evaluate the indefinite integral as a power series. t 1 − t9 dt c [infinity] n = 0 what is the radius of convergence r?

Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

1/38

Step-by-step explanation:

1/4 ÷ 19/2

1/4 × 2/19

1 × 2 over 4 × 19 = 2/76

2 ÷ 2 over 76 ÷ 2 = 1/38

Therefore:

1/4 ÷ 19/2 =

1/38

Hope this helps!

Answer: #x^3

Step-by-step explanation:

        x^3

note: An algebraic expression doesn't have an equal sign (=)

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Answer:

The dimensions of the cube would be:

Step-by-step explanation:

For this exercise, I suppose the measure of each cube is 1 unit, because there no says what is (you can replace it for ft, in, or another unit you need). How the big cube is formed by the 100.000 cubes smaller, and how a cube has its three measures equal: base, height, and width, you only need to obtain the cubic root of the total cubes (you use cubic root because you're gonna calculate a cube, for example, if you'd wanna calculate a square, you must obtain the square root of the total cubes):

How each cube measure is 1 unit, when you calculate the volume of the cube with the value obtained, you must obtain the total of the cubes:

In this form, you know the answer 46,41588834 is the right answer. I use the number with just two decimals (46,42 approximately) but you can use the complete number if you need.

The factor of the symmetric matrix into  A = LDL^T is equal to

\(\left|\begin{array}{ccc}\sqrt{29}-3/2 &-\sqrt{29}-3/2\\1&1\\\end{array}\right|\).

Factor the matrices into A=LDL^T$ form, follow these steps,

Find the eigenvalues and eigenvectors of the matrix A.

Construct the diagonal matrix D using the eigenvalues.

Construct the matrix L using the eigenvectors.

Let us apply these steps to each matrix,

\($A = \begin{bmatrix} 1 & 3 \ 3 & 2 \end{bmatrix}$\)

The eigenvalues can be found by solving the characteristic equation

det(A−λI)

= \(\left|\begin{array}{ccc}1-\lambda&3\\3&2-\lambda\\\end{array}\right|\)

⇒ λ²-3 λ -7 = 0

Solving for λ using the quadratic formula gives,

\($\lambda = \frac{3 \pm \sqrt{29}}{2}$.\)

The eigenvectors can be found by solving for each eigenvalue,

\($(A-\lambda I)x = 0$\)

\($\lambda_1 = \frac{3 + \sqrt{29}}{2}$\)

(A−λ₁ I)x = 0

⇒ \(\left|\begin{array}{ccc}1-\lambda_{1} &3\\3&2-\lambda_{1} \\\end{array}\right|x\) = 0

⇒ \(\left|\begin{array}{ccc}-\sqrt{29} -1/2 &3\\3&-\sqrt{29} -1/2\\\end{array}\right|x\) = 0

Solving this system of equations gives the eigenvector.

\(x_1 = \begin{bmatrix} \frac{\sqrt{29}-3}{2} \ 1 \end{bmatrix}$.\)

Similarly for,

\($\lambda_2 = \frac{3 - \sqrt{29}}{2}$\)

(A−λ₂I)x = 0

⇒ \(\left|\begin{array}{ccc}1-\lambda_{2} &3\\3&2-\lambda_{2} \\\end{array}\right|x\) = 0

⇒  \(\left|\begin{array}{ccc}\sqrt{29}+1/2 &3\\3&\sqrt{29} -1/2\\\end{array}\right|x\) =0

Solving this system of equations gives the eigenvector

\($x_2 = \begin{bmatrix} \frac{-\sqrt{29}-3}{2} \ 1 \end{bmatrix}$\)

Now we can construct the diagonal matrix D using the eigenvalues,

D = \(\left|\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2} \\\end{array}\right|\)

   = \(\left|\begin{array}{ccc}\frac{3+\sqrt{29} }{2} &0\\0&\frac{3-\sqrt{29} }{2} \\\end{array}\right|\)

And we can construct the matrix L using the eigenvectors,

L = \(\begin{bmatrix} x_{1} \ x_{2} \end{bmatrix}$\)

  = \(\left|\begin{array}{ccc}\sqrt{29}-3/2 &-\sqrt{29}-3/2\\1&1\\\end{array}\right|\)

So we have A = LDL^T$ with

L = \(\left|\begin{array}{ccc}\sqrt{29}-3/2 &-\sqrt{29}-3/2\\1&1\\\end{array}\right|\)

Therefore, the value of the matrix is equal to \(\left|\begin{array}{ccc}\sqrt{29}-3/2 &-\sqrt{29}-3/2\\1&1\\\end{array}\right|\).

