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given <BCA =<DCE

<B and < Dareright angles

C is the midpoint of BD

prove BA=DE

<B and < Dareright angles

C is the midpoint of BD

prove BA=DE

In the diagram below of ΔABC , AB ≅ AC , m∠A = 3x , and m∠B = x + 20.

What is the value of x?

What is the value of x?

Q. Which of the following curves are regular?

(i) γ(t) = (cos^2 t, sin^2 t) for -∞<t<∞

(ii) γ(t) = (cos^2 t, sin^2 t) for 0<t<π/2

(iii) γ(t) = (t, cosh t) for -∞<t<∞

Find unit speed reparametrisation of regular curve(s).

(i) γ(t) = (cos^2 t, sin^2 t) for -∞<t<∞

(ii) γ(t) = (cos^2 t, sin^2 t) for 0<t<π/2

(iii) γ(t) = (t, cosh t) for -∞<t<∞

Find unit speed reparametrisation of regular curve(s).

Q. Show that the following curves are unit–speed:

(i) γ(t) = (1/3 〖(1+t)〗^(3/2),1/3 〖(1-t)〗^(3/2),t/√2 )

(ii) γ(t) = (4/5 cost,1-sint,-3/5 cost)

(i) γ(t) = (1/3 〖(1+t)〗^(3/2),1/3 〖(1-t)〗^(3/2),t/√2 )

(ii) γ(t) = (4/5 cost,1-sint,-3/5 cost)

Q. Calculate the arc–length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).

Q. Calculate the arc length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).

Q. Calculate the tangent vectors of the following curves:

(i) γ(t) = (cos^2 t, sin^2 t)

(ii) γ(t) = (e^t, t^2)

(i) γ(t) = (cos^2 t, sin^2 t)

(ii) γ(t) = (e^t, t^2)

Q. Find the cartesian equations of following parametrized curves:

(i) γ(t) = (cos^2 t, sin^2 t)

(ii) γ(t) = (e^t, t^2)

(i) γ(t) = (cos^2 t, sin^2 t)

(ii) γ(t) = (e^t, t^2)

Q.Find the length of the astroid x=acos^3 t, y=asin^3 t, [0, 2π].

Q. Find parametrisations of following level curves

Y^2-x^2=1, x^2/4+y^2/9 =1

Y^2-x^2=1, x^2/4+y^2/9 =1