the surface area of the figure below is 50.80m^2 True or False

Assume a general solution of the form

[tex]y(x)=\displaystyle\sum_{n\ge0}a_nx^n[/tex]

with derivatives

[tex]y'(x)=\displaystyle\sum_{n\ge0}na_nx^{n-1}=\sum_{n\ge1}na_nx^{n-1}[/tex]

[tex]y''(x)=\displaystyle\sum_{n\ge0}n(n-1)a_nx^{n-2}=\sum_{n\ge2}n(n-1)a_nx^{n-2}[/tex]

Substituting into the ODE gives

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-2\sum_{n\ge1}na_nx^n+4\sum_{n\ge0}a_nx^n=0[/tex]

The first sum starts with degree 0; the second starts with degree 1; and the third starts with degree 0. So remove the first term from the first and third sums, then consolidate everything into one sum by shifting indices as needed.

First sum:

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge3}n(n-1)a_nx^{n-2}[/tex]

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n[/tex]

Third sum:

[tex]\displaystyle\sum_{n\ge0}a_nx^n=a_0+\sum_{n\ge1}a_nx^n[/tex]

So the ODE can be expressed as

[tex]\displaystyle\left(2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n\right)-2\sum_{n\ge1}na_nx^n+4\left(a_0+\sum_{n\ge1}a_nx^n\right)=0[/tex]

[tex]\displaystyle2a_2+4a_0+\sum_{n\ge1}\bigg((n+2)(n+1)a_{n+2}+(4-2n)a_n\bigg)x^n=0[/tex]

Then the coefficients are given by the recurrence,

[tex]\begin{cases}a_0=a_0\\a_1=a_1\\2(2-n)a_n+(n+2)(n+1)a_{n+2}=0&\text{for }n\ge0\end{cases}[/tex]

Notice that we should have [tex]a_0\neq0[/tex] and [tex]a_1\neq0[/tex] in order to get non-zero solutions.

For [tex]n=2[/tex], we would find that [tex]a_4=0[/tex], which would imply that [tex]a_n=0[/tex] for all even [tex]n\ge2[/tex]. Then the even-indexed terms in the series contribute one solution,

[tex]y_1(x)=a_0+a_2x^2=a_0(1-2x^2)[/tex].

On the other hand, for odd [tex]n\ge1[/tex] we have

[tex]a_{n+2}=\dfrac{2(n-2)}{(n+2)(n+1)}a_n[/tex]

With [tex]n=1[/tex]:

[tex]a_3=\dfrac{2\cdot(-1)}{3\cdot2}a_1=-\dfrac2{3!}a_1[/tex]

With [tex]n=3[/tex]:

[tex]a_5=\dfrac{2\cdot1}{5\cdot4}a_3=-\dfrac{2^2\cdot1}{5!}a_1[/tex]

With [tex]n=5[/tex]:

[tex]a_7=\dfrac{2\cdot3}{7\cdot6}a_5=-\dfrac{2^3\cdot3\cdot1}{7!}a_1[/tex]

So the general pattern for [tex]n=2k+1[/tex], [tex]k\ge1[/tex], is

[tex]a_{2k+1}=-\dfrac{2^k\prod\limits_{i=1}^{k-1}(2i-1)}{(2k+1)!}a_1[/tex]

and we get a second (linearly independent) solution

[tex]y_2(x)=a_1x+\displaystyle\sum_{k\ge1}a_{2k+1}x^{2k+1}[/tex]

Answer:

UT

Step-by-step explanation:

The projection of ST on QT is found by locating the points on QT that are nearest the endpoints S and T of the original segment. On QT, U is the point closest to S, and T is the point closest to T. Then the projection is the segment between those identified points: UT.

Answer:

UT

Step-by-step explanation:

Answer:

the solution is (-3, -2)

Step-by-step explanation:

Please, separate your equations with a (;) or a (.).  Better yet, write only one equation per line:

y=2x+4

3x−6y=3

Substitute 2x + 4 for y in the second equation:

3x - 6(2x + 4) = 3, or

3x - 12x - 24 = 3

Combining like terms, we get -9x = 27, and so x = -27/9, or x = -3.

Since we know that y=2x+4, we replace x in this equation with -3 and calculate y:

y = 2(-3) + 4 = -2

Then the solution is (-3, -2).

