Find the equation of a curve passing through the point (0, –2), given that at any point (x, y) on the curve, the product of the slope of its tangent any y-coordinate of the point is equal to the x-coordinate of the point.
At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve, given that it passes through (–2, 1)
The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units, find the radius of balloon after t second.
In a bank principal increases at the rate of 5% per year. An amount of Rs.1000 is deposited with this bank, how much it worth after 10 years (e0.5 = 1.648).
In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. It how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.