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mariarad [96]
2 years ago
8

Complete the following exercises by applying polynomial identities to complex numbers.

Mathematics
1 answer:
erik [133]2 years ago
6 0

1.)

   =(x-8i)(x+8i)

x^2+8ix-8ix-64i^2

x^2-64i^2

x^2-64(-1)

x^2+64

2.)

    =(4x-7i)(4x+7i)

16x^2+28ix-28ix-49i^2

16x^2-49i^2

16x^2-49(-1)

16x^2+49

3.)

    =(x+9i)(x+9i)

x^2+9ix+9ix+81i^2

x^2+18ix+81(-1)

x^2+18ix-81

4.)

    =(x-2i)(x-2i)

x^2-2ix-2ix+4i^2

x^2-4ix+4(-1)

x^2-4ix-4

5.)

    =[x+(3+5i)]^2

(x+5i+3)^2

(x+5i+3)(x+5i+3)

x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9

x^2+6x+10ix+30i+25i^2+9

x^2+6x+10ix+30i+25(-1)+9

x^2+6x+10ix+30i-25+9

x^2+6x+10ix+30i-16

Hope this helps :)

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max2010maxim [7]

<u>Answer</u>:

The velocity of the tennis racket after the collision 14.966 m/s.

<u>Step-by-step explanation:</u>

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.

So, the total kinetic energy before collision = the total kinetic energy after collision.

For the given problem let the following:

m₁ = mass of tennis racket = 0.311 kg

m₂ = mass of the ball = 0.057 kg

u₁ = velocity of tennis racket before collision = 30.3 m/s

u₂ = velocity of the ball before collision = -19.2 m/s

v₁ = velocity of tennis racket after collision

v₂ = velocity of the ball after collision

Right ⇒east  (+) , Left⇒ west (-)

v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)

  = ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)

  = 14.966 m/s.

So, the velocity of the tennis racket after the collision 14.966 m/s.

5 0
3 years ago
What is the domain and range for g(x)=2/3x
labwork [276]

Answer:

Domain - all real numbers except 0

Range - all real numbers

Step-by-step explanation:

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5 0
2 years ago
Check whether <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20" id="TexFormula1" title=" \frac{4}{5} " alt=" \f
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Answer:

Non terminating

Step-by-step explanation:

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Hope this helps :D

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Renaldo catches the bus at 4:00 pm to ride 3.2 miles from his house to the dentists office. he arrives at 4:30 pm, for a one hou
andrew11 [14]

Answer:

Step-by-step explanation:

speed = distance/time

so renaldo speed = 3.2/0.5 = 6.4miles/hr (since time taken is 1/2 hr)

now after 1 hr of his appoinment i.e at 5:30pm he took bus whose speed is same as before i.e 6.4 miles/hr

now time taken to cover this 4.8 miles = 4.8/6.4 = 3/4 hr (since time = distance /speed )

3/4 hr = 3/4 * 60 = 45 minutes

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8 0
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Answer:

360 pi in ^3

Step-by-step explanation:

The volume of a cylinder is given by

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We know the diameter is 12 so the radius is 1/2  the diameter

r = d/2 = 12/2 = 6

V = pi (6)^2 * 10

V = pi (36)*10

V = 360 pi in ^3

We can approximate pi by 3.14

V =1130.4 in ^3

Or we can approximate pi by using the pi button

V =1130.973355  in ^3

6 0
3 years ago
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