Which expressions can be used to find the coordinates of the midpoint of PQ with endpoints P(3, –1) and Q(–7, –6)? Check all tha
2 answers:
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Answer:
The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables
= -3072uv
Step-by-step explanation:
<u>Step :-(i)</u>
Given x = 1 6 (u + v) …(i)
Differentiating equation (i) partially with respective to 'u'
Differentiating equation (i) partially with respective to 'v'
Differentiating equation (i) partially with respective to 'w'
Given y = 1 6 (u − v) …(ii)
Differentiating equation (ii) partially with respective to 'u'
Differentiating equation (ii) partially with respective to 'v'
Differentiating equation (ii) partially with respective to 'w'
Given z = 6uvw ..(iii)
Differentiating equation (iii) partially with respective to 'u'
Differentiating equation (iii) partially with respective to 'v'
Differentiating equation (iii) partially with respective to 'w'
<u>Step :-(ii)</u>
The Jacobian ∂(x, y, z)/ ∂(u, v, w) =
Determinant 16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv
= -3072uv
<u>Final answer</u>:-
The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv
Answer: ∠B = 50°
∠BCD = 40°
<u>Step-by-step explanation:</u>
ACB is a right triangle where ∠A = 40° and ∠C = 90°.
Use the Triangle Sum Theorem for ΔABC to find ∠B:
∠A + ∠B + ∠C = 180°
40° + ∠B + 90° = 180°
∠B + 130° = 180°
∠B = 50°
BCD is a right triangle where ∠B = 50° and ∠D = 90°.
Use the Triangle Sum Theorem for ΔBCD to find ∠C:
∠B + ∠C + ∠D = 180°
50° + ∠C + 90° = 180°
∠C + 140° = 180°
∠C = 40°
