Hi there can anyone help me out with this please please please

Mathematics

1 answer:

ivolga24 [154]3 years ago

3 0

So how you wold do this problem, would be to count how many numbers fit into each category and type in that value in the according box.
So for 35-44 you would have 1 because only 1 of the values is between 35 and 44.
For 45-54 you would have 19 because there are 19 values that fit into that category.
Just continue that trend for the rest of the categories and you will have your answer!

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3 years ago

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .