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When mixing a certain cocktail a barperson starts with a 5 litre solution of 10% alcohol. Into this solution the barperson mixes vodka (40% alcohol) at the rate of 2 litres/minute and pours into glasses at the rate of 3 litres/minute.
a. Find a formula for the volume V(t) of the mixture at time t minutes.
b. Find a differential equation that tells the rate of change of the amount of alcohol A(t) at time t minutes.
c. Solve the differential equation and use the initial condition to find a formula for A(t).
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Starting with a hyperplane that does not separate the points, use the perceptron algorithm to find a separating hyperplane. Did the algorithm find the maximum margin separating hyperplane.
Engineer collegues requires applicants. Asssume that the average score was 498 with standard deviation of 77 . Assume that scores are normally disturbuted
The height in feet for a ball thrown upward at 48 feet per second is given by s(t)=-16t^(2)+48t, where t is the time in seconds after the ball is tossed.
Probability Definition of Continuity. Suppose that f_x is the probability density function (PDF) of a continuous random variable X. Also suppose that f_x is continuous on (a, b)
Two cars start moving from the same point. one travels south at 30 mi/h and the other travels west at 70 mi/h. At what rate is the distance between the cars increasing 2 hours later?
1) A Batch of 40 good workpieces is to be produced using a sand casting process with a starting material thatcosts $40 a piece. The time it takes to fill the mold is 10 seconds, while the solidification time is 1minute. The casting is removed from th..
An open rectangular box is to be constructed from material that costs $12/ft2 for the bottom and $10/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $81.
1. explain which of the two options below results in a lower balance after 6 months on a debt of 2500.annual simple
Prove that in Sn with n > = , any even permutation is a product of cycles of length three. Hint: (a,b)(b,c) = (a,b, c) and (a,b)(c,d) = (a,b,c)(b, c, d)
question a building is located at the end of a street that is inclined at an angle of 8.4ordm with the horizontal. at a
Prove that 1/(2n) is less than or equal to [ 1 * 3 * 5 *...* (2n - 1)] / (2 * 4 *...* 2n) whenever n is a positive integer.
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