Which of the following are roots of the following polynomial x^3-11x^2+33x+45

1 answer:

8 0

For x^3-11x^2+33x+45 , we can make it an equation so x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get

x^2-12x+45
___ ________________________
x+1 | x^3-11x^2+33x+45

- (x^3+x^2)
_________________________
-12x^2+33x+45
- (-12x^2-12x)
______________
45x+45
-(45x+45)
___________
0

Since that works, it's either B or D. We just have to figure out when
 x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer

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Urgent help please

rosijanka [135]

Let's assume the frequency of sound be f and wave length is w.

Given that, the frequency of sound varies inversely as the wavelength.

So, we can set up an equation as following:

f*w = k Where k= constant of variation.

Other information is, the frequency of a musical note is 276 cycles per second when the wavelength is 1.2m.

So, next step is to plug in f = 276 and w = 1.2 in the above equation to get the value of k.

276 * 1.2 = k

So, k = 331.2

Next step is to plug in k = 331.2 in the above equation. So,

f * w = 331.2

Now we need to find the wave length : w when frequency : f = 600.

Therefore,

600 * w = 331.2

$w = \frac{331.2}{600}$

So, w = 0.552

Hence, the wave length is 0.552 m.

Hope this helps you!.

5 0

3 years ago

Consider the function f ( x ) = 1 − 4 x 2 on the interval [ − 1 , 3 ] . Find the average or mean slope of the function on this i

Blababa [14]

Answer:

The average slope is 8.

Step-by-step explanation:

Let f be defined on the closed interval [a, b]. The average slope of f between a and b is the quotient

average slope = $\frac{f(b)-f(a)}{b-a}$

To find the average slope of the function $f(x)=1-4x^2$ on the interval [-1, 3] you have to evaluate your function in the interval and then divide by the interval.