question content area top part 1 write a differential formula that estimates the change in the surface area of a cube when the edge lengths change from x0 to x0dx

Answers

Answer 1

Differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

As per the given data:

The surface area is given by

[tex]$$S = 6 x^2$$[/tex]

Differentiate both sides with respect to  f(x)

[tex]$$S^{\prime}(x)=\frac{d}{d x}\left(6 x^2\right)\\\\=6(2) x^{2-1}$$[/tex]

= 12 x

The estimated change in surface area is given by

[tex]$$d S=S^{\prime}(x) d x= > d S\\\\$$[/tex]

= (12 x) dx

The change in surface area at [tex]$x=x_{0} $[/tex] is

[tex]$$d S=\left(12 x_0\right) d x$$[/tex]

Therefore the answer is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

For more questions on differential equation

https://brainly.com/question/14620493

#SPJ4

Write a differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx


Related Questions

Find the length of the triangle.

Answers

The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.

What is the area of the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle.

Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is 7 ⁷/₈ cm² and the base length of the triangle is 5 ¹/₄ cm.

Convert the mixed fraction number into a fraction number. Then we have

7 ⁷/₈ = 63/8

5 ¹/₄ = 21/4

The height of the triangle is given as,

63/8 = (1/2) x h x (21/4)

Simplify the equation, then we have

63/8 = (1/2) x h x (21/4)

63/8 = (21/8)h

21h = 63

h = 3 cm

The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.

More about the area of the triangle link is given below.

https://brainly.com/question/19305981

#SPJ1

Aid!! It's for today​

Answers

Using theory about stereotypes and different associated thoughts, we have to:

''A girl who has a boy-friend cannot have frie-nds'', this affe-cts us because the thought promotes restrictions on the freedoms of a woman when she has a boy-friend. ''A boy should not show his affection or be tender'', this affects us because it is a thought that promotes stereotypes that do not allow the proper development of people. ¿What is a stereotype?

A stereotype, basically, can be defined as an idea that is already pre-established and accepted, it is applied to different individuals.

¡Hope this helped!

A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. (3 points)

6.2
7.2
9.4
13.4

Answers

Answer:

so (-5.2,-2) and (4.2,-2) are 9.4 units apart  away from each other

Step-by-step explanation:

so (4.2,-2) and (-5.2,-2) add together and get 9.4

-3x^2-6x+24 factor this equation by any means

Answers

Step-by-step explanation:

-3x² - 6x + 24

this is an expression, not an equation.

for an equation this would have to look like e.g.

-3x² - 6x + 24 = 0

anyway, yes, we can factor this expression :

-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)

why ?

x² + 2x - 8 corresponds to

(x + a)(x + b) = x² + (a+b)x + ab

so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?

-8 has the factors

4, -2

-4, 2

8, -1

-8, 1

only (4, -2) covers the both criteria.

therefore, the correct factorization is

-3(x + 4)(x - 2)

A rock falls from a tower that is 352 feet high. As it is falling, its height is given by the formula h=352-16t^(2). How many seconds (in tenths ) will it take for the rock to hit the ground (h)=(0)?

Answers

The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).

The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.

t= sqrt((352-0)/16)

t= sqrt(22)/4

t= 10.25

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

Please help will mark Brainly

Answers

Answer:

120 children

Step-by-step explanation:

c=children

a=adults

c+a=237

1.75c+2a=444

(c+a=237)*2 ==> make a in the equation equal to 2a

       2c+2a=474

- (1.75c+2a=444)  ==> eliminate a from the equation

2c-1.75c + 2a-2a = 474-444

2.00c-1.75c = 30

0.25c = 30

4 * 0.25c = 4 * 30   ==> remove decimals by multiplying each side by 4

c = 120 children

Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers.



f(x)=sqrt(x)+8 , g(x)=x^2+1


f(g(x))=
g(f(x))=

Answers

The solution to the given composite functions are;

f(g(x)) = √(x² + 1) + 8

g(f(x)) = [√(x) + 8]² + 1

How to solve composite functions?

