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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) = 130 e-(x^2/3) - (y^2/4)
A) If the bug is at the point P=(2,3) and moving towards the point Q=(-1,2), what is the rate of change in the temperature in the direction of its motion?
B) In what direction should the bug move from P for the temperature to increase the fastest? (Give your answer as a unit vector.)
C) What is the magnitude of the rate of change of temperature in that direction?
Determine the braking force required to slow the train of cars by this ammount by using the following method; the laws of motion and d'alemberts principle.
How fast is the volume increasing at this moment, assuming that the diameter is always equal to the height, and the height is increasing at a rate of 1cm/min
find the equation of the tangent line to the curve f(x)=4/(5x + 7) at the point (-1.2). (use the definition of derivative (not short cut) to find f'(x))
Find the rate of change of quantity with respect to price, dD/dp. How many units will consumers want to buy when the price is $25 per unit? Find the rate of change at p = 25, and interpret this result.
You want to see if the number of minutes cell phone users use each month has changed from its mean of 120 minutes 2 years ago. You take a random sample of 100 cell phone users and find an average of 135 minutes used.
q1. show all workings.dont count the number of divisions. do not use asymptotic notation instead provide exact
A company produces very unusual CD's for which the variable cost is $12 per CD and the fixed costs are $25,000. They will sell the CD's for $98 each. Let x be the number of CD's produced.
thirty randomly selected students took the calculus final. if the sample mean was 89 and the standard deviation was 6.2
Find the vertices of the rectangle with maximum area.
A wad of putty of mass 0.025 kg drops vertically onto the record from above and sticks to the edge of the record. What is the angular speed of the record immediately after the putty sticks to it?
Prove the triangle inequality starting with: |V+W|^2. You must use Re (less than or equal to) | | and the Schwarz inequality.
an embroidered placement costs 2.95. an embroidered table cloth is similar to the placemat but four times as long
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