Lucy's final exam has true/false questions, worth 2 points each, and multiple choice questions, worth 3 points each. Let x be th
2 answers:
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Solution :
We have been given a parametric curve :
x = sin t , y = cos t , 0 < t < π
In order to determine concavity of the given parametric curve, we need to evaluate its second derivative first.
Therefore,
Taking double derivatives of the above equation:
For the concave up, we have
∴
For the concave down, we have
Answer:
The solution of the Given matrix
( x₁ , x ₂ ) = ( - 5 , 4 )
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given equations are x₁+4 x₂ = 11 ...(i)
2 x₁ + 7 x₂= 18 ...(ii)
The matrix form
A X = B
<u>Step(ii):-</u>
The Augmented Matrix form is
Apply Row operations, R₂ → R₂-2 R₁
The matrix form
The equations are
x₁ + 4 x₂ = 11 ...(a)
- x ₂ = - 4
x ₂ = 4
Substitute x ₂ = 4 in equation (a)
x₁ + 4 x₂ = 11
x₁ = 11 - 16
x₁ = -5
<u>Final answer</u>:-
The solution of the Given matrix
( x₁ , x ₂ ) = ( - 5 , 4 )