Composite functions are usually formed when one function is used as the input of another function.

We are given the functions;

f(x) = √(x) + 8

g(x) = x² + 1

1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;

f(g(x)) = √(x² + 1) + 8

2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1

Read more about composite functions at; https://brainly.com/question/10687170

#SPJ1

Match the inequality on the left with the appropriate graph on the right

Answers

Answer:

i got the last two but i am confused on the first two

Step-by-step explanation:

good luck

have fun

bye

Solve the following equation for x

Answers

The answer would be B
X=0,-2
You could try plugging each set of points into the equation and seeing which one fits the problem.

F.ds = 4 pi, F.ds = 9 pi Use Green's Theorem to determine the circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =

Answers

F.ds = 4 pi, F.ds = 9 pi

circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =

c1-9 (52-12-12) π+9л+4л=(207+12)л=219л

Green's Theorem =Green's Theorem states that a line integral around the boundary of the plane region D can be computed as the double integral over the region D. where the path integral is traversed anti-clockwise. Green's Theorem Area

Therefore, the line integral defined by Green's theorem gives the area of the closed curve. Therefore, we can write the area formulas as: A = − ∫ c y d x. A = ∫ c x d y. Green's theorem relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C. The theorem is useful because it allows us to translate difficult line integrals into more simple double integrals, or difficult double integrals into more simple line integrals.

learn more about Green's Theorem here

https://brainly.com/question/23265902

#SPJ4

help meeeee last question ​

Answers

The number of cubical boxes that can contain in the rectangular box is 36.

What is the volume of a cuboid?

Volume is defined as the space occupied by an object.

The volume of a cuboid is (length×width×height).

Given, Length of the rectangle box is 16 cm and the width of the box is

12 cm.

We know the volume of a cube is (side)³.

Therefore, given that the volume of a cubical 64 cm³ and we know (4)³ is 64.

Hence the height of the rectangular box is 3 layers so (4×3) = 12 cm

So, the volume of the rectangular box is (16×12×12) cm³ = 2304 cm³.

Therefore, The maximum number of boxes that can be contained is

= (2304/64)

= 36.

learn more about cuboids here :

https://brainly.com/question/29568631

#SPJ1

an fda representative randomly selects 8 packages of ground chuck from a grocery store and measures the fat content (as a percent) of each package. assume that the fat contents have an approximately normal distribution. the resulting measurements are given below.fat contents (%)12 15 16 1315 13 15 13step 1 of 2 : calculate the sample mean and the sample standard deviation of the fat contents. round your answers to two decimal places, if necessary.

Answers

We calculated sample mean 14 and standard deviation 1.32

What is sample mean?

A sample mean refers to the average of all values included in the data list.

How to calculate sample mean and standard deviation from the list of data?

When we have a list of data set, we can calculate the mean value of the data set by adding all the values and divided by the amount of data.

We are given, 8 packages of ground chuck

 number of samples, N = 8

fat contents (%) for 8 packages, X= 12, 15, 16, 13, 15, 13, 15, 13

Sum of X= ∑X= 112

sample mean= sum of all data values/ number of data items in the sample

   X= ∑X/N

  sample mean X = 112/8 =14

we calculate   X² for 8 sample = 144, 225, 256, 169, 225, 169, 225, 169

∑X² = 1582

standard deviation is calculated by using the formula bellow

√[∑X²/N-(∑X/N)²] = √[1582/8-(112/8)²]  

standard deviation = 1.32

To learn more about sample mean and standard deviation visit:

https://brainly.com/question/29954879

#SPJ4

Last year the depth of the river was 4.2 feet deep. This year it dropped 24%. Find the depth of the river this year to cross it.

Answers

The depth of the river is 3.192 feet.

How to illustrate the percentage?

