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A bag of sand originally weighing 136lb was lifted at a constant rate. As it rose, sand also leaked out at a constant rate. The sand was half gone by the time the bag had been lifted to 17 ft. How much work was done lifting the sand this far? (Neglect the weight of the bag and lifting equipment.)
The base of an aquarium with volume V = 390 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
Find the condition that the curve y = mx + c to be a tangent to the parabola y^2 = 4 ax and also determine the point of contact.
A tennis court has a perimeter of 228 feet. The length of the tennis court is 42 feet longer than the width. Write a linear equation of the problem. What is the length and width of the court?
Teachers also found that strength of class is maximum satisfying all above conditions. Determine the total no. chocolates got by student A of the first class.
Is it possible to have a triangle with sides measuring 10ft, 12 ft, and 23 ft.? A mountain road is inclined 30 degrees with the horizontal, if a pick-up truck drives 2 mi. on this road , what change in altitude has been achieved?
at 2p.m., the shadow of a lighthouse is 19 feet long and the angle of elevation is 75 degrees. find the height of the lighthouse.
Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imag..
the volume of a cone with a height of 18 millimeters is 471 cubic millimeters. find the area of the base to the nearest tenth.
A random variable defined on all real numbers has a probability density proportional to: c/ X2 + 1. What is c? What is the probability that the random variable lies between 0 and 1?
Examine several newspapers and magazines and describe at least 3 examples of functions that you find. What is the domain and range of each function?
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 10-x^2. What are the dimensions of such a rectangle with the greatest possible area?
suppose the rectangular plot runs along a building, so that you need to fence only three sides. What dimensions will now yield a maximum area with 100 meters of fencing?
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