Answer:
B
Step-by-step explanation:
So I won't tell you the answer but I will give you a clue. do 120 times 16 - 8 + 6
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:
Answer:
t = 3.8 s
option 3
Step-by-step explanation:
For this case we have the following equation:
h (t) = at ^ 2 + v * t + h0
Substituting values we have:
h (t) = - 16 * t ^ 2 + 60 * t + 3
We equate the equation to zero:
-16 * t ^ 2 + 60 * t + 3 = 0
We look for the roots of the polynomial:
t1 = -0.04935053979258153
t2 = 3.7993505397925817
We are left with the positive root and round:
t2 = 3.8 s