Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.

Answer:

That's your answer

x= 125

3x= 375

2x-1= 249

Answer:

1 square foot is the answer

Answer:

1 ft^2

Step-by-step explanation:

We know 12 inches = 1 ft

12 inches by 12 inches

1 ft by 1 ft

The area is 1 * 1 = 1 ft^2

Answer:

≈ 3.6

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)

d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]

   = [tex]\sqrt{(-2)^2+3^2}[/tex]

   = [tex]\sqrt{4+9}[/tex]

    = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )

Answer:

3.6

Step-by-step explanation:

Look above bru

Answer:

P value = 0.1575

Step-by-step explanation:

Data provided in the question

t = 1.021

n = 33

[tex]\mu[/tex] = 98.6° F

Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment

So, the P value is 0.1575

The 1.021 denotes the test statistic

32 denotes degrees of freedom

And,

1 denotes one tailed alternative hypothesis.

                                                0        0

                                                      ,    

                                              ---------------

Answer:

3 only

Step-by-step explanation:

Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.

Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.

Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.

Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.

Therefore, the true statement is III only.

More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

Data given in the table shows the data of elections between two candidates among the different cities.

Statistics is the study of mathematics that deals with relations between comprehensive data.

I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.

II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false

III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.

IV. Overall, more residents support candidate A than candidate B. it is also false.

Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

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Answer:

Put 0 in the box.

Step-by-step explanation:

The value x = 0 if replaced in the given equation will always make the denominator zero.

Best Regards!

Answer:

f(2) = 2

Step-by-step explanation:

f(x)=x^2-2x+2

Let x=2

f(2)=2^2-2*2+2

    = 4 -4 +2

    = 2

Answer:

{x | x < 0} and {x I x > 0} has no solution

Step-by-step explanation:

x cannot be less than zero AND more than zero at the same time, so the first inequality has no solution.

{x | x < 0} and {x I x > 0}

Answer:

A

Step-by-step explanation:

Choice A has the two options:

[tex]x<0 \text{ and } x>0[/tex]

In other words, x must be a number such that it is negative (left option) and positive (right option) at the same time.

There can't be such number (and 0 is not included in the answer choices since it is not less/more than or equal to). Thus, Choice A has no solution.

The keyword here is and. If instead of and it was or, then the choice does indeed have a solution.

==================================================

Explanation:

Dividing the side lengths, the scale factor is 6/3 = 2. This means the larger figure has a side length twice as long compared to its smaller counterpart.

How can we use this to figure out how the areas are connected? By simply squaring the scale factor to get 2^2 = 2*2 = 4, then we divide the larger area over 4 to get 24/4 = 6.

The longer side is 2 times longer

The larger area is 4 times larger

--------------------

Let's say we had a 3 by 3 square. It's area would be 9.

Also, let's say we had a 6 by 6 square. It's area is 36.

Notice the ratio of areas is 36/9 = 4, so the larger square is 4 times larger than the smaller. This 4 matches with what we got earlier.

----------------------

Another example:

square A is 7 by 7 with area 49

square B is 21 by 21 with area 441

ratio of areas is 441/49 = 9, which is exactly equal to 3^2, and the 3 comes from the ratio of the sides 21/7 = 3.

------------------------

So in short, you find the linear scale factor by dividing the sides. Then you square the result to get the area scale factor, which you use to find the smaller area.

linear scale factor = (new side)/(old side)

area scale factor = (linear scale factor)^2

smaller area = (larger area)/(area scale factor)

The correct answer is A. y = 2x +1

Explanation:

An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.

