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3 years ago

What is the multiplicity of the root 2 in the equation x^3-8x^2+20x-16=0?

1 answer:

mote1985 [20]3 years ago

8 0

Factoring the cubic you get: <span>(x - 2)^2 (x-4) , so we know the multiplicity is the amount of times a root shows in an equation because the equation (x-2) has a exponent of 2 that means the root 2 has a multiplicity of 2.</span>
Answer: 2

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At time t equals0, a particle is located at the point (2,1,6). It travels in a straight line to the point (9,8,5), has

Lana71 [14]

Answer:

$r(t)=$

Step-by-step explanation:

We are given that

Initial position of particle = $r_0=r(0)=$

Initial speed of the particle = 8 m/s

Acceleration=7 i+7j-k=<7,7,-1>

We have to find the equation of position vector r(t) of the particle at time t.

We know that

Acceleration=a= $\frac{dv}{dt}$

$dv=adt$

$dv=(7i+7j-k)dt$

Integrating on both sides then, we get

$v(t)=+v_0$

Where $v_0=,v_1,v_2,v_3>$

$v_0=v(0)=8$

$\mid \mid=8$

Since, the particle travel in straight line to (9,8,5) and (9,8,5)-(2,1,6)=<7,7,-1>

There exist a constant s such that

$v_1=7s, v_2=7s, v_3=-s$

$\sqrt{v^2_1+v^2_2+v^2_3}=8$

$\sqrt{49s^2+49s^2+s^2}=8$

$\sqrt{99s^2}=8$

$99s^2=64$

$s^2=\frac{64}{99}$

$s=\sqrt{\frac{64}{99}}=\frac{8}{3\sqrt{11}}$

$v_0=$

$v(t)=+$

$v(t)=$

$dr=vdt$

Integrating on both sides then we get

$r(t)=\int dt$

$r(t)= +r_0$

Where $r_0=r(0)=$ =Some constant vector

$r_0=$

Substitute the value

$r(t)=+$

$r(t)=$

This is required equation of the position vector r(t) of the particle at time t.

3 0

3 years ago

(36 - 4)(6+2)<br> Standard form

jolli1 [7]

The answer is 256 ,

explanation- 6+2 is 8 and 36-4 is 32. 8 times 32= 256

3 0

3 years ago

How many constant terms are in this expression?<br><br> 11a + 9b + c + 2a

zzz [600]

Answer:

Step-by-step explanation:

11a + 9b + c + 2a

a constant is just a number...it has no variables (letters).

there are no constants in this expression

example :

3x + 2b + 7 + 4c + 2 x + 5 = 8

the constants in this are 7 and 2 constants are 5 and 8

7 0

3 years ago

Use the Hermit method to calculate a curve (parametric equation) for the cases where the known quantities are the starting and e

s344n2d4d5 [400]

Answer:

The graph is in the attachment below

Step-by-step explanation:

The solution is attached below

5 0

3 years ago

50 points help (show ur work)<br> Answer all of them

salantis [7]

Answer:

5. $40

6. 500 students

7. 60 books

8. 63 pages

Step-by-step explanation:

<h3><u>Question 5</u></h3>

Given:

Aiden spent $18 on souvenirs.
$18 is 45% of the money he brought on the trip.

Let x be the money Aiden brought on the trip.

Create equivalent ratios with the given information and defined variable, and <u>solve for x</u>:

$\implies 18:45\%=x:100\%$

$\implies 18:0.45=x:1$

$\implies \dfrac{18}{0.45}=\dfrac{x}{1}$

$\implies 18=0.45x$

$\implies x=\dfrac{18}{0.45}$

$\implies 40$

Therefore, Aiden brought $40 on the trip.

<h3><u>Question 6</u></h3>

Given:

Angel received 300 votes.
300 votes was 60% of all the votes.

Let x be the number of students who voted in the election.

Create equivalent ratios with the given information and defined variable, and <u>solve for x</u>:

$\implies 300:60\%=x:100\%$

$\implies 300:0.6=x:1$

$\implies \dfrac{300}{0.6}=\dfrac{x}{1}$

$\implies 300=0.6x$

$\implies x=\dfrac{300}{0.6}$

$\implies x = 500$

Therefore, there were 500 students who voted in the election.

<h3><u>Question 7</u></h3>

Given:

The students sold 80% of the books.
The total number of books they sold is 48.

Let x be the number of books in the sale.

Create equivalent ratios with the given information and defined variable, and <u>solve for x</u>:

$\implies 80\%:48=100\%:x$

$\implies 0.8:48=1:x$

$\implies \dfrac{0.8}{48}=\dfrac{1}{x}$

$\implies 0.8x=48$

$\implies x=\dfrac{48}{0.8}$

$\implies x=60$

Therefore, there were 60 books in the book sale.

<h3><u>Question 8</u></h3>

Given:

Aiyana read 147 pages of the book.
She completed 70% of the book.

If she has completed 70% of the book, then she still has 30% left to read, as 100% - 70% = 30%.

Let x be the number of pages Aiyana still has to read.

Create equivalent ratios with the given information and defined variable, and <u>solve for x</u>:

$\implies 70\%:147=30\%:x$

$\implies 0.7:147=0.3:x$

$\implies \dfrac{0.7}{147}=\dfrac{0.3}{x}$

$\implies 0.7x=44.1$

$\implies x=\dfrac{44.1}{0.7}$

$\implies x=63$

Therefore, Aiyana still has 63 pages left to read.

5 0

1 year ago