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Darshan M.

Problem-Solver & Math Educator!

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Trigonometry

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Question:

Solve the trigonometric equation given by cos(2x) cos(x) - sin(2x) sin(x) = 0 for 0 <= x <= 2 pi

Darshan M.

Answer:

Given identity is of Cos(a-b) So, Cos(2x-x)=0 Cosx=0 x=(2n+1)pi/2 n=0; x=pi/2 n=1; x=3pi/2

Pre-Algebra

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Question:

The Rooney family drives to Pittsburg at 60 mph and returns by a road 10 miles shorter at 65 mph. The return trip takes 30 minutes less. How long is each road?

Darshan M.

Answer:

Let to Going trip distance be d miles & time taken is t hr so, d=60t . . . .(1) Return journey distance is d-10 Time taken is t-0.5 So, d-10=(65)(t-0.5) . . . . (2) Solving 1 & 2 you will get t=4.5hr. d=270miles. Retuen distance = 260miles

Calculus

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Question:

Find if x^3/3 -x^2 +2x +Sinx is one-one function ?

Darshan M.

Answer:

Differentiate the above function ; x^2 -2x +2 +Cosx Find the minima of the quadratic function (it will come out as 1) Next term will be Cosx whose Minima is -1. So the minima of overall funtion is 0. It means that curve is always greater than or equal to zero. It means that graph is increasing. And every increasing graph is one-one function!!

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