Answer:
Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
- The vertex is the point at which the graph changes direction as we go from left to right.
- Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
- Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
- Now the answers:
- Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so <em>minimum</em>
- vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so <em>minimum</em>
- vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is <em>maximum</em>
- Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is <em>maximum</em>
- vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is <em>minimum</em>
- vertex is (0.5,5) because it was getting big then changed and started getting smaller so <em>maximum</em>
Explanation:
A sequence is a list of numbers.
A <em>geometric</em> sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.
<u>Examples</u>
- 1, 2, 4, 8, ... common ratio is 2
- 27, 9, 3, 1, ... common ratio is 1/3
- 6, -24, 96, -384, ... common ratio is -4
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<u>General Term</u>
Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...
a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence
where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...
- a(n) = 2^(n -1)
- a(n) = 27×(1/3)^(n -1)
- a(n) = 6×(-4)^(n -1)
You can see that these formulas are exponential in nature.
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<u>Sum of Terms</u>
Another useful formula for geometric sequences is the formula for the sum of n terms.
S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence
When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...
S = a(1)/(1-r)
The answer is in the image. We need 3.625 gallons to fill the tank.
B. are parallel.
<span>Line m is drawn so that it is perpendicular to two distinct planes, Q and R. Therefore, planes Q and R are parallel.
Since it doesn't state that two planes intersect with each other, it is safe to assume that only line m is their connection. The planes are parallel with each other. </span>
