Answer: 0.512
Step-by-step explanation:
256/32=8
8*(0.4)^3=
8*0.064=0.512
y=0.512
Answer:
the asnwer is YES
Step-by-step explanation:
Answer:
Characteristic equation:
Eigen values:
Step-by-step explanation:
We are given the matrix:
![\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-14%26-6%266%5C%5C28%2612%26-4%5C%5C0%260%264%5Cend%7Barray%7D%5Cright%5D)
The characteristic equation can be calculated as:
We follow the following steps to calculate characteristic equation:
![=det\Bigg(\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]-\lambda\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\Bigg)\\\\= det\Bigg(\displaystyle\left[\begin{array}{ccc}-14-\lambda&-6&6\\28&12-\lambda&-4\\0&0&4-\lambda\end{array}\right]\Bigg)\\\\=(-14-\lambda)[(12-\lambda)(4-\lambda)]+6[28(4-\lambda)]-6[(28)(0)-(12-\lambda)(0)]\\\\= -\lambda^3 + 2\lambda^2 + 8\lambda](https://tex.z-dn.net/?f=%3Ddet%5CBigg%28%5Cdisplaystyle%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-14%26-6%266%5C%5C28%2612%26-4%5C%5C0%260%264%5Cend%7Barray%7D%5Cright%5D-%5Clambda%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%5CBigg%29%5C%5C%5C%5C%3D%20det%5CBigg%28%5Cdisplaystyle%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-14-%5Clambda%26-6%266%5C%5C28%2612-%5Clambda%26-4%5C%5C0%260%264-%5Clambda%5Cend%7Barray%7D%5Cright%5D%5CBigg%29%5C%5C%5C%5C%3D%28-14-%5Clambda%29%5B%2812-%5Clambda%29%284-%5Clambda%29%5D%2B6%5B28%284-%5Clambda%29%5D-6%5B%2828%29%280%29-%2812-%5Clambda%29%280%29%5D%5C%5C%5C%5C%3D%20-%5Clambda%5E3%20%2B%202%5Clambda%5E2%20%2B%208%5Clambda)
To obtain the eigen values, we equate the characteristic equation to 0:
![p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda = 0\\-\lambda(\lambda^2-2\lambda-8) = 0\\-\lambda(\lambda^2-4\lambda+2\lambda-8) = 0\\-\lambda[(\lambda(\lambda-4)+2(\lambda-4)] = 0\\-\lambda(\lambda+2)(\lambda-4) = 0 \\\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4](https://tex.z-dn.net/?f=p%28%5Clambda%29%20%3D%20-%5Clambda%5E3%20%2B%202%5Clambda%5E2%20%2B%208%5Clambda%20%3D%200%5C%5C-%5Clambda%28%5Clambda%5E2-2%5Clambda-8%29%20%3D%200%5C%5C-%5Clambda%28%5Clambda%5E2-4%5Clambda%2B2%5Clambda-8%29%20%3D%200%5C%5C-%5Clambda%5B%28%5Clambda%28%5Clambda-4%29%2B2%28%5Clambda-4%29%5D%20%3D%200%5C%5C-%5Clambda%28%5Clambda%2B2%29%28%5Clambda-4%29%20%3D%200%20%5C%5C%5Clambda_1%20%3D%200%2C%20%5Clambda_2%20%3D%20-2%2C%20%5Clambda_3%3D%204)
We can arrange the eigen values as:
If the pyramid fits perfectly in a cube, this means that its base is a square and its height has the same value as the side of the square. Let x be the measure of the sides of the cube. The volume of the cube (Vc),
Vc = x³ ; 49 ft³ = x³ ; x = 49^(1/3)
The volume of the pyramid is,
Vp = (1/3)(x²)(x) = (1/3)(x³)
Substituting the known values,
Vp = (1/3)((49^(1/3))³ = 16 1/3 ft³
Thus, the volume of the pyramid is approximately 16.33 ft³.
Hey there Panda!
Question #1
(3.5*3.14 = 10.99 rounded would be 11) 11 is your answer.
Question #2
The circumference equals 21.99, but rounding it would be 22.00
Question #3
We divide 12/2 and from this we get 6. We doing (6*3.14) and then multiply by 2 and then divide by it's circumference and then we get it area. The answer that I got was 452.39, but from looking at your options, your correct answer would be 452.2 (ft)
Question #4
So, by looking at this weird shape, we see that the integer's are 8 by 5. When doing area, we often multiply. As we do this with these number's, we get 40.
We do 8/4 = 2; 5/2 = 2.5. So, from doing this, we get 90.2 (ft).
Question #5
With this last question, I believe that the answer may be C.) So, what I did was I did the radius x's 3.14 and got 6.28 then minus 10 and got around 3.
Hope this helps.
~Jurgen
