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What is the LCM of 8 and 8? The LCM of 8 and 8 is 8.Nikhi/Neha
The Ganga is not merely a river for all the Indians and more particularly to the Hindus, but it is the lifeline of India and the physical and spiritual nourisher of crores of its people. It is a symbol of India’s great heritage, ancient traditions, cultures, songs and stories. We can’t think of India without the Ganga and the Himalayas. Unfortunately, the sacred Ganga has become one of the most polluted rivers of the world in recent years. Fortunately, the Modi government has shown its commitment to clean and rejuvenate the Ganga. Uma Bharti heads a specially created ministry for cleaning the holy river. Cleaning the Ganga will be an unprecedented national social effort. What makes the Ganga a heavily polluted river? Various factors and causes contribute to make the river what it is. The worst criminals are more than one thousand industries that discharge their toxic wastes into the river. The government will have to take strict measures to treat solid and liquid discharges making them totally pollution free. The sewerage infrastructure will have to be exteftded and updated. The people residing on the banks will be involved and enlightened. Burning and throwing of dead bodies into the river must be stopped. Open defecation on the banks will have to be stopped.The bumper car ride, Rue le Dodge, opened at Six Flags in 1976. A bumper car with a small child, the total mass of 855 kg, moving 3.0 m/s slams into another bumper car with a heavier couple, the total mass of 995 kg, moving -3.0 m/s. The small child bounces back and ends up moving in the opposite direction with a speed of -3.4m/s.
1) What type of collision is this?
2) How fast does the couple move after the
collision?
Final Mass 1 -
Final Velocity 1
Final Mass 2 -
Final Velocity 2 -In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangleSymptoms
Feeling sad or down.
Confused thinking or reduced ability to concentrate.
Excessive fears or worries, or extreme feelings of guilt.
Extreme mood changes of highs and lows.
Withdrawal from friends and activities.
Significant tiredness, low energy or problems sleeping.
Answer:
Given, u = tan-¹ (x²+y²/x+y)
=> tan u = x²+y²/ (x+y)
=> sec²u du/dx = 2x(x+y) - (x²+y²) /(x+y)².........(1)
and sec²u du/dy = 2y(x+y) - (x²+y²)/(x+y)² .......(2)
Multiplying x with Equation (1) and y to equations (2)
Therefore, x sec²u du/dx = x³+2x²y-xy²/(x+y)²..(3)
and y sec²u du/dy = y³+2x²y-x²y/(x+y)² .......(4)
Adding equations (3) and (4) we get :-
sec²u (x du/dx + y du/dy) = x³+2x²y-xy²+y³+2xy²-x³y/(x+y)²
=> x³+x²y+y³+xy²/(x+y)²
=> (x+y)(x²+y²) / (x+y)²
=> x²+y²/x+y
=> tan u
Thus, x du/dx + y du/dy = sin u cos u
=> ½sin 2u