Find the Taylor Series and its circle of convergence.
a) f(z)= e^z about z=0
b) f(z) = e^z/cosz about z=0
(Please provide answers step by step process - (fully))

Answer: 11 weeks

Step-by-step explanation:

G(t) = 25 + 14t

A(t) = 80 + 9t

set G equal to A and find t

25 + 14t = 80 + 9t

5t = 55

t = 11

Answer: y=7(5)^x

Step-by-step explanation:

original equation

\(\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}\)

multiply by lcd

\(12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8\)

isolate for x

\(-1x=-8\\\\x=8\)

verify

\(\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS\)

Tt is also possible neither y nor z is x.

Now, According to the question;

The x and y-axis are two important lines of the coordinate plane. The x-axis is a horizontal number line and the y-axis is a vertical number line. These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.

If x is true, a non true statement cannot be the same as it.

Now, In symbolic logic, = doesn't mean two statements have the same value—it means they are the same literal statement.

So, if x is true, and y and z contradict, at least one of y and z is false, and that false statement cannot possibly be x.

Hence,  it is also possible neither y nor z is x.

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Answer:

the answer is number 2

Step-by-step explanation:

hope this helps u

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points. These angles represent whether the two given lines are parallel to each other or not. If these angles are equal to each other then the lines crossed by the transversal are parallel. In this article, we will discuss what are alternate interior angles, the theorem statements and proofs based on the alternate interior angles, what is a co-interior angle, and many solved examples.

An interior angle is a shape's internal angle. The closed form with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has internal angles that are all exactly right angles, or 90 degrees.

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Answer:

Step-by-step explanation:

3x + 4x + x = 16

7x + x = 16

8x = 16

x = 16 : 8

x = 2

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

3 × 2 + 4 × 2 + 2 = 16  (remember PEMDAS)

6 + 8 + 2 = 16

16 = 16

same value the answer is good

The bit pattern 1001001 represents the letter I. The letter represented by the decimal value 73 in ASCII is the uppercase letter "I".

The ASCII value for the letter A is indeed 65 in decimal. To find the letter represented by the bit pattern 1001001, we need to convert this binary value to decimal.

Step 1: Write down the binary value:
1001001

Step 2: Identify the position of each digit (starting from right to left):
2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6

Step 3: Multiply the binary digit by its corresponding position value:
(1*2^6) + (0*2^5) + (0*2^4) + (1*2^3) + (0*2^2) + (0*2^1) + (1*2^0)

Step 4: Calculate the decimal value:
(64) + (0) + (0) + (8) + (0) + (0) + (1) = 73

The decimal value for the binary number 1001001 is 73. Now, we can find the ASCII character that corresponds to this decimal value.

The letter represented by the decimal value 73 in ASCII is the uppercase letter "I".

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Answer:

x = 6

y = \(3\sqrt{2}\)

Step-by-step explanation:

Thats a 45 45 90 triangle, one of my favorite and you'll come to miss it later because of how easy it is.

See the file provided for the trick

Because \(3\sqrt{2}\) falls where a 1 is in the diagram that means y is also \(3\sqrt{2}\) because you multiply \(3\sqrt{2}\) by 1, and to get x you'll multiply the value we're given, \(3\sqrt{2}\), by the value in the spot in the given diagram, \(\sqrt{2}\).

\(3\sqrt{2}\) ×\(\sqrt{2}\)

Note; a radical multiplied by itself is the value in the radical

Therefore,

\(3\sqrt{2}\) ×\(\sqrt{2}\) = 3(2) = 6

Thus x = 6

The explanation for this;

\(\sqrt{2}\) * \(\sqrt{2}\) = \(\sqrt{2}^2\)

And if you square a square root you have its square root times its square root squared, which if it was \(\sqrt{4}^2\) it'd ultimately be \((2)^2\) which is 2x2 which equals 4

Hope this helps

Answer: It’s adjacent I’ll draw what vertical is. And M is 180-106 which is 74. Adjacent means next to...

Step-by-step explanation:

The number of different ways that can be use to form a four digit number  using digits 0,1,2,2 where 0 can not in the first place is 18

1st place: The first place can be filled by three different ways i.e. 1,2,2 as a number can not start with zero

2nd place: The second place is can be filled by three ways ( remaining 2 numbers+ zero)

3rd place : The third place can be filled by two ways with the remaining two numbers.

4th place: The fourth place be filled by only one way with that remaining one number after filling all places.

