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A function f(x,y) is harmonic if fxx + fyy = 0. Determine if the function g(x,y) = e^(-x) cos(y) + e^(y) cos(x) is harmonic.
Each glass of 2% milk contains 9 g of protein, 13 g of carbohydrates, and 300 mg of calcium. How many servings of each food should the dietician provide for the patient?
You can afford to put $1,500 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much wil
For how long (to the nearest year) should you lease the car so that your monthly payments are lower than if you were purchasing it with an 7%-per-year loan? You should lease the car for how many yea
If you are being charged 15% interest per year, how long (to the nearest 0.5 years) will it take you to repay your debt?
A buyer orders 3 Dogs houses and 2 Windows, 1 Side panel, and 2 Windows as spare parts. How many of each part are required to fill the order?
At what price is the elasticity of demand unitary (unit)? If the price increases by 3% from $100 per wigit, what is the approximate percentage change in demand?
Assuming that Calculus and You currently sells 5,000 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text.
Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic.
Find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymp
If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes.
There are currently 61 million car in a certain country increasing by 3.9% annually. How many years will it take for this country to have 82 million cars round to nearest year.
Find the local extrema for the revenue function, and find over which intervals is the graph of the revenue function concave upward or concave downward.
With the rational function f(x)=(3-3x^2)/(x^2-4), find any intercepts for the graph, find any vertical and horizontal asymptotes for the graph, and sketch the graph.
If the money is worth 9% compounded annually, what yearly payments will the person receive for the last twenty years?
Find the area of a regular dodecogon with sides length S. Use the fact that area of the dodecagon with side S sqrt(2-sqrt(3)) equals.
Find the exact value of the expression whenever is it defined sin [arcsin (-3/10)] and cos (arccos 1/4).
Three kinds of boats are available, and they respectively carry 10, 15, or 20 passengers. How many of each kind of boat should be rented?
For some reason, I am reluctant to sell the stock and swallow my losses. Determine when, to the nearest year, my investment will drop below $50.
Show that N is normal in G, H n N = 1 and G = HN, so G is the semi-direct product of N and H. Show also that if K/F and L/F are normal then G = H x N.
Find an equation of one variable for the volume of a right circular cylinder inscribed in a cone of height h and radius r with the base of the cylinder on the base of the cone.
What is the area of the triangle formed by their positions after 2 seconds? What is the peremeter? How long until the area of the triangle formed by their positions is 10cm^2? How long until the perem
Find the solution set of the linear system. For dependent equations, write your answer as an ordered triple in terms of z.
Find the equation of one variable for the surface area of a right circular cylinder inscribed in a cone of a height h and radius r with the base of the cylinder on the base of the cone.
The distance between the marks along the wheel is found to be 14 inches. What is the angle between the radii to the two marks?