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3 years ago

Multiplicity of x^3+3x^2+3x+1=0

1 answer:

3 0

If x = -1 this gives -1 + 3 - 3 + 1 = 0

so x = -1 is one root

if we divide the expression by (x + 1) we get the quotient x^2+2x+1
which factors to (x+1)(x+1)

so the multiplicity is 3

You might be interested in

The sum of 5 times a larger number and twice a smaller is 5. The difference of 4 times the larger and the smaller number is 4. F

Gemiola [76]

Answer:

1 and 0

Step-by-step explanation:

Let's call the smaller number x and the larger number y.

This means 5y+2x=5.

Also, 4y-x=4.

This is a system of equations. There are two main ways two solve this.

Method 1: Substitution

5y+2x=5

4y-x=4

Solve for one of the variables, then substitute it back into one of the equations to solve for the other variable.

I will take 4y-x=4 and solve for x.

4y=4+x

x=4y-4

Then substitute for x in the other equation and solve for y.

5y+2x=5

5y+2(4y-4)=5

5y+8y-8=5

13y=13

y=1

Now we can go back to our equation for x and substitute for y.

x=4y-4

x=4(1)-4=0

y, the larger number, is 1 and

x, the smaller number, is 0

Method 2: Elimination

5y+2x=5

4y-x=4

Change the equations so that the coefficient of one of the variables in an equation is opposite the one in the other equation. Then add the equations and solve for each variable.

If I multiply both sides of the second equation, 4y-x=4, by 2, the coefficient of x will become -2. In the first equation, the coefficient is 2, so they will become opposites.

4y-x=4

becomes

8y-2x=8

Now we have 5y+2x=5 and 8y-2x=8.

Add the sides of both equations to cancel the x values.

5y+2x+8y-2x=5+8

13y=13

y=1

like last time, we can substitute for y in any of the original equations to get x.

5y+2x=5

5(1)+2x=5

5+2x=5

2x=0

x=0

y, the larger number, is 1 and

x, the smaller number, is 0

6 0

3 years ago

The volume of the prism shown is 84 cubic yards. What is the Height of the prism

Salsk061 [2.6K]

Answer:

4 yd

Step-by-step explanation:

If l×w×h=v, then v÷l÷w=h

84÷7÷4=h

12÷3=h

h=4

The height of the prism is 4 yards.

4 0

3 years ago

From the Pythagorean theorem, what can you infer

mestny [16]

Answer:

It's always longer than either of the legs

Step-by-step explanation:

The hypotenuse is always longer than either of the legs.

6 0

3 years ago

What is the inverse of f(x) = 1x+2?

jeka57 [31]

For this specific equation the answer is x - 2

3 0

3 years ago

Paint manufacturer uses a machine to fill 1- gallon cans with paint- they want to estimate the mean volume of paint the machine

Triss [41]

Answer:

$n=(\frac{1.64(0.85)}{0.25})^2 =31.09$

So the answer for this case would be n=32 rounded up to the nearest integer

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=0.85$ represent the sample standard deviation

n represent the sample size (variable of interest)

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05,0,1)", and we got $z_{\alpha/2}=1.64$ , replacing into formula (2) we got:

$n=(\frac{1.64(0.85)}{0.25})^2 =31.09$

So the answer for this case would be n=32 rounded up to the nearest integer

5 0

3 years ago