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A tank initially contains 10 gallons of brine in which 3 pounds of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 2 gal/min. The mixture is well stirred and ows out of the tank at the rate of 1 gal/min.
(a) What is the volume of the brine in the tank at the time t?
(b) State and solve the I.V.P. describing this process(remember to include the initial condition).
A box with no top is to be built by taking a 6'' - by - 10'' sheet of cardboard and cutting x - in. squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box.
The monthly cost in dollars of a phone plan is a linear function of the calling time in minutes. The monthly cost for 40 minutes of calls is $14.18 and the monthly cost for 96 minutes is $19.22.
Find the velocity of the top of the ladder at time t=3.
Each of the letters in the word MENDOCINA is written on a card, and the cards are mixed thoroughly. You draw one card and replace it. You draw a second card. find the probability that the first card is E and the second card is N.
Why can't a rational function have both a horizontal and an oblique asymptote? Construct your own rational functions to give examples.
The weights of full-grown adult female okapis are normally distributed with a mean of 500 pounds and a standard deviation of 30 pounds. What is the probability that
How many gallons of water are being pumped out each hour?
An orchard contains 53 peach trees with each tree yielding an average of 51 peaches. For each 5 additional trees planted, the average yield per tree decreases by 12 peaches. How many trees should be planted to maximize the total yield of the orcha..
Find an equation of the tangent plane to the given surface at the specified point.
What are the practical uses of scientific notation? Why is scientific notation so important in modern-day society?
The circumference of a sphere was measured to be 80.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.
Let v1 and v2 be vectors in R^n. Show that (prove) the set of all vectors w, an element of R^n such that w is orthogonal to both v1 and v2, is a subspace of R^n.
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