10. Which of the following is the best financial situation?

For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = \lim_{z\to\frac\pi4}\frac1{(3-1)!} \frac{d^{3-1}}{dz^{3-1}}\left[e^z\cos(z)\right][/tex]

We have

[tex]\dfrac{d^2}{dz^2}[e^z\cos(z)] = -2e^z \sin(z)[/tex]

and so

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = - \lim_{z\to\frac\pi4} e^z \sin(z) = -\frac{e^{\pi/4}}{\sqrt2}[/tex]

Then by the residue theorem,

[tex]\displaystyle \int_C \frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3} \, dz = 2\pi j \left(-\frac{e^{\pi/4}}{\sqrt2}\right) = \boxed{-\sqrt2\,\pi e^{\pi/4} j}[/tex]

For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:

[tex]\displaystyle \mathrm{Res}\left(\frac{\cosh(2z)}{(z-2j)^2\left(z-\frac j2\right)^2}, z=\frac j2\right) = \lim_{z\to\frac j2}\frac1{(2-1)!} \frac{d^{2-1}}{dz^{2-1}}\left[\frac{\cosh(2z)}{(z-2j)^2}\right] = \frac{16\cos(1)-24\sin(1)}{27}j[/tex]

The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.

Answer:

n = 1/2 or 0.5

Step-by-step explanation:

Answer:

n=1/2

Step-by-step explanation:

EXPLANATION:

Given that

sin θ = 1/2

We know that

sin 3θ = 3 sin θ - 4 sin³ θ

⇛sin 3θ = 3(1/2)-4(1/2)³

⇛sin 3θ = (3/2)-4(1/8)

⇛sin 3θ = (3/2)-(4/8)

⇛sin 3θ = (3/2)-(1/2)

⇛sin 3θ = (3-1)/2

⇛sin 3θ = 2/2

⇛sin 3θ = 1

and

cos 2θ = cos² θ - sin² θ

⇛cos 2θ = 1 - sin² θ - sin² θ

⇛cos 2θ = 1 - 2 sin² θ

Now,

cos 2θ = 1-2(1/2)²

⇛cos 2θ = 1-2(1/4)

⇛cos 2θ = 1-(2/4)

⇛cos 2θ = 1-(1/2)

⇛cos 2θ = (2-1)/2

⇛cos 2θ = 1/2

Now,

The value of sin 3θ /(1+cos 2θ

⇛1/{1+(1/2)}

⇛1/{(2+1)/2}

⇛1/(3/2)

⇛1×(2/3)

⇛(1×2)/3

⇛2/3

Answer : Hence, the req value of sin 3θ /(1+cos 2θ) is 2/3.

also read similar questions: If sin Θ = 2/3 and tan Θ < 0, what is the value of cos Θ?

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if cos θ -sin θ =1, find θ cos θ +sin θ?

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Answer:

$41.89

Step-by-step explanation:

18% of %35.50 is $6.39.

$6.39+$35.50= $41.89

Answer:

She should leave $6.39 tip for the server. She paid $41.89 in all. Hope this helped! if the answer is wrong im super sorry!

Step-by-step explanation:

0.18 x 35.50 = 6.39

6.39 + 30.50 = 41.89

Answer:

11, 12, 13

Step-by-step explanation:

let's put the first number of the three as a:

a; a+1; a+2

The sum of the first and the twice second is 35 means:

a + 2(a+1) = 35

a + 2a + 2 = 35

3a = 33

a=11

now that we know a, we just need to add 1 and 2 as they are consecutive:

11, 12, 13

Answer:

C for each additional hour of service, the price of the dog walker increases by $10

Step-by-step explanation:

substitute any hour in f(n)=5+10n

for example, 1hr is 5+10×1=$15

2hr is 5+10×2=$25

3hr is 5+10×3=$35

4hr is 5+10×4=$45

and so on....

you can see that the price increases every $10

Answer:

I would go option a

Step-by-step explanation:

Option 2

Option 2 is better because for option one after 15 years your going up $7500 and with option 2 your going up 14062.5 in 15 years.

Answer:

The Balina is faster than the Delfino.

Step-by-step explanation:

Divide the amount of miles covered by the amount of hours it took for each one.

