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The height on the surface of the mountain is described by the h(x,y) = 4000 - .001 x2 - .004 y2 for each of the following parts assume that you are currently standing at the point on the surface corresponding to x = 500 y = 300.
a) How steep is the incline at this point if you are walking in the positive y direction?
b) At what rate is your height on the surface changing at this point if you are walking toward x = 400 y = 200?
c) In what (instantaneous) direction should you move in order to descend at the greatest rate?
chocolate bars produced by a certain machine are labeled with 8.0 oz. the distribution of the actual weights of these
the measurement of a side of a square is found to be 12 inches, whith a possible error of 1/64 inch. Use differentials to approximate the possible error in computing the area of the square.
if q is the number of quarts of lemonade, then 1/4 q can be used to fine the number of cups of lemonade mix needed to make the lemonade. how much mix is need to make each amount of lemonade ?
Assume you have noted the following prices for paperback books and the number of pages that each book contains. Develop a least-squares estimated regression line.
solve the system of equation by matrix method.use augmented matrices to solve the following 2 x 2 systems of equations.
A 26 foot is placed against a vertical wall of a building with the botton of the ladder standing on level ground 10 feet from the base of the building. how high up the wall does the ladder reach.
Which variable in the simple interest equation I = prt represents the original amount of money borrowed or invested?
A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.
Solve the constant-coefficient equation in u to find two linearly independent solution. Use part (b) to find solution of the DE when a = 1 and b = -1/2. FInd the solution when y(1) = 0 and y'(1) = 1.
Draw the diagram for each and discuss the part of the solution that would be different to finding the requested probabilities.
Find all points of intersection of the curves (r^2)=4sin(2x) and (r^2)=4cos(2x). Give your answers as ordered pairs in cartesian coordinates, in order of increasing radius and increasing angle.
If t=0 at the start, for what values of t will the velocity of the particle A exceed the velocity of particle B.
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