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2 years ago

Calculate using Cauchys integral formula

Mathematics

1 answer:

zhuklara [117]2 years ago

5 0

Answer:

9πi/2

Step-by-step explanation:

$\oint\limits_C {\frac{5z^{2}+4}{(z-1)(z+3)} } \, dz,\ C: |z|=2$

Let f(z) = (5z² + 4) / (z + 3).

$\oint\limits_C {\frac{f(z)}{z-1} } \, dz,\ C: |z|=2$

Using Cauchy's integral formula:

$2\pi i\ f(1)\\2\pi i\ (\frac{5(1)^{2}+4}{1+3}) \\2\pi i\ (\frac{9}{4}) \\\frac{9\pi i}{2}$

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A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

3 years ago

hey can someone please help me i don’t understand this? the question says “find the surface area of the rectangular prism.”

ASHA 777 [7]

Answer:

170 in^2

Step-by-step explanation:

you have to find the area of each surface of the square

1) the square on the right side:

5x5=25 in^2

there are 2 of these on opposite sides

2)the of the rectangle facing us;

6x5=30in^2 (5 because 5 is the height)

there are 4 of these

3)add up all the areas

25+25+30+30+30+30=170in^2

6 0

2 years ago

How much will it cost to fill up an empty 12-gallon take if gasoline costs $1.1599 per gallon

aliina [53]

Answer:

13.9188 dollars

Step-by-step explanation:

1.1599 * 12 = 13.9188

8 0

3 years ago

Read 2 more answers

For f(x)=4x+1 and g(x)=x^2-5,find(f•g)(4)

RoseWind [281]

Answer:

(f•g)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f•g)(x) = 4(x^2 -5)+1

(f•g)(4) = 4(4^2 -5)+1

(f•g)(4) = 4(16-5)+1

(f•g)(4) = 4(11)+1

(f•g)(4) = 44 + 1

(f•g)(4) = 45

8 0

3 years ago

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The sum of two numbers is 240. If one number is twice the other number, find the two numbers.

Deffense [45]

Answer:

The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.

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Let the smaller be "x" ; Larger is "2x-6"

EQUATION:

x + 2x-6 = 240

3x= 246

x = 82 (smaller)

2x-6 = 158 (larger)

Step-by-step explanation:

7 0

2 years ago

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