92.1-32.6 what's the answer
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:
Total number of puppies in the litter = 11
Step-by-step explanation:
Let the number of yellow puppies in the litter = y
And the number of black puppies in the litter = b
If there was one less black puppy, ratio of yellow to black puppies =
2(b - 1) = 3y
3y - 2b = -2 -----(1)
If there was one more black puppy, ratio of yellow puppies to black puppies =
2y = b + 1
2y - b = 1 -------(2)
Equation (1) - 2× equation (2)
(3y - 2b) - 2(2y - b) = -2 - 2
3y - 4y - 2b + 2b = -4
y = 4
From equation (1),
3×4 - 2b = -2
12 - 2b = -2
-2b = -14
b = 7
Total number of puppies in the litter = 7 + 4 = 11
A^2 + b^2 = c^2
base lines: home to first is a, first to second is b, home to second is c.
90^2 + 90^2 = c^2
or
...approximately
base lines: home to first is a, first to second is b, home to second is c.
90^2 + 90^2 = c^2
or
...approximately