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:

= 4.2 - (24% × 4.2)

= 4.2 - 1.008

= 3.192 feet

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

y-2x=4 please help i’m
stuck

Answers

Answer:

To find x and y intercept .... y = 4, and x = -2

Step-by-step explanation:

y-2x=4

y = 4

-2x=4

-2x/-2 = 4/-2

x = -2

Is this equation for solving y and x

Question 1 of 10
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?
A. Increasing linear
B. Decreasing linear
C. Exponential growth
D. Exponential decay

Answers

The type of function is it is C . Exponential growth .

Given :

For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because  because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

Learn more about the function here :

https://brainly.com/question/9046022

#SPJ4

Review of logarithms (logs)
For each of the following equations, write down the
name of the operation that occurs in the equation and
the name of the inverse operation that helps you
solve the equation.
Equation
x+10=25
2x=28
4²=64
Name of operation
Name of inverse
operation

Answers

The operations, along with their inverses are given as follows:

x + 10 = 25: Operation of addition, the inverse is of subtraction.2x = 28: Operation of multiplication, the inverse is the division.4^x = 64: The operation is the exponential, the inverse is the logarithm.

How to solve the operations?

The operations are solved applying the inverse operations.

The first operation is solved as follows:

x + 10 = 25

x = 25 - 10

x = 15.

Hence the addition operation was solved applying the subtraction operation, which is the inverse operation of the addition.

The second operation is solved as follows:

2x = 28

x = 28/2

x = 14.

Hence the multiplication operation was solved applying the division operation, which is the inverse operation of the multiplication.

The third operation is given as follows:

4^x = 64.

log4(4^x) = log4(64)

x = 3. (as 4³ = 64, hence log4(64) = 3).

Hence the exponential operation was solved applying the logarithm operation, which is the inverse operation of the exponential.

More can be learned about exponential and logarithm at https://brainly.com/question/25537936

#SPJ1

in non-degenerate cases of the logistic regression model, the maximum likelihood estimator always exists and is always unique. assume the design matrix is of full rank.

Answers

For regression and classification predictive modeling, the Maximum Likelihood Estimation framework can be used as a foundation for estimating the parameters of numerous machine learning models.

The logistic regression model is a part of this.

Is MLE always present?

For species distribution models, maximum likelihood is a common parameter estimation method. A popular species distribution model, the Poisson point process, does not always have maximum likelihood estimates.

In logistic regression, how is the maximum likelihood determined?

At the end of the day, the most extreme probability gauge for p is the mean of the y variable from the N draws. According to the result, p=n1/N=y is the value of p that maximizes the above log-likelihood function.

To learn more about logistic regression model here:

https://brainly.com/question/15326879

#SPJ4

the ration of hugs to kisses at the family reunion was 4:1 if there were 148 hugs how many kisses were there

Answers

There were 37 kisses at the family reunion. Probability is used to make predictions and inform decision-making.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

To find the number of kisses at the family reunion, you can set up the ratio 4 hugs : 1 kiss as a proportion and solve for the number of kisses. Here's how you can do this:

First, cross-multiply to find the total number of hugs and kisses:

4 hugs * 1 kiss = 148 hugs

4 kisses = 148 hugs

Then, divide both sides of the equation by 4 to find the number of kisses:

4 kisses / 4 = 148 hugs / 4

1 kiss = 37 hugs

Learn more about probability, here https://brainly.com/question/30034780

#SPJ4

What is the equation of this function after it is reflected over the x-axis?

Answers

Answer:

Below

Step-by-step explanation:

Multiplying the equation by -1 will flip it around the x - axis

so    3(x-2)^3

use the factor theorem to determine whether is a factor of . specifically, evaluate at the proper value, and then determine whether is a factor.