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Answer:

x= 40

so

3x-5= 115

2x-15= 65

Step-by-step explanation:

C is the correct answer. I see that you put a mark on that choice so you are right if you thought that. I hope this helps!

Answer:

C

Step-by-step explanation:

The 2 angles are same- side interior angles and are supplementary, thus

3x - 5 + 2x - 15 = 180, that is

5x - 20 = 180 ( add 20 to both sides )

5x = 200 ( divide both sides by 5 )

x = 40

Thus

3x - 5 = 3(40) - 5 = 120 - 5 = 115°

2x - 15 = 2(40) - 15 = 80 - 15 = 65°

Answer: Jana

Step-by-step explanation: because she has the highest ratio 48 over 60 > 45 over 60

I did the test

Answer: 1 tablespoon

Step-by-step explanation:

Answer:

Is that all...

Step-by-step explanation:

Is there any other information if not then it is impossible to answer that question.

a) The number of rabbits that escaped from the ship is 24.

b) P(6) = 1 + 24 (0.85)^6 = 91.7, and P(24) = 1 + 24 (0.85)^24 = 436.8.

c) The graph of P(t) for 0 ≤ t ≤ 80 is an exponential curve that increases steadily over time.

d) The graph of P(t) is increasing.

e) The graph shows that the population of rabbits has increased exponentially since they escaped from the ship.

f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.

g) The graph suggests that it will take approximately 65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.

a)This can be calculated by taking the initial population, 1, and multiplying it by the given rate of growth, 0.85, and raising that to the 1000th power.

b) The meaning of these numbers in the context of the problem is that P(6) represents the total rabbit population after 6 months, and P(24) represents the total rabbit population after 24 months.

c)It is labeled with the variable t on the x-axis and the word "Population" on the y-axis, with each axis scaled appropriately.

f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.

g)The graph suggests that it will take  65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.

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Answer:yes

Step-by-step explanation:

The λ factor is not added to x' and t' because they are not related to mass, and they are not affected by time dilation.The Lorentz transformation helps in making predictions about how physical measurements will vary for different observers.

It helps in defining the relationship between the space-time coordinates of events as measured by two inertial frames of reference moving relative to each other with a constant velocity.The Lorentz transformation equation is given as follows:x' = (x - vt)γt' = (t - vx/c²)γwhere γ = 1/√(1-v²/c²) is the Lorentz factor.The Lorentz transformation can also be applied to the energy and momentum of a particle. The energy E and momentum p of a particle can be related to its mass m and velocity v through the following equations:E = γmc²p = γmv

Energy and momentum are related to the space-time coordinates of events as well. Therefore, the Lorentz transformation can be applied to them as well. The energy E' and momentum p' of a particle as measured in a frame of reference moving with a velocity v relative to a stationary frame of reference are given by the following equations:E' = γ(E - vp) p' = γ(p - vE/c²).

The energy E' includes a factor of γ in its equation because of the need to account for the effects of time dilation and length contraction on the energy of a moving particle. The momentum p' also includes a factor of γ because of the need to account for the effects of time dilation and length contraction on the momentum of a moving particle.

In conclusion, the λ factor is added to the energy equation because energy is related to mass, and mass increases with velocity. The effect of time dilation on mass is accounted for by the λ factor. On the other hand, the λ factor is not added to x' and t' because they are not related to mass, and they are not affected by time dilation.

