Im not sure how to answer this question.

Mathematics

1 answer:

bonufazy [111]3 years ago

3 0

9514 1404 393

Answer:

(-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k

Step-by-step explanation:

To answer this question, you need to know two things:

1) the direction of vector v

2) the magnitude of vector u

direction of v

A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.

The unit vector in the v direction is ...

v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13

magnitude of u

The magnitude of vector u is ...

|u| = √(5² +(-2)² +3²) = √38

Then the desired vector is ...

(2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k

_____

Additional comment

We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.

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The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27

Naddik [55]

ANSWER
$3\pi sq.\: in.$

EXPLANATION

Let R be the radius of the bigger circle and r, be the radius of the smaller circle.

Then their ratio is given as,

$R:r=3:1$

We can rewrite it as fractions to get,

$\frac{R}{r} = \frac{3}{1}$

We make R the subject to get,

$R = 3r$

The area of the bigger circle can be found using the formula,

$Area=\pi {r}^{2}$

This implies that,

$Area=\pi ({3r})^{2}$

$Area=9\pi {r}^{2}$

But it was given in the question that, the area of the bigger circle is 27π.

$27\pi=9\pi {r}^{2}$

We divide through by 9π to get,

$3 = {r}^{2}$

This means that,
$r = \sqrt{3}$

The area of the smaller circle is therefore

$= \pi {( \sqrt{3}) }^{2}$

$= 3\pi$