Answer:

[tex]\large\boxed{x=11}[/tex]

Step-by-step explanation:

Use Angel Bisector Theorem (look at the picture),

[tex]\dfrac{3x-3}{24}=\dfrac{5x}{44}\qquad\text{cross multiply}\\\\44(3x-3)=24(5x)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(44)(3x)+(44)(-3)=120x\\\\132x-132=120x\qquad\text{add 132 to both sides}\\\\132x=120x+132\qquad\text{subtract}\ 120x\ \text{from both sides}\\\\12x=132\qquad\text{divide both sides by 12}\\\\x=11[/tex]

The recursive function describes the number of bacteria observed at the nth hour is; aₙ = 5 * (4)ⁿ ⁻ ¹

We are given the geometric sequence as; 5, 20, 80, 320, 1,280

We know that the general formula to find the nth term of a geometric sequence is; aₙ = arⁿ ⁻ ¹

Where;

a is first term

r is common ratio

Thus, the recursive function is;

aₙ = 5 * (4)ⁿ ⁻ ¹

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The recursive function for the number of bacteria observed at the nth hour is B(n) = 4 × B(n-1), where B(1) is 5 and n > 1, indicating that the number of bacteria quadruples every hour.

To describe the number of bacteria observed at the nth hour, we need to devise a recursive function based on the given sequence: 5, 20, 80, 320, 1280. Analyzing the sequence, we see that each term is four times the previous term. Therefore, the recursive function that describes this sequence is:

B(n) = 4 × B(n-1), where B(1) = 5 and n > 1.

This recursive function states that to obtain the number of bacteria at any hour n, you multiply the number of bacteria from the previous hour by 4. For example, to find the number of bacteria at hour 3 (third term), you would calculate 4 times the number of bacteria at hour 2, which is 4 × 20 = 80, matching the given sequence.

Answer:

The average rate of change for this quadratic function is -2.

Step-by-step explanation:

In this question, we have f(x) = y = x^{2} + 4x + 5.

Given a function y, the average rate of change S of y=f(x) in an interval  [x_s, x_f] will be given by the following equation:

S = \frac{f(x_{f}) - f(x_s)}{x_f - x_s}

So, in  your problem, f(x) = x^{2} + 4x + 5, x_{f} = -2 and x_{s} = -4.

Applying these informations to the equation S above, we have:

S = \frac{f(-2) - f(-4)}{-2-(-4)}

Where

f(-2) = (-2)^{2} + 4(-2) +5 = 4-8+5 = 9-8 = 1

f(-4) = (-4)^{2} + 4(-4) +5 = 16-16+5 = 5

So, the average rate of change S will be

S = \frac{1-5}{2} = -4

Answer:

43 is the smaller angle

Step-by-step explanation:

greater angle is 47

43+47=90

43 is 4 less than 47

Answer:

x≥38 points

Step-by-step explanation:

Julio wants to break his school’s scoring record of 864 points during his 24-game basketball season. During the first 8 games of the season, he scored a total of 256 points. Which inequality can be used to find x, the number of points Julio must average per game during the rest of the season to break the record?

julio has a 24 game basketball season.

he has played 8, it means there are 16 more games to go

therefore=

he has scored 256 nts, wic means there are still 608 points to go .

864-256=608

x is the points he more score per every game.

16x=608

to break the records ,he must score an extra point 1

so 16x≥608

x≥38

Answer:

256 + 16x > 864

Answer:

See below in bold.

Step-by-step explanation:

Here is 1 grain on square 1 , 2 on square 2, 4 on square 3  and so on. This is a geometric sequence with the nth term = a1r^(n - 1) where a1 = first term , r = common ratio.

So the 20th term  (the number of grains on square 20) would be

 1*2^(20-1)  = 524,288.

Total =   a1 * (r^n - 1) / (r - 1)

=  (2^20 - 1)  / 2-1 =  1.048,575

Answer:

Good ways to sample

Simple random sample: Every member and set of members has an equal chance of being included in the sample. Technology, random number generators, or some other sort of chance process is needed to get a simple random sample.

Example—A teachers puts students' names in a hat and chooses without looking to get a sample of students.

Why it's good: Random samples are usually fairly representative since they don't favor certain members.

Stratified random sample: The population is first split into groups. The overall sample consists of some members from every group. The members from each group are chosen randomly.

Example—A student council surveys 100 students by getting random samples of 25 freshmen, 25 sophomores, 25 juniors, and 25 seniors.

Why it's good: A stratified sample guarantees that members from each group will be represented in the sample, so this sampling method is good when we want some members from every group.

Cluster random sample: The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.

Example—An airline company wants to survey its customers one day, so they randomly select 555 flights that day and survey every passenger on those flights.

Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.

Example—A principal takes an alphabetized list of student names and picks a random starting point. Every 20th student is selected to take a survey.

Bad ways to sample

Convenience sample: The researcher chooses a sample that is readily available in some non-random way.

Example—A researcher polls people as they walk by on the street.

Why it's probably biased: The location and time of day and other factors may produce a biased sample of people.