Answers

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

The factor theorem states

[tex]$(x-a)$ is a factor of $f(x) \Leftrightarrow f(a)=0$[/tex]

f(x)=4 x^3-3 x^2-8 x+4

we have (x-2)[tex]\Rightarrow a=2[/tex]

& [tex]f(2)=4 \times 2^3-3 \times 2^2-8 \times 2+4 \\& f(2)=4 \times 8-3 \times 4-16+4 \\& f(2)=32-12-16+4 \\& f(2)=8 \neq 0\end{aligned}[/tex]

[tex]$\therefore x-2$ is not a factor of $4 x^3-3 x^2-8 x+4$[/tex]

however by the remainder theorem when

[tex]$f(x)=4 x^3-3 x^2-8 x+4$[/tex] is divided by [tex]$(x-2)$[/tex] the remainder is 8

the factor theorem being a special case of the remainder theorem

To learn more about visit:

https://brainly.com/question/13547729

#SPJ4

Answer:

Step-by-step explanation:

Use the factor Theorem to determine whether x =3 is a factor of P (x)=x-2x2-6. Specifically, evaluate P at the proper value, and then determine whether X-3 is a factor. P (UI) - 0 P 0 1 - 3 is a factor of P (*) O +- 3 is not a factor of P (x) This problem has been solved!

sweet-fit jeans has a factory that makes two styles of jeans; super-fit and super-hug. each pair of super-fit takes 20 minutes to cut and 30 minutes to sew and finish. each pair of super-hug takes 20 minutes to cut and 55 minutes to sew and finish. the plant has enough workers to provide at most 18,999 minutes per day for cutting and at most 40,999 minutes per day for sewing and finishing. the profit on each pair of super-fit is $6.50 and

Answers

The profit earned per day is $6674.695 at point (449.93,500.02).

Let the number of pair of super-fit jeans = x

Let the number of pair of super-hug jeans = y

We know that x,y≥0.

Total time provided for cutting per day = 18,999 minutes

Total time provided for sewing and finishing per day = 40,999 minutes

Therefore, the inequalities are:

20x+20y ≤ 18,999

30x+55y ≤ 40,999

The shaded region is the feasible region and the point of intersection is (449.93,500.02).

The profit on Super-fit jeans = $6.50

The profit on super-hug jeans = $7.50

To maximise the profit in a day, we maximize z = (6.50 x x) + (7.50 x y)

The maximum profit is obtained at (449.93,500.02).

Therefore, z = (6.50 x 449.93) + (7.50 x 500.02)

z = 2924.545 + 3750.15

z = 6674.695

The profit earned per day is $6674.695.

To know more about profit here:

https://brainly.com/question/23638439

#SPJ4

write an equation of the line that is parallel to the graph of 3x-5=y and whose y intercept is (0,7).

Answers

Parallel Lines

Parallel lines always have the same slope and different y-intercepts.

Slope-intercept form: [tex]y=mx+b[/tex]

m = slopeb = y-intercept

Solving the Question

We're given:

[tex]3x-5=y[/tex]b = (0,7)

We can see that in [tex]y=3x-5[/tex] that the slope of the line is 3. Parallel lines have the same slope, so therefore:

m = 3

We're also given that the y-intercept is (0,7).

b = 7

Plug m and b into slope-intercept form:

[tex]y=3x+7[/tex]

Answer

[tex]y=3x+7[/tex]

If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?
answer choices
O If you flip three coins 1000 times, you will get three heads exactly 125 times.
O If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.
O If you have 20 sets of three coin flips, then at least one set of flips will be three heads.
O If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
O If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.

Answers

Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

According to the given question:

Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?

The solution is 1/8, or 12.5%.

coin flipped = 3 times.

probability of getting three heads = 0.125

Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .

So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.

To learn more about probability visit:

brainly.com/question/30034780

#SPJ4

tara has 5/8 gallons of glue. She uses 2/5 of the glue to make blue slime, 1/5 of the glue to make green slime, and the rest of the glue to make purple slime. How many gallons of glue does tara use to make purple slime

Answers

Answer:

We can say that he used a total of 5/8 gallons of glue

let x - glue to make purple slime

5/8 = 2/5 + 1/5 + x

5/8 = 3/5 + x             (LCD of 5 and 8 is 40)

25/40 = 24/40 + x

25/40 - 24/40 = 24/40 - 24/40 + x    (subtract 24/40 both sides)

x = 1/40

CHECKING:

5/8 = 2/5 + 1/5 + 1/40

5/8 = 3/5 + 1/40

25/40 = 24/40 + 1/40

25/40 = 25/40

Therefore, the glue to make purple slime is 1/40 gallons.

