maths homework help

[tanupriya]

plz help me with these questions given in the attachment!

thankyou

Question 1: Find all the sixth roots of (12+5i).


Question 2:

a) Find the equation of the line joining the points
(?7, 6, ? 3) and (7, ? 6, 3).
b) Find the equation of the sphere, which contains the circle
x[sup:10p03pyq]2[/sup:10p03pyq] + y[sup:10p03pyq]2[/sup:10p03pyq] + z[sup:10p03pyq]2[/sup:10p03pyq] = 18 , 3x + 3y + 3z = 11 and passes through the origin.

Question 3:

a) Find the area bounded by the x-axis, the curve y = e[sup:10p03pyq]2x[/sup:10p03pyq] and the ordinates x = 2 and x = 3.

b) Prove that tan[sup:10p03pyq]-1[/sup:10p03pyq] x < x for all x > 0
(Using mean value theorem on {o,x} for tan-1x)

Question 4:
Find the area of the region included between the circle:
x[sup:10p03pyq]2[/sup:10p03pyq] + y[sup:10p03pyq]2[/sup:10p03pyq] + 2x + 10y + 27 = 0
and the parabola
y[sup:10p03pyq]2[/sup:10p03pyq] + 10y – x + 23 = 0




Q5
Prove the following inequalities:
(i) tan[sup:10p03pyq]-1[/sup:10p03pyq] x<x for all positive x.
(ii) e[sup:10p03pyq]x[/sup:10p03pyq]- e[sup:10p03pyq]-x[/sup:10p03pyq] >= 2x for all x > 0.

 

[Deleted member 4993]

plz help me with these questions given in the attachment!

thankyou

Question 1: Find all the sixth roots of (12+5i).


Question 2:

a) Find the equation of the line joining the points
(?7, 6, ? 3) and (7, ? 6, 3).
b) Find the equation of the sphere, which contains the circle
x[sup:r60541h3]2[/sup:r60541h3] + y[sup:r60541h3]2[/sup:r60541h3] + z[sup:r60541h3]2[/sup:r60541h3] = 18 , 3x + 3y + 3z = 11 and passes through the origin.

Question 3:

a) Find the area bounded by the x-axis, the curve y = e[sup:r60541h3]2x[/sup:r60541h3] and the ordinates x = 2 and x = 3.

b) Prove that tan[sup:r60541h3]-1[/sup:r60541h3] x < x for all x > 0
(Using mean value theorem on {o,x} for tan-1x)

Question 4:
Find the area of the region included between the circle:
x[sup:r60541h3]2[/sup:r60541h3] + y[sup:r60541h3]2[/sup:r60541h3] + 2x + 10y + 27 = 0
and the parabola
y[sup:r60541h3]2[/sup:r60541h3] + 10y – x + 23 = 0




Q5
Prove the following inequalities:
(i) tan[sup:r60541h3]-1[/sup:r60541h3] x<x for all positive x.
(ii) e[sup:r60541h3]x[/sup:r60541h3]- e[sup:r60541h3]-x[/sup:r60541h3] >= 2x for all x > 0.

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