Voluntary response sample: The researcher puts out a request for members of a population to join the sample, and people decide whether or not to be in the sample.

Example—A TV show host asks his viewers to visit his website and respond to an online poll.

Step-by-step explanation:

In a statistical study, sampling methods refer to how we select members from the population to be in the study.

If a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.

There are many ways to select a sample—some good and some bad.

Answer:

It will take Eva 4 hours to catch up with Seth on the trail.

Step-by-step explanation:

1. Seth: 4/hour Eva: 6/hour

2. Hour 1: S:12 E:6

Hour 2: S:16 E:12

Hour 3: S:20 E:18

Hour 4: S:24 E:24

___

Hope this helps you! :)

Answer:

It will take Eva 4 hours to catch up with Seth on the trail.

Answer:

The answer is R0, 90° and (x , y) → (-y , x) ⇒1st and 4th

Step-by-step explanation:

* Lets revise the rotation rules

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

 (+90° or -270°)

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

 (-90° or +270°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

 (+180° or -180°)

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

  anti-clockwise around the origin

* Lets solve the problem

∵ Δ XYZ has vertices⇒ X (0 , 0) , Y (0 , -2) , Z (-2 , -2)

∵ Δ X'Y'Z' has vertices X' (0 , 0) , Y' (2 , 0) , Z' (2 , -2)

* From them

# Y = (0 , -2) and Y' = (2 , 0), that means the image is (-y , x)

# Z = (-2 , -2) and Z' = (2 , -2), that means the image is (-y , x)

∴ The rotation is around the origin with angle 90° anti-clockwise

V.I.N: Anti-clock wise means positive angle , clockwise means

negative angle (90° means anti-clockwise , -90° means clockwise)

∴ The answer is: R0, 90° and (x , y) → (-y , x)

The expected gain or loss for this store is a gain of $79,750.

Gain is defined as the profit occurred by a store or a shopkeeper when an item is sold at a higher price than it was originally bought.

Loss is defined as the money lost by a store or a shopkeeper when an item is sold at a lower price than it was originally bought.

Both gain or loss is calculated by the formula -

Cost Price (CP) - Selling price (SP)

It is given that the company estimates that there is an 80% chance the store will have a profit of $100,000, a 10% chance of the store will break even, and a 10% chance of the store will lose $2,500.

Calculating the net gain or loss or the company -

= (80% * $100,000) + (10% * $0) - (10% * $2,500)

= (80/100 * $100,000) - (10/100 * $2,500)

= $80,000 - $250

= $79,750

Thus the net gain involved in the business by the company is $79,750 .

Therefore, the expected gain or loss for this store is a gain of $79,750.

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Answer:8 meters

z^2=x^2+y^2

10^2=x^2+6^2

100-36=x^2

x=swrt(64)=8

By applying the Pythagorean Theorem, we find out that the width of Blake's living room is 8 meters. This theorem helps to calculate the unknown side of a right triangle when the other two sides are known.

To answer this question, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal across the rectangular room is the hypotenuse of a right triangle, with the length and width of the room as the remaining sides.

Given that the length of the room is 6 meters and the hypotenuse is 10 meters, we can substitute these values into the formula of the Pythagorean Theorem:

Width² = Hypotenuse² - Length²

Substituting the known values gives:

Width² = 10² - 6²

Width² = 100 - 36

Width² = 64

Then, taking the square root of both sides:

Width = 8 meters

Therefore, the width of Blake's living room is 8 meters.

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Answer:

C

Step-by-step explanation:

y= -1 just like the other one

The horizontal asymptote is y=−1 and the x-intercept is at (2,0).

The answer is option C.

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Answer: 144°

Step-by-step explanation:

It is a regular pentagon which means all five sides are the same length. This also means that the angle between any two adjacent vertices is the same. So to find the angle between two adjacent vertices we take 360° and divide it by 5 which equals 72°. But A and D are not adjacent to each other, they have E in the middle (it also has B and C in the middle on the other side, but that's the bigger angle, and we usually label angles through their smaller angle. ex: a 30° angle is 30° if you look at it on the smaller angle (∠ ← here), but if you look at the bigger side of the angle (here →∠) it is 330°, yet we still call it a 30° angle). So, between A and D are two equal angles A to E, and E to D. So we multiply 72° by 2 which equals 144°.

So the answer is 144°.

Answer:

144

Step-by-step explanation:

plato

It should be $879.34, already rounded.

