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assume that the positive x-axis points East and the positive y-axis points North. Suppose you arc hiking on a terrain modeled by z = x^2-+y^2 - y. You are at the point (1, 2, 3). Determine the slope you would encounter if you headed due East from your position. What angle of inclination docs that correspond to? Determine the slope you would encounter if you headed due North from your position. What angle of inclination does that correspond to? Determine the slope you would encounter if you headed due North-East from your position.
Why is dy/dx = (dy/du)(du/dx) an insufficient proof of the Chain Rule? In almost all Calculus textbooks, dy/dx = (dy/du)(du/dx) is given as a good rationale for the Chain Rule.
When is the particle moving in the positive direction? (Enter your answer using interval notation.) Find the total distance traveled during the first 6 s. ft Find the acceleration at time t (in ft/s2).
Construct a stem and leaf plot of the data.
A surveyor fins that a tree on the opposite bank of a river, flowing due east, has a bearing of N 22 degrees 30' E from a certain point and a bearing of N 15 degrees W from a point 400 feet downstream. Find the width of the river.
Find the maximum value attained by the function f on the whole real line.
A plane leaves an aircraft carrier and files due north at 500km/hr. the aircraft carrier proceeds 30 degree west of south at 35km/h. if the plane has enough fuel for 4h of flying, what is the maximum distance north it can fly,
Let f:R->R be a function that satisfies f(x+y) = f(x)+f(y) for all x,y in R. Suppose that f is continuous on R and that f(1)=k. Prove that f(x)=kx for all x in R.
Determine the following before deciding a prescription: (a) maximize effectiveness at the least cost; (b) maximize effectiveness at a fixed cost of $10,000; (c) achieve a fixed-effectiveness level of 6,000 units of service at a fixed cost of $20,0..
What do these results indicate? How might you use this information in your practice?
a paint mixture contains 14 gallons of base for every gallon of color. in 510 gallons of paint, how many gallons of color are there?
Let (xn) be a sequence such that xn does not equal 0 for each n and xn →x as n→∞,where x does not equal 0. Prove, using the definition of convergence, that (1/xn)→(1/x) as n→∞.
The demand for Carolina Industries' product varies greatly from month to month.
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