B=cost per boquet
v=cost per vase
3b+5v=25.75
8b+2v=29.00
use eliminateion
divide 2nd equation by 2
4b+v=14.50
multiply it by -5 and add to other equation to eliminate v
-20b-5v=-72.5
<span><u>3b+5v=25.75 +</u></span><u />
-17b+0v=-46.75
-17b=-46.75
divide both sides by -17
b=2.75
a boquet costs $2.75
Answer:
I'm sorry what do you mean
We can use the formula for a parabola:
where
is the origin of the parabola and
is some constant scaling factor.
We are given that the center of the arch on the bridge is
. This is our origin. So our equation is:
Now we just need to find c. We can do this by plugging in one of the other points given:
So our final equation for the arch of the bridge is:
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:
the answer is 5 I think I hope