Answer:
120.5 is your answer
Step-by-step explanation:
We know that
To generate the equation of the parabola, we start with this equation
(x -h)²= 4p * (y -k)
where "h" and "k" are the (x, y) values of the vertex.
"p" is the difference between the focus "y-value" and the vertex y-value.
p = (6-5) = 1
Now we put these numbers into the equation:
(x -h)² = 4p * (y -k)
(x +2)² = 4 * 1 * (y -5)
(x +2)² = 4*(y -5)
the answer is
(x +2)² = 4*(y -5)
Answer:
sure?
Step-by-step explanation:
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.