Answer:
Step-by-step explanation:
As I mentioned earlier with a single side (line), rotations do not change the size of something. Only dilations do that. This goes for both lines AND shapes.
However, if the question said she dilated the piece, then yes, the length in inches would be different. However, rotation just changes the position and nothing happens to the length.
Hope this helped!
-8 = -7x-1
bring -1 to the other side as we are isolating for x so it will be
-7 = -7x then divide -7 from each side
-7/-7 = (-7/-7)x
1 = x
Answer is f(1)= -8
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
Answer as an improper fraction = 13/8
This is equivalent to the mixed number 1 & 5/8
In decimal form, 13/8 = 1.625
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Work Shown:
3/4 = (3/4)*(2/2)
3/4 = (3*2)/(4*2)
3/4 = 6/8
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7/8 + 3/4
7/8 + 6/8
(7+6)/8
13/8
So 7/8 + 3/4 = 13/8
