#5) HELP WITH QUESTION!!!! MARKING BRAINLIEST!!! :)
1 answer:
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Answer:
a and b are perpendicular to each other, as are b and d, b and g
Step-by-step explanation:
To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.
We can find the angle between to vectors a and b from the following relation:
The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.
So
cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.
Now, for your exercise, let's compute the dot product between these vectors.
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a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0
So a and b are perpendicular to each other.
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a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5
a and c are not perpendicular to each other.
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a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7
So not perpendicular
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a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11
Not
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b.c = (1,1,4).(1,3,1) = 1+3+4 = 8
Not
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b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0
b.d = 0, so b and d are perpendicular to each other
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b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0
b.g = 0, perpendicular
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c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9
No
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c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5
No
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d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7
No
Answer:
The sum of the first 20 terms is -1440.
Step-by-step explanation:
We want to find the sum of the first 20 terms of the arithmetic sequence:
4, -4, -12, -20...
The sum of an arithmetic sequence is given by:
Where <em>k</em> is the number of terms, <em>a</em> is the initial term, and <em>x</em>_<em>k</em> is the last term.
Since we want to find the sum of the first 20 terms, <em>k</em> = 20.
Our initial term <em>a</em> is 4.
Our last term is also the 20th term as we want the sum of the first 20 terms.
To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:
Where <em>a</em> is the initial term, <em>d</em> is the common difference, and <em>n</em> is the <em>n</em>th term.
Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:
Then the last or 20th term is:
Therefore, the sum of the first 20 terms are:
Answer:
y = - 2x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (1, 4 ) and (x₂, y₂ ) = (2, 2 )
m = =
= - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 2 ) , then
2 = - 4 + c ⇒ c = 2 + 4 = 6
y = - 2x + 6 ← equation of line