First  column

5 = 2 · 2 + 1

5 = 4 + 1

5 = 5

Second Column

9 = 2 · 4 + 1

9 = 8 + 1

9 = 9

Third column

13 = 6 · 2 + 1

13 = 12 + 1

13 =  13

Fourth column

17 = 8 · 2 + 1

17 = 16 + 1

17 = 17

Answer:

a. t = 2.48 will be a period within 2009.

b. 56.16 million

Step-by-step explanation:

Here is the complete question

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the

END OF THE IPOD ERA

players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007

through 2011 (in millions) were

approximately

N(0= -2.65t2 + 13.13t+ 39.9 (0 < t< 4)

in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

a. Show that the worldwide sales of the iPod peaked sometime in 2009

N(t) = -2.65t² + 13.13t + 39.9

To find the maximum value of N(t), we find dN(t)/dt and equate it to zero

dN(t)/dt = d[-2.65t² + 13.13t + 39.9]/dt

dN(t)/dt = -5.3t + 13.13 = 0

-5.3t = - 13.13

t = -13.13/(-5.3)

t = 2.477

t ≅ 2.48

d²N(t)/dt² =d[-5.3t + 13.13]/dt = -5.3 < 0. So, t = 2.48 is a maximum point

Since t = 2 is 2009 and t = 3 is 2010, t = 2.48 will be a period within 2009.

b. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

The approximate largest number of ipods sold is when t = 2.48

N(2.48) = -2.65(2.48)² + 13.13(2.48) + 39.9

N(2.48) = -16.29856 + 32.5624 + 39.9

N(2.48) = 56.16384

N(2.48) ≅ 56.16 million

Answer:

Here's what I get  

Step-by-step explanation:

h = 0.5d + 4

A function rule tells you how to convert an input value (x) into an output value (y).

Your function rule is

ƒ(x) = 0.5x + 4

An easy way to represent your function is to make a graph.

The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.  

Here's a typical table.

[tex]\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}[/tex]

The graph is like the one below.

Answer:

Solution : ( - 5, 5π / 4 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.

( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.

( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.

And when r is negative ( r < 0 ),

( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.

Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.

Answer:

Step-by-step explanation:

f(x) = (x+1)³ + 4

To find f-¹(x) equate f(x) to y

That's

y = (x+1)³ + 4

Next interchange the terms x becomes y and y becomes x

That's

x = ( y+1)³ + 4

Make y the subject

(y+1)³ = x - 4

Find the cube root of both sides

That's

[tex]y + 1 = \sqrt[3]{x - 4} [/tex]

Send 1 to the right side of the equation

That's

[tex]y = \sqrt[3]{x - 4} - 1[/tex]

So we have the final answer as

[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]

Hope this helps you

Answer:

option 1

Step-by-step explanation:

f(x)=(x+1)³+4

to find the inverse interchange the variable and solve for y

inverse f(x)=(y+1)³+4

x=(y+1)³+4

x-4=(y+1)³

y+1=∛x-4

y=∛x-4 -1

Answer:

5

Step-by-step explanation:

Just multiply 5/7 by 7 since his dog retrieved 5/7 out of the 7 ducks he shot.

Answer:

5

Step-by-step explanation:

7*5/7

7 represents the # of ducks

5/7 represents the # of ducks that were recovered

The question asks the number of ducks that were recovered so you should multiply the total # of ducks there are by the fraction that were recovered.

Answer:

[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]

Step-by-step explanation:

Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).

Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0

To find b we use the equation of the focus which is:

[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]

Substituting the values of a, b, h and k:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]

Answer:

Step-by-step explanation:

Q(x)=x² − 6x − 2

To find Q(−4) substitute the value of x which is - 4 into Q(x)

That's

Q(-4) = (-4)² - 6(-4) - 2

Q(-4) = 16 + 24 - 2

We have the final answer as

Hope this helps you

Answer:

The equation for a unit radius circle, centered at the origin is:

x^2 + y^2 = 1

Now, if we want to move it horizontally, you can recall to the horizontal translations:

f(x) -----> f(x - a)

Moves the graph to the right by "a" units.

A vertical translation is similar.

Then, if we want a circle centered in the point (a, b) we have:

(x - a)^2  + (y - b)^2 = 1.

Now, if you want to change the radius, we can actually write the unit circle as:

x^2 + y^2 = 1^2

Where if we set x = 0, 1 = y, this is our radius

So if we have:

x^2 + y^2 = R^2

And we set the value of x = 0, then R = y.

So our radius is R.

