Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
P+Q+R=180
80+70+Q=180
Q=30
PQR = angle Q
Answer:
- d, series and sequence diverge
- d, geometric/divergent
- c, e (geometric, |r|<1)
Step-by-step explanation:
<h3>1.</h3>
The sequence terms have a common difference of -5/8. That make it a non-trivial arithmetic sequence, so it diverges.
The series is the sum of terms of the sequence. Any non-trivial arithmetic series diverges.
(A "trivial" arithmetic series has a first term of 0 and a common difference of 0. It is the only kind of <em>arithmetic</em> series that doesn't diverge.)
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<h3>2.</h3>
The terms of the series have a common ratio of -2. That makes it a geometric series. The ratio magnitude is greater than 1, so the series diverges.
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<h3>3.</h3>
A sequence will converge only if the terms have a common difference of 0 or a common ratio with a magnitude less than 1. Of the offered choices, only C and E will converge:
c. geometric, r = 3/5
e. geometric, r = -1/6
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<em>Additional comment</em>
The convergence criteria stated for problem 3 applies only to arithmetic and geometric sequences. There are many other kinds of sequences that converge, but these are the kinds being considered in this problem set.
Answer:
70 m × 10 m
Step-by-step explanation:
At a geological site, Judith is digging for sandstone. To mark off a rectangular area, Judith has 160 meters of rope and 4 stakes.
We have to choose from the given dimensions of rectangles where Judith can use all the rope she has to cover the rectangular area.
It is clear from the given conditions that the perimeter of the rectangular area should be exactly 160 meters.
So, the required dimensions of the rectangle are 70 m × 10 m, because the perimeter of this rectangle is exactly 160 meters. (Answer)
