Answer:
12 hours per week
Step-by-step explanation:
1. Find how many hours she worked to make $3,000 (36x10=360 hours)
2. divide 360 hours by 30 weeks
she would need to work 12 hours per week to make $3,000
At 1/8 of a gallon you can mow 2 1/4 so for 1 gallon just multiply 2 1/4 by 8
16+2 is 18
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:
y=2x+2
Step-by-step explanation:
The * stands for multiplication.
0*2+2=2
3*2+2=8
6*2+2=14
All of these statements are true, so this should be the correct answer.
Answer:
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Step-by-step explanation:
common sense