Option C: ![r = \sqrt[3]{\frac{3V}{4\pi} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%20%7D)
is the right answer
Step-by-step explanation:
Given formula for volume of a sphere is:
We have to make r the subject of the formula
Multiplying equation by 3/4
Dividing both sides by pi
Taking cube root on both sides
![\sqrt[3]{\frac{3V}{4\pi} } = \sqrt[3]{r^3} \\ r = \sqrt[3]{\frac{3V}{4\pi} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%20%7D%20%3D%20%5Csqrt%5B3%5D%7Br%5E3%7D%20%5C%5C%20r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%20%7D)
Hence,
Option C: is the right answer
Keywords: Volume, Sphere
Learn more about volume at:
#LearnwithBrainly
Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area = ![\int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx](https://tex.z-dn.net/?f=%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5Bf%28x%29-g%28x%29%5Ddx%3D%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5B6x%5E%7B2%7D-%28x%5E%7B2%7D%2B9%29%5Ddx)
= 
= ![[\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7Dx%5E%7B3%7D-9x%5D_%7B-1.34%7D%5E%7B1.34%7D)
= ![[\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7D%28-1.34%29%5E%7B3%7D-9%28-1.34%29-%5Cfrac%7B5%7D%7B3%7D%281.34%29%5E%7B3%7D%2B9%281.34%29%5D)
= ![[-4.01+12.06-4.01+12.06]](https://tex.z-dn.net/?f=%5B-4.01%2B12.06-4.01%2B12.06%5D)
= 16.1 unit²
4 because if u where to fold it
Answer: 142°
Step-by-step explanation:
∡BAC= 38°
∡BAN= 180°-38° = 142°
Answer:
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Step-by-step explanation:
It is given that the coefficient of the matrix of a linear equation has a pivot position in every row.
It is provided by the Existence and Uniqueness theorem that linear system is said to be consistent when only the column in the rightmost of the matrix which is augmented is not a pivot column.
When the linear system is considered consistent, then every solution set consists of either unique solution where there will be no any variables which are free or infinitely many solutions, when there is at least one free variable. This explains why the system is consistent.
For any m x n augmented matrix of any system, if its co-efficient matrix has a pivot position in every row, then there will never be a row of the form [0 .... 0 b].
