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1. The area of a sector in a circle is given by the formula: A=1/2r2θ, where r is the radius and θ is the central angle measured in radians. Find the rate of change of A with respect to θ if r remains constant. What is the rate when r=3?
2. An object moves along a coordinate line, its position at each time t ≥ 0 is given by x(t)=t2+5t+1. Find the velocity at time t0=5.
The length of a rope required to wrap around a circular wheel exactly is 8.8cm. What is the diameter of the wheel to the nearest tenth?
Find the break-even point for the firm
the sweet smell fertilizer company markets bags of manure labeled exactly 60 lb dry weight . the packaged manure is a
"If the price falls and, as a result, the total revenue decreases, demand is elastic." Is the previous assertion correct?
Suppose that X and Y are two mathematical objects of the same sort (two sets, two rings, etc.), and we consider the family of all homomorphisms among them. What structure does this system have?
From a total of 15 people, three committees consisting of 3, 4, and 5 people, respectively, are to be chosen. How many such sets of committees are possible if there is no restriction on the number of committees on which a person may serve?
Show that the greedy algorithm for making change for n cents using quarters, dimes, nickels and pennies has O(n) complexity measured in terms of comparisons needed.
Write a script and a function to implement the secant algorithm - function will implement the secant algorithm and return the root of the function.
The radius of the tank is 3 feet. How fast is the level of the water in the tank rising when the tank is half full? The level of the water is rising at feet per minute.
the turkeys found in a particular county have an average weight of 15.6 pounds with a standard deviation of 4.0
Develop a probability distribution for the job satisfaction score of an executive manager. Develop a probability distribution for the job satisfaction score of a financial adviser.
Determine the number of moles of atoms in a 22.89 g sample of a metal whose molar mass (MM) is 58.69 g.
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