PLEASE HELP!!!! Find the solution to the inequality
1 answer:
You might be interested in
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.
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 distance between E and F is 5 units
Step-by-step explanation:
<em>E</em><em> </em><em>and</em><em> </em><em>F</em><em> </em><em>are</em><em> </em><em>share</em><em> </em><em>the</em><em> </em><em>same</em><em> </em><em>y-coordinates</em><em>.</em><em> </em><em>So</em><em> </em><em>for</em><em> </em><em>this</em><em> </em><em>part</em><em> </em><em>it</em><em> </em><em>is</em><em> </em><em>okay</em><em> </em><em>to not</em><em> </em><em>use</em><em> </em><em>the</em><em> </em><em>distance</em><em> </em><em>formula</em><em>.</em><em> </em>
<em>So</em><em> </em><em>you</em><em> </em><em>will</em><em> </em><em>be</em><em> </em><em>having</em><em>:</em>
<em>E</em><em> </em><em>(</em><em>5</em><em>,</em><em>8</em><em>)</em><em> </em><em>and</em><em> </em><em>F</em><em> </em><em>(</em><em>5</em><em>,</em><em>3</em><em>)</em>
<em>EF</em><em> </em><em>=</em><em> </em><em>8-3</em><em>=</em><em>5</em>
<em>OR</em><em> </em>
<em>YOU</em><em> </em><em>CAN</em><em> </em><em>USE</em><em> </em><em>THE</em><em> </em><em>DISTANCE</em><em> </em><em>FORMULA</em><em> </em><em>AS</em><em> </em><em>INDICAYED</em><em> </em><em>IN</em><em> </em><em>THE</em><em> </em><em>PICTURE</em><em>.</em>
<em>Hopefully</em><em> </em><em>the picture</em><em> </em><em>is clear and understandable</em><em> </em><em>and</em><em> </em><em>younger</em><em> </em><em>the</em><em> </em><em>explanation</em><em>.</em>
