Welding and cutting done in confined spaces must

Given the complex numbers A1 5 6/30 and A2 5 4 1 j5, (a) convert A1 to rectangular form; (b) convert A2 to polar and exponential

Deffense [45]

This question is incomplete, the complete question is;

Given the complex numbers A₁ = 6∠30 and A₂ = 4 + j5;

(a) convert A₁ to rectangular form

(b) convert A₂ to polar and exponential form

(c) calculate A₃ = (A₁ + A₂), giving your answer in polar form

(d) calculate A₄ = A₁A₂, giving your answer in rectangular form

(e) calculate A₅ = A₁/( $A^{*}$ ₂), giving your answer in exponential form.

Answer:

a) A₁ in rectangular form is 5.196 + j3

b) value of A₃ in polar form is 12.19∠41.02°

The polar form of A₂ is 6.403 ∠51.34°, exponential form of A₂ = 6.403 $e^{j51.34 }$

c) value of A₃ in polar form is 12.19∠41.02°

d) A₄ in rectangular form is 5.784 + j37.98

e) A₅ in exponential form is 0.937 $e^{j81.34 }$

Explanation:

Given data in the question;

a) A₁ = 6∠30

we convert A₁ to rectangular form

so

A₁ = 6(cos30° + jsin30°)

= 6cos30° + j6cos30°

= (6 × 0.866) + ( j × 6 × 0.5)

A₁ = 5.196 + j3

Therefore, A₁ in rectangular form is 5.196 + j3

b) A₂ = 4 + j5

we convert to polar and exponential form;

first we convert to polar form

A₂ = √((4)² + (5)²) ∠tan⁻¹( $\frac{5}{4}$ )

= √(16 + 25) ∠tan⁻¹( 1.25 )

= √41 ∠ 51.34°

A₂ = 6.403 ∠51.34°

The polar form of A₂ is 6.403 ∠51.34°

next we convert to exponential form;

A∠β can be written as A $e^{j\beta }$

so, A₂ in exponential form will be;

A₂ = 6.403 $e^{j51.34 }$

exponential form of A₂ = 6.403 $e^{j51.34 }$

c) A₃ = (A₁ + A₂)

giving your answer in polar form

so, A₁ = 6∠30 = 5.196 + j3 and A₂ = 4 + j5

we substitute

A₃ = (5.196 + j3) + ( 4 + j5)

= 9.196 + J8

next we convert to polar

A₃ = √((9.196)² + (8)²) ∠tan⁻¹( $\frac{8 }{9.196}$ )

A₃ = √(84.566416 + 64) ∠tan⁻¹( 0.8699)

A₃ = √148.566416 ∠41.02°

A₃ = 12.19∠41.02°

Therefore, value of A₃ in polar form is 12.19∠41.02°

d) A₄ = A₁A₂

giving your answer in rectangular form

we substitute

A₄ = (5.196 + j3) ( 4 + j5)

= 5.196( 4 + j5) + j3( 4 + j5)

= 20.784 + j25.98 + j12 - 15

A₄ = 5.784 + j37.98

Therefore, A₄ in rectangular form is 5.784 + j37.98

e) A₅ = A₁/( $A^{*}$ ₂)

giving your answer in exponential form

we know that $A^{*}$ ₂ is the complex conjugate of A₂

so

$A^{*}$ ₂ = (6.403 ∠51.34° )*

= 6.403 ∠-51.34°

we convert to exponential form

A∠β can be written as A $e^{j\beta }$

$A^{*}$ ₂ = 6.403 $e^{-j51.34 }$

also

A₁ = 6∠30

we convert to polar form

A₁ = 6 $e^{j30 }$

so A₅ = A₁/( $A^{*}$ ₂)

A₅ = 6 $e^{j30 }$ / 6.403 $e^{-j51.34 }$

A₅ = (6/6.403) $e^{j(30+51.34) }$

A₅ = 0.937 $e^{j81.34 }$

Therefore A₅ in exponential form is 0.937 $e^{j81.34 }$

6 0

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Waterjet cutting uses a _____. a) Very-small-diameter jet of water that exits the cutting nozzle at approximately the speed of s

Paul [167]

Answer:

a

Explanation:

Waterjet cutting uses a very-small-diameter jet of water that exits the cutting nozzle at approximately the speed of sound. A water jet cutter, is oftentimes simply called a water jet is an industrial tool, like its name suggests, with the capabilities of cutting a different types of materials. Like its name suggests again, it uses water, although an extremely high-pressure jet of water to do the cutting. Other times, it uses a mixture of water and an abrasive substance to facilitate the cutting.

7 0

3 years ago

Noooo plssschvwekjshdjkshdjkshdjksahdk

sashaice [31]

Huh? Kffjkdkdodjenxkrkdkre

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3 years ago

Read 2 more answers

The radial component of acceleration of a particle moving in a circular path is always:________ a. negative. b. directed towards

lesya [120]

Answer:

d. all of the above

Explanation:

There are two components of acceleration for a particle moving in a circular path, radial and tangential acceleration.

The radial acceleration is given by;

$a_r = \frac{V^2}{R}$

Where;

V is the velocity of the particle

R is the radius of the circular path

This radial acceleration is always directed towards the center of the path, perpendicular to the tangential acceleration and negative.

Therefore, from the given options in the question, all the options are correct.

d. all of the above

7 0

3 years ago

7. You sometimes service vehicles with rust damage. It's safe to lift them on a two-post,

solong [7]

You sometimes service vehicles with rust damage. It's safe to lift them on a two-post frame-engaging lift without checking the vehicle lifting points. This is false.

Rust is an iron oxide, a typically reddish-brown oxide created when iron and oxygen react catalytically with moisture from the air or water. Iron(III) oxide-hydroxide and hydrous iron(III) oxides make up rust, which is often linked to the corrosion of refined iron.

Rusting is the chemical process that causes a red or orange coating to form on the surface of metals. Corrosion incorporates rusting. Steel and iron rust when they come into contact with oxygen and water, which are both necessary for rusting to take place.

It should be noted that when servicing vehicles with rust damage, It's not safe to lift them on a two-post frame-engaging lift without checking the vehicle lifting points. This can cause an accident.

Learn more about rust on:

brainly.com/question/1477535

#SPJ1

You sometimes service vehicles with rust damage. It's safe to lift them on a two-post frame-engaging lift without checking the vehicle lifting points.

True

False

8 0

2 years ago