Using the scale 1/2 inch = 100 miles, figure out the number

Mathematics

1 answer:

Wittaler [7]2 years ago

5 0

Answer:

50 miles

Step-by-step explanation:

Multiply the given scale numbers by 1/2 to find your answer:

1/2 in = 100 mi

(1/2)(1/2 in) = (1/2)(100 mi) . . . . multiply the ratio values by 1/2

1/4 in = 50 mi

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If a=i+7j+k and b=i+11j+k, find a unit vector with positive first coordinate orthogonal to both a and

Scilla [17]

Take the cross product, then normalize the result.

$\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&7&1\\1&11&1\end{vmatrix}=-4\,\mathbf i+4\,\mathbf k$

This has norm

$\|\mathbf a\times\mathbf b\|=\sqrt{(-4)^2+4^2}=4\sqrt2$

and so a unit vector orthogonal to both given vectors is

$\dfrac{\mathbf a\times\mathbf b}{\|\mathbf a\times\mathbf b\|}=-\dfrac1{\sqrt2}\,\mathbf i+\dfrac1{\sqrt2}\,\mathbf k$

An equally correct answer would be the negative of this vector, since $\mathbf b\times\mathbf a=-\mathbf a\times\mathbf b$ .

5 0

3 years ago

15 points for someone who can answer & explain this to me thanks

iris [78.8K]

Answer:

see explanation

Step-by-step explanation:

Given

$\frac{9}{a^2+9a+20}$ , $\frac{7a}{a^2+11a+28}$