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A happy heat-loving bug is wandering on a hot plate. The temperature at any point on the plate is given by
T(x, y) = 210e-(x^2/5)-(y^2/2)
If the bug is at the point P = (-3,3) and moving towards the point Q = (3,2), what is the rate of change in the temperature in the direction of its motion?
In what direction should the bug move from P for the temperature to increase the fastest?
What is the magnitude of the rate of change of temperature in that direction?
Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. Round your answers to four decimal places.
Blending Coffees. The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound?
Describe one real-life example of where rational equations are used at home. For ideas, look in the textbook or online. Describe one of them in detail.
For three topics/problems from this semester (calculus 2) that interest you, describe it, give an example, and solve it. Your score will depend on the difficulty of the problems/topics you choose and the clarity, completeness, and correctness of your..
What was the acceleration of the car, assuming it was constant? (Round your answer to two decimal places.)
The region bounded by the curves y=x^2 and y=sqrt(x) is revolved about the y-axis. Use the method of cylindrical shells to set up the integral that represents the volume of the solid. Do NOT evaluate the integral.
Provide a logical explanation for this relationship (Hint: consider n objects as consisting of n-1 existing objects plus a new nth object.
Convert the data from your chosen source into an index.
A wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years.)
a number has 3 digits. it is an even square number less than 500.the product of its digits is evenly divisible by 15. what is the number?
Find the dimensions of the largest acceptable box with square front and back. (Let x be the measurement of one side of the square front. Let y be the length of the box.)
A committee consists of 8 married couples. In how many ways can a subcommitee of 5 people be chosen so that at most one married couple
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