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1. Find the isosceles triangle of smallest area (Figure) that circumscribes a circle of radius 1 (from Thomas Simpson's The Doctrine and Application of Fluxions, a calculus text that appeared in 1750).
2. A box of volume 72 m3 with a square bottom and no top is constructed out of two different materials. The cost of the bottom is $40/m2 and the cost of the sides is $30/m2. Find the dimensions of the box that minimize total cost.
A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.5 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?
Write out the probability distribution for of sales during a five-day week. What is the mean and variance of this distribution? Assume that the profit from each sale is $750 for the situation in additional problem. What is the expected weekly profi..
two car models are tested for a difference in average gas mileage. ten cars of model a averaged 32.1 miles per gallon
Indicate, by checking the appropriate box, whether the given points below are on line 1 , on line 2 , on both line 1 and line 2 , or on neither one of the two lines:
The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?
in football teams can score 6 points with a touchdown 3 points with a field goal or 2 points with a safety.
A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in.
Dissolve the polynomial equation 3x3+13x2+7x+1=0 Solving quadratic equations by completing the squar
Find the area enclosed by the given curve and the y-axis.
how much energy is needed to increase the temperature of 755 g of iron from 283 k to 403 k.
What is the largest possible area for a right triangle in which the sum of the lengths of the two shorter sides is 100 in.
1. Two friends A and B go on a date and agree to meet at 7pm. Friend A is an impatient person and will scold b if A arrives before B and B arrives later than 7.15pm. Let X denote the number of minutes after 7pm that A arrives and Y denote the numb..
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