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MaRussiya [10]
4 years ago
8

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

Mathematics
1 answer:
Mandarinka [93]4 years ago
8 0
For x^3-11x^2+33x+45 , we can make it an equation so <span>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
</span> 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 <em>f</em> be defined on the closed interval [a, b]. The average slope of <em>f </em>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.

So,

f(-1)=1-4(-1)^2=-3\\\\f(3)=1-4(3)^2=-35

The average slope is  \frac{f(3)-f(-1)}{3+1}= \frac{-3+35}{3+1}=\frac{32}{4}=8

4 0
3 years ago
An NBA corner 3-pointer is 264 inches away from the hoop. One day, you measure it to be 270.6 inches. What is the measurement er
vesna_86 [32]
Plz give me more to explain
5 0
3 years ago
find the area of a right angle triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long​
Lelu [443]

Answer:

30 cm^2

Step-by-step explanation:

a = 13 cm

b = 12 cm

using Pythagorean theorem:

a^2 = b^2 + c^2

--> c^2 = a^2 - b^2 = 13^2 - 12^2 = 169 - 144 = 25

--> c = √25 = 5

The area of that right triangle is:

S = b.c / 2 = 12 . 5 / 2 = 30 (cm^2)

6 0
3 years ago
List 3 effects that an increase in urbanization can have on air quality
soldi70 [24.7K]
More cars = more pollution. 
<span>More industry buildings = more pollution. </span>
<span>More people = more people breathing carbon dioxide = more pollution</span>
4 0
4 years ago
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