For the Delfino:

57.5 / 5 = 11.5

For the Balina:

54 / 4.5 = 12

You're welcome T^T

Answer:

Step-by-step explanation:

a+√b

a-√b

Answer:

Step-by-step explanation

RHS = cos 105° + cos 15°

         = cos (90° + 15°) + cos (90° – 75°)  

         = – sin 15° + sin 75°

         = sin 75° – sin 15°

          = LHS

Answer:

Step-by-step explanation:

sin75-sin15

=sin (90-15)-(-cos (90+15))

=cos 15+cos 105

Answer:

[tex]\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}[/tex]

Step-by-step explanation:

Step 1: Solve the system of equations

[tex]\begin{bmatrix}-x+y>2\\ x+2y>2\end{bmatrix}[/tex]

Isolate [tex]y[/tex] for [tex]-x+y>2[/tex]

[tex]\mathrm{Add\:}x\mathrm{\:to\:both\:sides}[/tex]

[tex]-x+y+x>2+x[/tex]

[tex]y>2+x[/tex]

Isolate [tex]y[/tex] for [tex]x+2y>2[/tex]

[tex]\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}[/tex]

[tex]2y>2-x[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]

[tex]\frac{2y}{2}>\frac{2}{2}-\frac{x}{2}[/tex]

[tex]y>\frac{2-x}{2}[/tex]

[tex]\bold{=\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}}[/tex]

Step 2: Graph

Instructions for graphing:

[tex]\mathrm{1.\:Graph\:each\:inequality\:separately.}[/tex]

[tex]\mathrm{2.\:Choose\:a\:test\:point\:to\:determine\:which\:side\:of\:the\:line\:needs\:to\:be\:shaded.}[/tex]

[tex]3. \mathrm{The\:solution\:to\:the\:system\:will\:be\:the\:area\:where\:the\:shadings\:}\\\mathrm{from\:each\:inequality\:overlap\:one\:another.}[/tex]

When done, it should look like this:

Answer:

i dont know how to do it231

Step-by-step explanation:

1123234

Answer:

Perimeter = 12 1/2 in

Area = 9.375 in

Step-by-step explanation:

Perimeter:

(3 3/4) + (3 3/4) + (2 1/2) + (2 1/2) = 12 1/2

Area:

(3 3/4) * (2 1/2) = 9.375

Answer:

P = 12 1/2 in

A = 9 3/8 in²

Step-by-step explanation:

L = 3 3/4 in

W = 2 1/2 in

Area:

A = L × W

A = (3 3/4 in)(2 1/2 in)

A = 15/4 in × 5/2 in

A = 75/8 in²

A = 9 3/8 in²

Perimeter:

P = 2(L + W)

P = 2(3 3/4 in + 2 1/2 in)

P = 2(15/4 in + 5/2 in)

P = 2(15/4 in + 10/4 in)

P = 2(25/4 in)

P = 25/2 in

P = 12 1/2 in

Answer:

1-2

Step-by-step explanation:

honestly idek what this stuff is I just need points

Recall that

(x + y)² = x² + 2xy + y²

Then if x + y = √7 and x² + y² = 6, we have

(√7)² = 6 + 2xy   ⇒   2xy = 1

We also have

(x - y)² = x² - 2xy + y²

so that

(x - y)² = 6 - 1   ⇒   (x - y)² = 5

which means x - y has two possible values, √5 or -√5.

Answer:

[tex]2\sqrt[3]{5}[/tex]

Step-by-step explanation:

40 = 8 x 5 and 8 is the cube of 2, so 2 goes on the outside but 5 can't be simplified

Answer:

Adelina

Step-by-step explanation:

The rates of change of points earned by both players tell us that;

Player A gains more point than Player B does for each correct answer in this round.

We are told that x is the number of

number ofquestions answered correctly and y is the score.

Now, for player B;

For 1 correct answer, he got a score of 4

For 2 correct answers, he got a score of 5

For 3 correct answers, he got a score of 6

For 4 correct answers, he got a score of 7

This means that rate of change of Player B is;

3 points for every extra question answered correctly. .

Now, the formula for player A's points is;

y = 4x + 3

Rate of change of points here is gotten by finding the derivative. Thus;

dy/dx = 4

This means player A earns 4 points for every extra question answered correctly.

In conclusion, it mean that Player A gains more point than Player B does for each correct answer in this round.

Read more on slope intercept form of equation at; https://brainly.com/question/19249035

Answer:

196

Step-by-step explanation:

Just plug in a -7 for everywhere there is a t:

[tex]g(t)=4t^2\\g(-7)=4(-7)^2\\g(-7)=4*49=196[/tex]

one hundred seventy nine

Part/whole= x/100

Let x= percentage of  

money

12/32=  x/100

1200/32= 37.5%

Answer:

Model B

Step-by-step explanation:

In Model A as x increases by 2 y decreases by 1. So as x increases by 1 y decreases by 0.5 giving us a rate of change of -0.5

In Model B we have a slope of 2/3 (because as x inreases 2 times y increases 3 times)

-0.5 < 2/3

Answer:

i think D. 4x4x4 = 64 is answer

Step-by-step explanation:

4³ = 4×4×4 = 64

Answer:

8.705-4.93=3.775

Hope This Helps!!!

Answer:

7

Step-by-step explanation:

63 / 9 = 7

Given function:-

Degree of the given function is the highest power of the variable.

We have variable x there.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞

Answer:

Step-by-step explanation:

Given isosceles trapezoid.

Its congruent sides are 4 and (2x + 2):

Solve for x:

Answer:

455554444444555556555555554444