Calculate the diameter of Circle J if the circumference is 100.48 centimeters

Mathematics

1 answer:

Svet_ta [14]4 years ago

5 0

Answer:

its 100.43 centimeters

Step-by-step explanation:

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the measure of an angle is 12 less than twice the measure of its supplement. what is the measure of the angle

Alex

Answer:

Two angles are said to be supplementary if they add up to 180 degrees. So the supplement of an angle is obtained by subtracting it from 180. i.e., if x is an angle, its supplement is 180−x

7 0

3 years ago

For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?

DaniilM [7]

<h2>Answer:</h2>

The values of x for which the given vectors are basis for R³ is:

$x\neq 1$

<h2>Step-by-step explanation:</h2>

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

$\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]$

Now, the determinant of this matrix is:

$\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1$