What is 30% of 10/16

Mathematics

2 answers:

BartSMP [9]3 years ago

8 0

Answer:

3/60

Step-by-step explanation:

Reduce the numbers
Reduce the fraction
Then multiple the fraction

Vanyuwa [196]3 years ago

3 0

Answer; 30% of 10/16 is

0.1875

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Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

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Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>

Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j