Answer:
50.7202
Step-by-step explanation:
(500ml+1000ml) / (29.574 ml per ounce) = 50.72 US Fluid Ounces
Answer:
GI or HJ
Step-by-step explanation:
Diagonals connect non-adjacent vertices.
That is, the diagonal with G as an endpoint will not connect to vertices H or J, but will connect to vertex I. Likewise the diagonal with H as one end will have J as the other end. A quadrilateral has only two (2) diagonals. Of course, each can be named two ways:
GI or IG
HJ or JH
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.
<span>A cross section parallel to any side other than the base that has a shape of a trapezoid.</span>
Answer:
y = 16 + 3/11
x = -76/11
Step-by-step explanation:
2y - 5x = -2
3y + 2x = 35
__________
(2y - 5x = -2)*3
(3y + 2x = 35)*2
__________
6y - 15x = -6
6y +4x = 70
__________
(6y - 15x = -6) - (6y +4x = 70)
15x - 4x = -6 -70
__________
11x = -76
x = -76/11
__________
3y +2(-76/11) = 35
3y = 35 + 152/11
3y = 13 + 35 + 9/11
3y = 48 + 9/ 11
y = 16 + 3/11