Adding 
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.
Consider the arithmetic sequence:
2 answers:
Answer:
<em>Answer: D</em>
Step-by-step explanation:
<u>Arithmetic Sequences </u>
The arithmetic sequences are those where any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the arithmetic sequence:
10, 12, 14, 16, ...
Where a1=10 and
r = 12 - 10 = 2
Thus the general term is:
Operating:
Answer: D
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Answer:
c. 6.2i - 4.2j
Step-by-step explanation:
The vector projection when the angle θ not known can be calculated using the following property of the dot product:
Where the dot product of two vectors is given by:
And the magnitude of a vector is given by:
Using the previous definition, let's calculate the projection of w onto u:
First let's calculate the dot product between w and u:
Now let's find the magnitude of u:
So:
Therefore:
Answer:
y = -27
Step-by-step explanation:
- Multiply the entire equation by 6
2*(y + 1) - (3y - 1 ) = 30
- Multiply (y +1) by 2 and (3y - 1) by (-1)
2y + 2 - 3y + 1 = 30
- Isolate y term by taking the constant term to RHS
2y - 3y = 30 - 2 - 1
- Combine like terms
-y = 27
y = -27