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Mathematics

2 answers:

Lorico [155]3 years ago

8 0

I think the answer is n-20- first choice.

Varvara68 [4.7K]3 years ago

4 0

ANSWER

n-20

EXPLANATION

The terms of the sequence are:

-19,-18,-17,-16,-15,...

The first term of the sequence is

a=-19 and the common difference is d=-18--19=1

The rule is given by:

f(n)=a+d(n-1)

f(n)=-19+1(n-1)

f(n)=-19+n-1

f(n)=n-20.

Therefore the rule for the given sequence is n-20.

The first option is correct.

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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

vivado [14]

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