Answer:
Reflection
Step-by-step explanation:
Figure A' is the reflection of A as it is reflected from A'
Answer:
x=-10
Step-by-step explanation:
4.5(8-x)+36=102-2.5(3x+24) first you multiply 10 to both sides
4.5(8-x)x10+36x10=102x10-2.5(3x+24)x10
Then you have to refine the equation
45(8-x)+360=1020-25(3x+24)
Then you expand it
45(8-x)+360
=360-45x+360
Simplify
360-45x+360 -45x+720
Expand it one more time
-45x+720=-75x+420
Subtract 720 from each side
-45x+720-720=-75x+420-720
Simplify
-45x=-75x-300
Add 75x to both sides
-45x+75x=-75x-300+75x
Simplify
Divide both sides by 30
30x/30=-300/30
Then you get -10
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.
Index of Multiplication
Hope this Helps:)