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3 years ago

What is the multiplicity of the root x = -4?

Engineering

1 answer:

just olya [345]3 years ago

8 0

Answer:

See explanation

Explanation:

The multiplicity of a root of a polynomial equation is the number of times the root repeats.

Let $x=a$ be the root of $f(x)$ , then;

$(x-a)^1=0$ has a multiplicity of 1.

$(x-a)^2=0$ has a multiplicity of 2.

$(x-a)^3=0$ has a multiplicity of 3.

$(x-a)^m=0$ has a multiplicity of m, where m is a positive integer.

We were given the root $x=-4$ .

If $f(x)=(x+4)(x-6)^3$

Then the multiplicity of the root $x=-4$ is 1.

If $f(x)=(x+4)^4(x-6)^3$

Then the multiplicity of the root $x=-4$ is 4.

Since the polynomial function or equation is not given in the question, we cannot determine the multiplicity of this root.

But I hope with this explanation, you can refer to the original(complete) question and choose the correct answer.

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Mrrafil [7]

We can actually deduce here that making a airtight seal will take different format. You can:

Use an epoxy-resin to create an airtight seal
Create a glass-metal airtight seal
Make a ceramic-metal airtight seal.

<h3>What is an airtight seal?</h3>

An airtight seal is actually known to be a seal or sealing that doesn't permit air or gas to pass through. Airtight seal are usually known as hermetic seal. They are usually applied to airtight glass containers but the advancement in technology has helped to broaden the materials.

We can see that epoxy-resin can used to create an airtight seal. They create airtight seals to copper, plastics, stainless steels, etc.

When making glass-metal airtight seal, the metal should compress round the solidified glass when it cools.

Learn more about airtight seal on brainly.com/question/14977167

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6 0

2 years ago

Two identical billiard balls can move freely on a horizontal table. Ball a has a velocity V0 and hits balls B, which is at rest,

Lyrx [107]

Answer:

Velocity of ball B after impact is $0.6364v_0$ and ball A is $0.711v_0$

Explanation:

$v_0$ = Initial velocity of ball A

$v_A=v_0\cos45^{\circ}$

$v_B$ = Initial velocity of ball B = 0

$(v_A)_n'$ = Final velocity of ball A

$v_B'$ = Final velocity of ball B

$e$ = Coefficient of restitution = 0.8

From the conservation of momentum along the normal we have

$mv_A+mv_B=m(v_A)_n'+mv_B'\\\Rightarrow v_0\cos45^{\circ}+0=(v_A)_n'+v_B'\\\Rightarrow (v_A)_n'+v_B'=\dfrac{1}{\sqrt{2}}v_0$

Coefficient of restitution is given by

$e=\dfrac{v_B'-(v_A)_n'}{v_A-v_B}\\\Rightarrow 0.8=\dfrac{v_B'-(v_A)_n'}{v_0\cos45^{\circ}}\\\Rightarrow v_B'-(v_A)_n'=\dfrac{0.8}{\sqrt{2}}v_0$

$(v_A)_n'+v_B'=\dfrac{1}{\sqrt{2}}v_0$

$v_B'-(v_A)_n'=\dfrac{0.8}{\sqrt{2}}v_0$

Adding the above two equations we get

$2v_B'=\dfrac{1.8}{\sqrt{2}}v_0\\\Rightarrow v_B'=\dfrac{0.9}{\sqrt{2}}v_0$

$\boldsymbol{\therefore v_B'=0.6364v_0}$

$(v_A)_n'=\dfrac{1}{\sqrt{2}}v_0-0.6364v_0\\\Rightarrow (v_A)_n'=0.07071v_0$

From the conservation of momentum along the plane of contact we have

$(v_A)_t'=(v_A)_t=v_0\sin45^{\circ}\\\Rightarrow (v_A)_t'=\dfrac{v_0}{\sqrt{2}}$

$v_A'=\sqrt{(v_A)_t'^2+(v_A)_n'^2}\\\Rightarrow v_A'=\sqrt{(\dfrac{v_0}{\sqrt{2}})^2+(0.07071v_0)^2}\\\Rightarrow \boldsymbol{v_A'=0.711v_0}$

Velocity of ball B after impact is $0.6364v_0$ and ball A is $0.711v_0$ .

5 0

3 years ago

A paper clip is made of wire 0.75 mm in diameter. If the original material from which the wire is made is a rod 25 mm in diamete

Mariana [72]

Answer:The right 1 is 25 mm in diameter

Explanation:

6 0

3 years ago

What is an advantage of using a fully integrated cloud-based data analytics platform?

sweet [91]

Answer:

It gives decision-makers the processing capacity they need to turn raw data into useful knowledge.

Explanation:

Data analysis and the associated cycles (data integration, aggregation, hoarding, and revealing) are totally or partially directed in the cloud with cloud analytics.

3 0

3 years ago

The accumulated value in an up-counter instruction is currently 7. What will be the accumulator value after the following series

harkovskaia [24]

Answer:

The correct answer is C, which is 9

Explanation:

UP COUNTER

Since the accumulated value is 7, when it increments by two pulses the value of the accumulator increase to 9.

Up counter counts a value from the current value when a signal arrives at the input terminal. There is a reset terminal and preset value too. The counter counts up until the count reaches the preset value and resets. Whenever the input value changes from 0 to 1 the counter increment 1 from the preset value.

The up-counter is an output instruction whose function is to increment its accumulated value on false-to-true transitions of its instruction. It thus can be used to count false-to-true transitions of an input instruction and then trigger an event after a required number of counts or transitions. The up-counter output instruction will increment by 1 each time the counted event occurs.

5 0

4 years ago