A piece of wire 20 cm long is to be cut into two pieces. One piece is bent into a square, and the other into a circle. How should the wire be cut so that the total area of the square and circle is maximized?
A company’s profit P(x) from selling x units is given by P(x) = -5x^2 + 150x – 1000. Find the number of units that should be sold to maximize profit.
A rectangular garden with an area of 200 square meters is to be fenced on three sides, with one side left open. The fencing on two adjacent sides costs ₹5 per meter, while the third side costs ₹10 per meter. Find the dimensions of the garden to minimize the cost.
The amount A in a bank account grows according to the formula A = Pe^(rt), where P is the principal, r is the rate, and t is the time in years. If P = 1000 and r=0.05, find the rate of change of A with respect to t when t = 3.
A factory produces two types of goods, A and B. Each unit of A requires 2 hours, and each unit of B requires 3 hours of labor. The factory has a total of 60 hours available per day. If profit per unit of A is ₹40 and per unit of B is ₹50, how many units of each should be produced to maximize profit?
Define greenhouse gases. Explain their role in global warming and suggest ways to reduce greenhouse gas emissions.
Define catalysis and explain how heterogeneous and homogeneous catalysts work with examples.
Describe the Cannizzaro reaction. Provide a reaction example and explain its mechanism.
Explain why carboxylic acids are more acidic than alcohols. Discuss the effect of substituents on their acidity.
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