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:
f(x)=sqrt(x-5) of f(x)=(x-5)^(1/2)
Step-by-step explanation:
Plug in f(x) for x
x=f(x)^2+5
x-5=f(x)^2
f(x)=sqrt(x-5)
28 cell phone cases in all.
6 of the 28 cases are fabric.
6/28 simplified to 3/14
So the answer to your question would be 3/14
Hope this helps! :)
<span>Simplifying
6x = 2x + 40
Reorder the terms:
6x = 40 + 2x
Solving
6x = 40 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
6x + -2x = 40 + 2x + -2x
Combine like terms: 6x + -2x = 4x
4x = 40 + 2x + -2x
Combine like terms: 2x + -2x = 0
4x = 40 + 0
4x = 40
Divide each side by '4'.
x = 10
so the answer is x = 10</span>
Answer: $804
Step-by-step explanation: 1. Set the equation to x/1200=67/100 2. Cross-multiply so you get 100x=80,400 3. Now divide both sides by 100 to get x=804 which is your final answer 4. Put the dollar sign in front to denote units.