Answer:
pic one is rock cycle, pic 2 crystaline structure, and pic three and 4 are the same pictures as question 2
Step-by-step explanation:
<h3>
Answer: 375</h3>
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Work Shown:
a = 300 = first term
r = 60/300 = 0.2 = common ratio
We multiply each term by 0.2, aka 1/5, to get the next term.
Since -1 < r < 1 is true, we can use the infinite geometric sum formula below
S = a/(1-r)
S = 300/(1-0.2)
S = 300/0.8
S = 375
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As a sort of "check", we can add up partial sums like so
- 300+60 = 360
- 300+60+12 = 360+12 = 372
- 300+60+12+2.4 = 372+2.4 = 374.4
- 300+60+12+2.4+0.48 = 374.4+0.48 = 374.88
and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.
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Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.
Finding a common denominator between 10 and 12 to be 10*12=120, we can multiply 9/10 by 12/12 and 3/12 by 10/10 to get 108/120 and 30/120 respectively. Dividing the 2 (as we want to know how much 3/12 or 30/120 goes into 9/10 or 108/120), we get
(108/120)/(30/120)=(108/120)*(120/30)=(108/30)=3+18/30 (as 30 goes into 90 3 times and 108-90=18)
Answer:
<em>-11, -10, -9, -8, -7, -6 and -5 </em>
Step-by-step explanation:
Given the inequality expressions
2x+9<0 and x>-12
2x+9<0
2x< 0-9
2x < -9
x < -9/2
x < -4.5
Since x >-12
-12 < x
Combining both inequalities
-12 <x < 4.5
<em>The integers between the intervals are -11, -10, -9, -8, -7, -6 and -5 </em>
