Answer:
7.13 each
Step-by-step explanation:
70 - 13 = 57. Divide 57/8 and get your answer
(7.125 rounded is 7.13)
Total of 5 times = 48 + 48 + 49 + 46 + 64 = 255 mins
Goal:
Average = 53 mins
Total = 53 x 6 = 318 mins
6th ride = 318 - 255 = 63 mins
Answer: She needs to attain 63 mins for her 6th ride.
3(9 - 8x - 4x) + 8(3x + 4) = 11
3(9 - 12x) + 8(3x + 4) = 11
27 - 36x + 24x + 32 = 11
59 - 12x = 11
-12x = 11 - 59
-12x = -48
x = 4
hope this helps, God bless!
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.
Nice to know how long parallelogram is 72 meters :)