Then:

"A circle of radius R, centered in the point (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Answer:

Step-by-step explanation:

[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]

Answer:

7

Step-by-step explanation:

because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7

Answer:

60/220

Step-by-step explanation:

we use combination,

[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]

[tex]5 \times 4 \times 3 = 60[/tex]

then, all divided by,

[tex] (\frac{12}{3}) = 220 [/tex]

[tex]60 \div 220[/tex]

The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{5}{12}[/tex]

Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is

[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{11}[/tex]

Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{10}[/tex]

Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is

[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]

Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

Learn more about Probability:

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Answer:

[tex]\huge\boxed{Q = \sqrt{A+2a}}[/tex]

Step-by-step explanation:

[tex]A = Q^2 -2a[/tex]

Adding 2a to both sides

[tex]Q^2 = A+2a[/tex]

Taking sqrt on both sides

[tex]Q = \sqrt{A+2a}[/tex]

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

Answer:

-11.2 pounds

Step-by-step explanation:

It is given that,

Shawna finds a study of American men that has an equation to predict weight (in pounds) from  height (in inches):

y = -210 + 5.6x

Height of Shawna's dad is 72 inches

Weight is 182 pounds

We need to find the residual of weight and height for Shawna's dad.

Predicted weight of 72 inches men,

y' = -210 + 5.6(72)

y' = 193.2 pounds

So, residual is :

Y = 182 - 193.2

Y = -11.2 pounds

So, the residual of weight and height for Shawna's dad is -11.2 pounds.

Answer:

-11.2 pounds

Step-by-step explanation:

Got it right on the test.

Answer:

symmetric

Step-by-step explanation:

it kind of evenly falls to the left and right from the highest value in the middle

skewed would be different and would look like a straight line not a quadratic equation

Answer:

75°

Step-by-step explanation:

Let's find the size of x°

BCFE has four sides so the sum of its angles sizes is 360°.

● CBE + 110 + 110 + CFE = 360

CFE is equal to 65° since they have the same vertex

● CBE + 220 + 65 = 360

● CBE + 285 = 360

● CBE = 360-285

● CBE = 75

CBE and x° have the same size since they share the same vertex.so:

● x° = 75°

Answer:

75°

Step-by-step explanation:

CBE = x (vertically opposite angles are equal)

CFR = 65° (vertically opposite angles are equal)

C+F+E+B= 360 (angles in a quadrilateral sum up to 360°)

110+65+110+x=360

x= 75°

Answer:

see below

Step-by-step explanation:

-33, -27, -21, -15,....

-33 +6 = -27  

-27+6 = -21

-21+6 = -15

This is an arithmetic sequence

The common difference is +6

explicit formula

an=a1+(n-1)d  where n is the term number and d is the common difference

an = -33 + ( n-1) 6

an = -33 +6n -6

an = -39+6n

recursive formula

an+1 = an +6

10th term

n =10

a10  = -39+6*10

      = -39+60

      =21

sum formula

see image

The sum will diverge since we are adding infinite numbers

Answer:x = 8, y = 5

Step-by-step explanation:The sum of two numbers is 13. Two times the first number minus three times the second numberis 1. If you let x stand for the first number and y for the second number, the two numbers are: A. x = 8, y = 5

Aswer:I am sure of the answer it is 6 and 42

Step-by-step explanation:

Answer:

We have to remember

slope = m

if the slope of line is parellel so it will be the same with other slope

m1= m2

2/3= 2/3

so the answer is 2/3

hope it helps ^°^

Answer:

2/3

Step-by-step explanation:

Parallel lines have the same slopes. Therefore,

[tex]m_{k} =m_{p}[/tex]

The slope of line k ([tex]m_{k}[/tex]) will be equal to the slope of the line parallel to k ([tex]m_{p}[/tex]).

We know that the slope of line k is 2/3.

[tex]m_{k}=\frac{2}{3}[/tex]

Therefore, the slope of the line parallel to line k is also 2/3.

[tex]\frac{2}{3}=m_{p}[/tex]

The slope of a line parallel to line k is 2/3.