given the equation, y = 1/2x + 3/2, the graph is plotted on a coordinate plane as shown below. It has a slope of 1/2, and a y-intercept of 3/2.

The graph shows that the following pair of the points are located on the line of y = 1/2x + 3/2:

Therefore, it is concluded that the pairs that are included as the solution to y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

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Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

The weights that separate the top and bottom 8% are approximately 5.26 ounces and 5.12 ounces, respectively.

I need to find the weight that separates the top 8% and bottom 8% of the normal distribution.

Let X be the weight of the mechanical part. \(X ~ N(5.19, 0.05^2)\), H. X is normally distributed with mean μ = 5.19 ounces and standard deviation σ = 0.05 ounces.

You'll be able to utilize the z-score equation to standardize the conveyance and discover the z-scores comparing to the best 8% and foot 8% of the dispersion. 

For the top 8%:

z = invNorm(1-0.08) = 1.405

For the bottom 8%:

z = invNorm(0.08) = -1.405

where invNorm is the inverse normal distribution function.

You can use the Z-score formula to find the corresponding weights.

For the top 8%:

z = (x - μ) / σ

1.405 = (x - 5.19) / 0.05

x - 5.19 = 0.07025

x = 5.26025 ounces

For the bottom 8%:

z = (x - μ) / σ

-1.405 = (x - 5.19) / 0.05

x - 5.19 = -0.07025

x = 5.11975 ounces

Therefore, the weights that separate the top and bottom 8% are approximately 5.26 ounces and 5.12 ounces, respectively. Components with weights outside this range may be rejected.

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Answer:

(-4,-3)

Step-by-step explanation:

Not sure if tht was what you were asking, but that's how u write it as a point or vertex

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer: x= 22.5, angle B = 67.5

Step-by-step explanation:

90+3x+x= 180

4x = 90

x=22.5

3(22.5)= 67.5

Answer:

x = 22.5° B = 67.5

Step-by-step explanation:

90° + 3x° + x° = 180°

4x = 90°

x = 22.5°

Answer: The statue is 9 feet tall.

Step-by-step explanation: Just double all of your values because 12 is 6x2.