Find a recursive formula for the sequence: 3, -5, 11, -21
1 answer:
The correct option is the last:
In fact, every term in the sequence is one more than twice the opposite of the previous one:
We start with 3. Twice its opposite is -6. Plus one, we get -5.
We start with -5. Twice its opposite is 10. Plus one, we get 11.
We start with 11. Twice its opposite is -22. Plus one, we get -21.
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Answer:
Step-by-step explanation:
Let
Subbing in:
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
Group together in groups of 2:
Now factor out what's common within each set of parenthesis:
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
Remember that
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring gives us that x = 1 and -1. The other set is a bit more tricky. If
then
and
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
±
which will simplify down to
±
Those are the 4 solutions to the quartic equation.
Answer:
Each inhalation has 750 micrograms of metaproterenol sulfate.
Step-by-step explanation:
First step: How many miligrams are there in each inhalation.This can be solved by a rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
In this step, our measures are:
- The number of inhalations.
- The quantity inhaled.
As the number of inhalations increases, so does the quantity inhaled. This means that this is a direct rule of problem.
300 inhalations contains 225mg of metaproterenol sulfate. How many miligrams are in a inhalation?
300 inhalations - 225mg
1 inhalation - xmg
300x = 225
x = 0.75mg
Each inhalation has 0.75mg of metaproterenol sulfate.
Final step: Conversion of 0.75mg to micrograms.
Each mg has 1000 micrograms. So:
1mg - 1000 micrograms
0.75mg - x micrograms
x = 1000*0.75
x = 750 micrograms
Each inhalation has 750 micrograms of metaproterenol sulfate.