#APPROVED

Step-by-step explanation:

heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ  -{ elyna s }-

Let X1,82 be independent random variables representing lifetimes (in hours) of two key components of a device that fails when and only when both components fail. Say each Xi has an exponential distribution with mean 1000. Let Y1 = min(X1,X2) and Y2 = max(X1,X2), so that the space of Y1,Y2 is 0 < y1 < y2 <. (a) Find G(y1, y2) = P(Y1 = 71,Y2 = y2).

Answers

To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).

To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is

P(X1 = 71, X2 = y2) = f(71) * f(y2) = 1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000).

Another possibility is that X1 = y2 and X2 = 71. The probability of this event is

P(X1 = y2, X2 = 71) = f(y2) * f(71) = 1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000).

Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,

G(y1, y2) = P(Y1 = 71, Y2 = y2) = P(X1 = 71, X2 = y2) + P(X1 = y2, X2 = 71) = (1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000)) + (1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000)) = 2/1000^2 * e^(-(71 + y2)/1000).

Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.

Learn More about Exponential Distribution here:

https://brainly.com/question/13339415

#SPJ4

The price of an item has been reduced by 95%. The original price was $65

Answers

The new price of the item is equivalent to $3.25.

What is percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. A percentage is a dimensionless number i.e. it has no unit of measurement.

Given is that the price of an item has been reduced by 95%. The original price was $65

Assume the new price to be $[x]. So, we can write -

x = 65 - {95% of 65}

x = 65 - {(95/100) x 65}

x = 65 - {6175/100}

x = 65 - 61.75

x = 3.25

Therefore, the new price of the item is equivalent to $3.25.

To solve more questions on percentage, visit the link below -

https://brainly.com/question/29011982

#SPJ1

Type the correct answer in each box. Use numerals instead of words.
If x>0, what values of c and d make the equations true?
Equation A √448 x⁽=8 x³ √7 x
Equation B ∛576 xᵃ=4 x ∛9 x²

In equation A, c is
In equation B, d is

Answers

The value of c in the equation A is 7 and the value of d in the equation B is 5

The first equation is

[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]

Move the term 8x^3 inside the square root

[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]

Multiply the terms in the equation

[tex]\sqrt{448x^c} = \sqrt{448x^7}[/tex]

Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.

Then the value of c = 7

Part 2

The second equation is

[tex]\sqrt[3]{576x^d}=4x \sqrt[3]{9x^2}[/tex]

Move the term 4x inside the square root

[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]

Multiply the terms in the equation

[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]

Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal

Then the value of d = 5

Therefore, the value of c = 7 and the value of d = 5

Learn more about equation here

brainly.com/question/22173286

#SPJ4

Let Sn be the number of lattice paths in the Cartesian plane that start at (0,0), end at (n,n), contain no points above the line y = x, and are composed only of steps (0, 1), (1,0), and (1, 1), i.e. 1, +, and /. So = 1. Consider the generating function S(x):=∑_(n=0)^[infinity]▒〖SnX^n〗. Prove that 1 + (x – 1)S(x) + xS(x)2 = 0.

Answers

A formal power series that encodes the coefficients of a sequence of numbers is a generating function.

Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.

Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,

Here, the functional equation is

S(x) = 1 + xS(x) + xS(x)²

This equation implies that

The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.

The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)

The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)

Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.

To learn more about Generating functions visit

https://brainly.com/question/13092641

#SPJ4

You bought 12 red apples and 15 green apples to make some pies.

What is the ratio of the number of red apples to the total number of apples?

Answers

Answer:

4.9

Step-by-step explanation:

find the arc length?

Answers

The length of the Arc of the circle is 17.00 units

How to find the length of arc?

We should know that the arc of the circle is part of the circumference of the circle cut off by the radii of the circle.

