The foci of a hyperbola are the same as those of the ellipse with equation $9 x^2+16 y^2=144$.
If the length of the transverse axis of this hyperbola is $2 \cos \alpha$, then its equation is:
$$ \frac{x^2}{7-\cos ^2 \alpha}-\frac{y^2}{\cos ^2 \alpha}=1 $$
$$ \frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{7-\cos ^2 \alpha}=1 $$
$$ \frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{7+\cos ^2 \alpha}=1 $$
$$ \frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{5-\cos ^2 \alpha}=1 $$
Suppose 'a' and 'b' are non-zero constants satisfying the following system of equations $\boldsymbol{a} \sin ^3 x+\boldsymbol{b} \cos ^3 x=\sin x \cos x$ and $\mathbf{a} \sin x-\boldsymbol{b} \cos x=0$, then $\mathbf{2}\left(\boldsymbol{a}^6+\boldsymbol{b}^6\right)-\mathbf{3}\left(\boldsymbol{a}^4+\boldsymbol{b}^4\right)+\mathbf{1}=$
1
-1
0
$2 \sin ^2 x$
The variance of a set of 20 observations is 16 . If 7 is added to each observation, and then $\mathbf{5}$ is subtracted from each resulting observation, what will be the new standard deviation?
4
9
18
2
$$ \text { If }(\vec{a}+\vec{b}) \perp \vec{b} \text { and }(\vec{a}+2 \vec{b}) \perp \vec{a} \text {, then } $$
$$ 2|\vec{a}|=|\vec{b}| $$
$$ |\vec{a}|=2|\vec{b}| $$
$$ |\vec{a}|=|\vec{b}| $$
$$ |\vec{a}|=\sqrt{2}|\vec{b}| $$
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