So, the total number of ways will be=3×3×2×1

                                                            =18

Therefore , 18 different numbers can be constructed using the digits 0,1,2,2 where all of the digits must be used each time and no number can begin with 0.

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Answer:

C

Step-by-step explanation:

Answer:

y = 1/8x

Step-by-step explanation:

Given Equation:

⇒ -8y = -1x + 48

⇒ y = 1/8x + 6

As a result, the equation of the parallal line to the given equation x - 8y = 48 is:

⇒ y = 1/8x

Answer:

you got it keep working

Step-by-step explanation:

Answer:

7. b = 8

8. a = 30

9. a = 3.46

Step-by-step explanation:

Our equation is a^2 + b^2 = c^2

Now let put the number in and solve

7. 225 + b^2 = 289

 b^2 = 64

 b= 8

8. a^2 + 1600 = 2500

 a^2 = 900

 a = 30

9. a^2 + 4 = 16

  a^2 = 12

  a= 3.46

Answer:

1)b=8,2)a=30and3)a=3.46410161514

Step-by-step explanation:

Mark me Brainliest Please

The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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Answer:

C

Step-by-step explanation:

first of all the situation is simply :

for the first position you have the full choice of the 30 members.

but then for the other positions you have taken 1 member out of the pool, and we have only 29 left to pick from.

after picking the second position, you have taken 2 members out of the pool, and we have only 28 choices for the 3rd position.

that is what the answer is

30×29×28

now to the theory :

well, the sequence is important.

if you go for the combinations of picking 3 people out of 30, you don't care, if m1 is in p1, m2 in p2, and m3 in p3, or m1 in p2, m2 in p3 and m3 in p1. since it is the same group of m1, m2, m3, both cases would be the same for combinations.

but for our purpose here, they are not the same.

it is important who is president, vice president and treasurer.

like in the Olympic games it makes a big difference, who wins gold, silver and bronze. it is not just to win a medal, and nobody cares about the color ...

they do, and therefore the sequence matters.

and therefore it is a permutation.

basically, the last division by 3×2×1 in the combinations is simply the removal of all the different sequences inside a group of 3.

as, in how many ways can you order 3 items ? 6 : 3×2×1.

3 options for the first, then 2 options for the second, and then one remaining for the third.

but again, if the sequence inside the group of 3 is important, you need to keep these extra 6 options per group of 3 in the calculation.

if the description would have been :

the club votes 3 members as board, and all 3 board members can fulfill all 3 roles at any time as needed, then the sequence would not matter, and it would be combinations.

but the sequence matters, and it is permutations.

\(Hiya!\)

The answer is....

Hopefully, this helps you!!

\(Sokka\)

Answer:

I hope it helps you :)

Thea are a of rectangle is base times the height of the rectangle

The length of third side is 4 cm. This can be solved using the concept of right angled triangle.

Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.

A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.

Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.

the triangle given is Right Angled Triangle because to find a third side provided two sides are given is only possible in a right angled triangle.

We know that the right-angled triangle follows Pythagoras Theorem

According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side:

(Perpendicular)² + (Base)² = (Hypotenuse)²

or, (2√3)² + (2)² = (Hypotenuse)²

or, 12 + 4 = (Hypotenuse)²

or, (Hypotenuse)² = 16

or, Hypotenuse = √16

or, Hypotenuse = 4 cm

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The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

Given are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).

The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -

R' (1, -6)

S' (5, -3)

T' (3, 2)

The graph is attached.

Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

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Answer:

\(a_{73}=367\)

Step-by-step explanation:

\(a_n=a_1+(n-1)d\\a_{73}=7+(73-1)(5)\\a_{73}=7+(72)(5)\\a_{73}=7+360\\a_{73}=367\)

Answer:

1

Step-by-step explanation:

7+1

=8

8*2

=16

Multiplication operation is the inverse of the one in the given equation which is 9 = p/8.

What is an inverse?

The opposite of another operation is referred to as the "inverse" in mathematics. The operations that cancel out or are the opposite of one another are referred to as inverse operations. The work of a pair is reversed by an inverse operation.

We are given an equation as 9 = p/8.

In this equation,  we can see that the operation used is division.

We know that inverse of division is multiplication.

Hence, multiplication operation is the inverse of the one in the given equation.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

1

Step-by-step explanation:

It is 1 because the laws of exponents state that anything raised to the power of 0 is 1.

Answer:

this is so easy and the answer of this all questions is54