The length of the arc is given by

L=[tex]\frac{A}{360} *2*\pi *r[/tex]   where A= angle made by the radii

[tex]\pi[/tex]=3.14, radius =10, L-length of arc = x

Applying the values in the formula we have

x=(x/3*2*3.14*10)÷360

Simplifying the expression

62.8x=1080x

Taking the ratio of both sides we have

62.8x:1080x

= 17.00 units

Therefore the length of the arc is 17.00 units

Learn more about length of arc on https://brainly.com/question/16403495

#SPJ1

Other Questions
the inhibitory effect of an uncompetitive inhibitor is greater at high [s] than at low [s]. Explain this observation. suppose the demand for the polymer (for the upcoming selling season) is forecasted to be normally distributed with a mean of 300 gallons and a standard deviation of 110 gallons. how many gallons should goop purchase to target 13% stock-out probability? whenever a website visitor views any page on your site, they trigger the page view event. what if you wanted to define a new event to trigger when visitors land on a particular page (e.g., the homepage)? once you've navigated to events in the analytics interface, which option would you choose to make this happen? True or False, during the process of bone remodeling, osteoblasts resorb existing bone and osteoclasts form new bone. Corresponding angles formed by two parallel lines intersected by a transversal are always:complementary.congruent.acute.obtuse.supplementary three less than twice an integer is greater than 1 please help put this in an equation are required to complete the work in ays! 12 workers can complete a piece of work in 20 days. How many workers are needed to complete the work in 16 days? canada's government owns the communications, transportation, and utilities industries; most other activities are carried on by private enterprises. canada is considered a economy. The tryptophan operon is a repressible operon that isturned off only when glucose is present in the growth medium.turned off whenever tryptophan is added to the growth medium.turned on only when glucose is present in the growth medium.turned on only when tryptophan is present in the growth medium.permanently turned on. one way to segment a market is according to whether the purchaser is a consumer or a business-to-business user. State True or False your answer: a. Trueb. False Read the excerpt from act 3, scene 5 of The Tragedyof Macbeth. Hecate is annoyed at the witches for notincluding her when they prophesied to Macbeth thathe would become king. The excerpt mentions theAcheron, a river in Greece that is featured prominentlyin Greek mythology as the entrance to the underworld.[Hecate.] And I, the mistress of your charms,The close contriver of all harms,Was never call'd to bear my part,Or show the glory of our art?And, which is worse, all you have doneHow does the allusion to Acheron add to the sinistermood in this part of the play?O by implying that Macbeth will gain connections tothe underworldO by establishing that Macbeth will assume control ofmore territoryOby suggesting that Macbeth is closer to death thanhe realizesO by explaining how Macbeth rose to his position ofprominence 31. What is the data type of the following function prototype's parameter variable?int myFunction(double);a. intb. doublec. voidd. cannot tell from the prototype the life cycle of disaster relief supply chains has five stages. which of the following is one of the stages of the life cycle of disaster relief supply chains? after studying the chemical reactions of many compounds made of carbon, august discovers a that says carbon always forms chemical bonds to other atoms when it forms a compound. which would be the priority nursing diagnosis for a client diagnosed with borderline personality disorder (bpd)?which would be the priority nursing diagnosis for a client diagnosed with borderline personality disorder (bpd)? Please Help!!\What additional information is needed to prove TUX DEO by HL? have you already completed your undergraduate education, have you had your college or graduate education interrupted, or do you plan not to be a full-time student during your application year? Emmett, age 4 months, looks and smiles more at video images of others than video images of himself. This discrimination reflects anA)explicit sense of self-world differentiation.B)internal working model.C)implicit sense of self-world differentiation.D)external working model. he risk-free asset has a return of 3.00%. the risky asset has a return of 24.89% and has a variance of 7.77%. karen has the following utility function:: LaTeX: U=a\times\ln\left(r_c\right)-b\times\sigma_cU = a ln ( r c ) b c, with a=5.1 and b=5.2. LaTeX: r_cr c and LaTeX: \sigma_c c denote the return and the risk of the combined portfolio. Compute the optimal to be invested in the risky asset. g carbon-14 radiometric dating can be used to date organic objects up to about 50,000 years old. to determine the age of an object, the following numbers are needed.