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Two forces of equal magnitude are acting simultaneously on a particle at an angle of separation between them 120 degrees.Find the resultant vector.I want to know about the concepts of logarithm. I have seen some practise question on the dashboard but they are of high level. And even still it is not clear to me that how we can find the values in a question through log, and please also provide me its table. Because it is quite difficult to understand and solve the practice question of logarithm.

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Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a

v = dx / dt = 3t + 2

Determine the distance (x) travelled by the body in time (t) using the method of integration.

^{1/2}+tan1) (31/2+tan2) (31/2+tan3) ..... (31/2+tan29)=Given that and

A^{2}+B^{2}=R^{2}then angle between and will be?^{2}...integrate the following:

∫2xydx + ∫x

^{2}dyi want a brief explaination

e

^{x/log x}36. To a person going east in a car with a velocity of 25 km.p.h. a train appears to move towards north with a velocity of $25\sqrt{3}$ km.p.h. What is the actual velocity and direction of motion of the train ?

[Ans. 50 km.p.h. $30\xb0$ east of north ]

37. A ship A is travelling at 12 km.p.h. in still water in a direction due east. A man on it observe another ship B due north of him which appears to moving directly towards him at a speed of 15 km.p.h. Find the actual speed of B and its direction of motion.

$\left[Ans.19.21km.p.h.;38\xb040\text{'}westofnorth\right]$

38. A cyclist moves horizontally at 10 km.p.h. There is no wind and rain drops appear to him to fall at an angle of $10\xb0$ to the vertical. Find the speed of the rain drops. [Ans. 56.71 km.p.h.]

39. T a person going westward with a velocity of 6 km.p.h.rain appears to fall vertically downward with a velocity of 8 km.p.h. Find the speed of the rain drops.

$[Ans.10km.p.h.,36\xb0-52\text{'}westofSouth]$

^{2}a+sin^{2}b=sinc then possible values of c are_{a}bc + 1, y= log_{b}ca + 1, z = log_{c}ab + 1, prove that xyz= xy+yz+zx