A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand co
1 answer:
Let the amount of the first brand be x, and let the amount of the second brand be y.
0.09x + 0.14y = 240 * 0.13 .................(1)
x + y = 240 ..............(2)
y = 240 - x .......................(3)
Plugging the value for y from equation (3) into equation (1), we get:
...............(4)
Equation (4) simplifies to:
-0.05x = -2.4
giving the value for the required amount of 9% vinegar as 48 ml and the required amount of 14% vinegar as 240 - 48 = 192 ml.
0.09x + 0.14y = 240 * 0.13 .................(1)
x + y = 240 ..............(2)
y = 240 - x .......................(3)
Plugging the value for y from equation (3) into equation (1), we get:
Equation (4) simplifies to:
-0.05x = -2.4
giving the value for the required amount of 9% vinegar as 48 ml and the required amount of 14% vinegar as 240 - 48 = 192 ml.
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Answer:
a)
Since the dot product is not equal to zero then the two vectors are not orthogonal.
If we replace we got:
Since the angle between the two vectors is 180 degrees we can conclude that are parallel
b)
Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.
c)
Since the dot product is equal to zero then the two vectors are orthogonal.
Step-by-step explanation:
For each case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.
Part a
u=[-3,9,6], v=[4,-12,-8,]
The dot product on this case is:
Since the dot product is not equal to zero then the two vectors are not orthogonal.
Now we can calculate the magnitude of each vector like this:
And finally we can calculate the angle between the vectors like this:
And the angle is given by:
If we replace we got:
Since the angle between the two vectors is 180 degrees we can conclude that are parallel
Part b
u=[1,-1,2] v=[2,-1,1]
The dot product on this case is:
Since the dot product is not equal to zero then the two vectors are not orthogonal.
Now we can calculate the magnitude of each vector like this:
And finally we can calculate the angle between the vectors like this:
And the angle is given by:
If we replace we got:
Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.
Part c
u=[a,b,c] v=[-b,a,0]
The dot product on this case is:
Since the dot product is equal to zero then the two vectors are orthogonal.