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Answer:

x= -9/4 or -3

second one is x=5/6 or -8

Answer:

see explanation

Step-by-step explanation:

Given

4x² + 21x + 27 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × 27 = 108 and sum = 21

The factors are 12 and 9

Use the factors to split the x- term

4x² + 12x + 9x + 27 = 0 ( factor the first/second and third/fourth terms )

4x(x + 3) + 9(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(4x + 9) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

4x + 9 = 0 ⇒ 4x = - 9 ⇒ x = - 2.25

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

Following the same method as the previous question

Given

6x² + 43x - 40 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × - 40 = - 240 and sum = + 43

The factors are + 48 and - 5, thus

6x² + 48x - 5x - 40 = 0

6x(x + 8) - 5(x + 8) = 0

(x + 8)(6x - 5) = 0

x + 8 = 0 ⇒ x = - 8

6x - 5 = 0 ⇒ 6x = 5 ⇒ x = \(\frac{5}{6}\)

The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

(a) perimeter of the drawing = (7 x2) + (4 x 2)

                                               = 22 inches

(b) perimeter of the actual garden = 2(7 x 35) + 2(4 x 35)

                                                         = 490 + 280

                                                         = 770 inches

(c) 22 x 35 = 770

i don't really understand the last question. sorry if i gave you the wrong answers

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Given:

The functions are:

\(f(x)=\log_4x\)

\(g(x)=f\left(\dfrac{1}{3}x\right)\)

The function f(x) is dilated to become g(x).

To find:

The effect on f(x).

Solution:

Transformation is defined as:

\(g(x)=f(kx)\)            ...(i)

Where, k is the factor of horizontal stretch and compression.

If 0<k<1, then the graph of f(x) stretched horizontally by factor \(\dfrac{1}{k}\).

If k>1, then the graph of f(x) compressed horizontally by factor \(\dfrac{1}{k}\).

It is given that

\(g(x)=f\left(\dfrac{1}{3}x\right)\)          ...(ii)

On comparing (i) and (ii), we get

\(k=\dfrac{1}{3}\)

Therefore, the graph of f(x) stretched horizontally by factor \(3\).

Answer:

4.8% of $4,500 = $216

Step-by-step explanation:

use https://www.calculator.net/percent-calculator.html?cpar1=4.8&cpar2=4500&cpar3=&ctype=1&x=112&y=12

it is a calculator for percentages i feel that this will help you out

hope this helps!

The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

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To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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Answer:-12x

Step-by-step explanation:

just trust me on this

Answer:

$10.64

Step-by-step explanation:

20% out of $53.18 is $10.636 rounded to $10.64

Answer:

2x-y=5...(1)

4x+y=7...(2)

2x-5=y...(3)

sub (3) into (2)

4x +2x. =7+5

6x/6 = 12/6

x=2

sub x=2 in (2)

4(2) +y

8+y=7

y=7-8

y=-1

therefore (2;-1)

The elementary skills have used so far in the course is explained below.

What is whole numbers?

An integer is the range zero, a high quality herbal range or a bad integer with a minus sign. The bad numbers are the additive inverses of the corresponding high quality numbers. In the language of mathematics, the set of integers is frequently denoted through the boldface Z or blackboard bold.

The cap potential to define entire numbers and differentiate them from natural numbers is a critical component of math.

complete numbers like 0, 1, and 2 are the constructing blocks to expertise greater complex wide variety identifiers like actual numbers, rational numbers, and irrational numbers.

The subset of numbers within integers is whole numbers. those are numbers that we're maximum used to working with, which include zero. We see entire numbers on nutrients labels, or signs on the toll road telling us how many miles are to the subsequent exit/city.

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The answer is B. Normal. For a normal distribution, the mean, median, and mode are all equal to each other.

- Mean: The mean of a normal distribution is the center of the distribution, which is also the highest point of the bell-shaped curve.

- Median: The median of a normal distribution is the same as the mean, since the distribution is symmetric around the center.

- Mode: The mode of a normal distribution is also the same as the mean and median, since the highest point of the curve (i.e. the mode) is at the center of the distribution.

For the other probability distributions:

- A. Uniform: A uniform distribution has no mode (or multiple modes), and the mean and median are equal but different from the mode (if it exists).

- C. Exponential: An exponential distribution has a mode of 0, a median of ln(2)/λ, and a mean of 1/λ. Therefore, the mean, median, and mode are not equal.

- D. Poisson: A Poisson distribution has a mode of the integer part of λ (i.e., the highest probability mass function value). The mean and median are both equal to λ. Therefore, the mode is not necessarily equal to the mean and median.

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Answer:

1 1/4

Step-by-step explanation:

2 1/4 ÷ 1 4/5

9/4 ÷ 9/5

9/4 x 5/9

5/4

1 1/4

Answer:

x = 9

Step-by-step explanation: