Brett bought three pairs of jeans and five polo shirts. the jeans that regularly sell for 79$ were 35% off and the polo shirts t
2 answers:
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The first term is 612.
The common ratio is 1.08 and
The recursive rule is
<u>Step-by-step explanation:</u>
the question to the problem is to write the values of the first term, common ratio, and expression for the recursive rule.
<u>The first term :</u>
In geometric sequence, the first term is given as .
⇒
Now, the geometric sequence follows as 612, 661, ........
<u>The common ratio (r) :</u>
It is the ratio between two consecutive numbers in the sequence.
Therefore, to determine the common ratio, you just divide the number from the number preceding it in the sequence.
⇒ r = 661 divided by 612
⇒ r = 1.08
<u>To find the recursive rule :</u>
A geometric series is of the form a,ar,ar2,ar3,ar4,ar5........
Here, first term and other terms are obtained by multiplying by r.
- Observe that each term is r times the previous term.
- Hence to get nth term we multiply (n−1)th term by r .
The recursive rule is of the form
This is called recursive formula for geometric sequence.
We know that r = 1.08 and = 612.
To find the second term , use the recursive rule
⇒
⇒
⇒
⇒
recall from the previous posting, 2⁸ = 256, so that's one way to represent it.
now, another way hmmm
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:
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
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:
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