Answer:
(4, -2) (see attached)
Step-by-step explanation:
Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.
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<h3>vector components</h3>
The components of the vectors are ...
u = (1, -2)
v = (-6, -6)
Then the components of the vector sum are ...
2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)
2u -1/3v = (4, -2)
<h3>graphically</h3>
The sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.
One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.
The resultant is in red in the attachment.
To do this problem you would first need to factor out a variable, which in this case I would want to do the first equation because it is isolated. Now the equations would look like this:
x = -2y - 1
4x - 4y = 20
Since we know that x is now equal to -2y - 1 we can plug it in to the x value in the second equation:
4 (-2y -1) - 4y = 20
-8y -4 - 4y
-12y - 4 = 20
-12y = 24
y = -2
Now that we know the y value plug the y value to one equation to find the x, I will be using the first equation
x + 2(-2) = -1
x - 4 = -1
x = 3
Solutions:
y = -2
x = 3
Answer:
The correct options are;
Answer to A1 is D
Answer to A2 is D
Answer to A3 is D
Answer to A4 is D
Answer to A5 is D
Answer to A6 is D
Answer to A7 is D
Answer to A8 is D
Answer to A9 is D
Answer to B1 is I
Answer to B2 is I
Answer to B3 is I
Answer to B4 is I
Answer to B5 is I
Answer to B6 is I
Step-by-step explanation:
The given function is f(x) = 9·x² + 54·x - 66
The extremum of the function are found as follows;
d(f(x))/dx = 0 = d(9·x² + 54·x - 66)/dx = 18·x + 54
∴ 18·x + 54 = 0 at the maximum or minimum points
x = -54/18 = -3
Given that d²(f(x))/dx² = 18 > 0. x = -3 is a minimum point
Given that the function is a quadratic function, we have;
1) Points to the left of x = -3 are decreasing
2) Points to the right of x = -3 are increasing.
Y-int . . . x=0 . . . y-3 = 3 (0+1) . . . y-3 = 3 . . y=6. . . . . . . X-int .. y=0 .. 0-3=3 (x+1) .. -3=3x+3 ... -6=3x ...x=-2
Answer:
V= 7,241.1
Step-by-step explanation:
V = 4/3 × π × r^3
V = 4/3 × 22/7 × 1,728
V = 88/21 × 1,728
V = 4.190 × 1,728
V= 7,241.1