Answer:

1) The height the ball will bounce after hitting the ground the fourth time = 2.0736ft

2) The building is strong enough to withstand the Denali earthquake

Step-by-step explanation:

1) According to the given statement Bradley dropped the ball from a roof 16 feet high.Each time the ball hits the ground, it bounces3/5 the previous height

Therefore,

First bounce = 16*3/5 = 9.6

Second bounce = 9.6 *3/5 = 5.76

Third bounce =  5.76*3/5=3.456

Fourth bounce = 3.456*3/5=2.0736

The height the ball will bounce after hitting the ground the fourth time = 2.0736ft....

2) The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7.

Denali earthquake = 6.7 * 70 =469

It means that the building in Denali should be strong enough to withstand an earthquake of that magnitude  

The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8

Rat Islands earthquake = 7.8 * 30 = 234

It means that the building in Rat Islands should be strong enough to withstand an earthquake of that magnitude....

Answer:

3:20

Step-by-step explanation:

The 360 degrees clockwise rotation of the minute hand corresponds to 60 minutes.

The 90 degrees clockwise rotation is one-fourth of the 360 degrees, and hence will corresponds to 15 minutes.

The time is now 3:05.

After 15 minutes the time will be 3:20

Therefore the teacher dismisses the class at 3:20

I only know the answer for number 4 and 5

4. You subtract the min from the max to find the range.

5. The number that occurs most often in a day's set is called the mode.

Answer:

The answers below are in order going from top to bottum, left to right.

Step-by-step explanation:

mean, dividing, median, average, range, mode

3x^3 and 2x^3 should be combined because if numbers have an exponent combine only if they both have matching exponents and variables as well

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

c

Step-by-step explanation:

Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term.  I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9).  If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.

The expasion is as follows (up to the 7th term):

[tex]1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6[/tex]

That last term is the 7th term.  You find out its value by multiplying all the numbers together and adding on the c^3d^6.  Again those come from Pascal's triangle, and it's one of the coolest math things ever.  I encourage you to take the time to explore how it works.

Answer:

A. 2 to 5

Step-by-step explanation:

x is being multiplied by 2.

y is being multiplied by 5.

Although there is an infinite amount of ratios we can use when we know the values,we don't have that right now, so we have to stick to 2 to 5, which is our answer.

Can you tell me what do you mean exactly by menu of 8, so i can help you.

Answer:

a, Addition is commutative, so n+23.4023.40+n equals 1.

Step-by-step explanation:

Answer:

surface area of a sphere= 4pi*r^2

S.A when radius is 7 is:

=4pi*(7)^2

=196pi cm^2

if you multiply radius by 4, the equation becomes:

4pi*(4r)^2

=4pi*16r^2

=64pi*r^2

substitute 7 into equation:

=64pi*(7)^2

=64pi*49

=3136pi cm^2

Divide new S.A. by old S.A. to show effect:

=3136pi/196pi

=16

If the radius is multiplied by 4, the effect on the surface area is that it is 16 times the surface area of the sphere where the radius is not multiplied.

If the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

For this case, we're specified that:

We've to find the effect on the surface area of the sphere.

Initial surface area:

[tex]S_i = 4\pi r^2 = 4 \pi (7)^2 \: \rm unit^2[/tex]
Final surface area:

[tex]S_f = 4\pi r^2 = 4 \pi (4 \times 7)^2 = 4^2 \times [4 \pi (7)^2] \: \rm unit^2\\\\S_f =16 \times S_i[/tex]

Thus, if the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

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For this case we have by definition, that the total surface area of a regular pyramid with a square base is given by:

[tex]SA = \frac {1} {2} p * S + A_ {b}[/tex]

Where:

p: It is the perimeter of the base

S: It's the inclination

[tex]A_ {b}:[/tex] It is the area of the base

Substituting:

[tex]A_ {b} = 7 ^ 2 = 49units ^ 2\\p = 7 + 7 + 7 + 7 = 28units\\S = 10units\\SA = \frac {1} {2} 28 * 10 + 49\\SA = 140 + 49\\SA = 189 \ units ^ 2[/tex]

ANswer:

Option B

Answer:

B. 189 units squared

Step-by-step explanation:

ap3x

ANSWER

-2,-1,0,+4,+6

EXPLANATION

The given integers are:

-1, +6, 0, +4, -2

To arrange from least to greatest means arranging in ascending order of magnitude.

We can observe that:

-2<-1<0<+4<+6

Therefore the numbers written in order from least to greatest is:

-2,-1,0,+4,+6

Answer:

-2

Step-by-step explanation:

It's when the graph crosses the y axis

Find the Y value when the graphed line is at X = 0

When X is 0, the line crosses The X- axis at Y = -2

[tex]6.75 \div 3 = 2.25[/tex]

A.$2.25

You take the total which is $6.75 and divide it by the number of dog treat bags she purchased and once you divide it you get the total of one bag which is $2.25 per bag.