Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
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Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
Answer:
Therefore the given vectors are orthogonal for b = 0,±3.
Step-by-step explanation:
If 
and 
are two vectors orthogonal, then the dot product of and will be zero.
i.e 
If 
and 
Given two vectors are (-18,b,9) and (b,b²,b)
Let
and
Therefore,
=(-18).b+b.b²+9.b
= -18b+b³+9b
= b³-9b
Since 
and 
are orthogonal. Then = 0.
Therefore,
b³-9b= 0
⇒b(b²-9)=0
⇒b =0 or b²=9
⇒b=0 or b =±3
Therefore the given vectors are orthogonal for b = 0,±3.
Answer:
your answer will be 24.2
Step-by-step explanation:
Answer:
b should be the answer
Step-by-step explanation:
