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1. Determine whether or not the following equation is exact. If it is exact, find the solution.
(exsin y - 5y sin x)dx + (ex cos y + 5 cosx)dy = 0.
2. Determine whether or not the following equation is exact. If it is exact, find the solution.
(7y + (1/x) - (x/y2)) dy/dx + (2x + (1/y) - (y/x2)) = 0.
3. Determine whether or not the following equation is exact:
2e(x/2)+y - y + 2 (xe(x/2)+y +1) (dy/dx) = 0. y(0)=1
If it is exact, find the solution. If it is not exact, multiplying the equation with an integrating factor F=e-x/2 and check if the new equation is exact. If the new equation is exact, find the solution.
To produce x units of a particular commodity, a monopolist has a total cost of C(x) = 2x^2 + 3x + 5. The unit price at which the x units will be sold is p(x) = 5-2x.
Find its maximum distance above the ground? After how many seconds will the object hit the ground.
Find the work needed to pump all the water out of the pyramid, assuming water is pumped out through an outflow pipe 1m from the top of the pyramid. Take the gravitational constant as 9.8m/s2.
illustrtes the impact of diversification. ignores the probability distribution of cash flows. can only measure one outcome at a time
A baseball diamond is square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?
of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time. She can walk at the rate of 4 mi/h and row a boat at 2 mi/h. How should she proceed?
Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 40% down. Assume that the monthly cost to finance $1,000 is $6.00. What are the monthly payments.
a family is canoeing downstream with the current. their speed relative to the banks of the river averages 2.75 mih.
Find the average velocity for the time period beginning when t = 2 and lasting 0.5 second.
A mall has three department stores, JC Penney, Macy's, and Sears. A survey of 2,118 people exiting the mall found that 433 made a purchase at JC Penney, 412 made a purchase at Macy's, 638 made a purchase at Sears
The Greeks would show that the square of side square root (11) and the rectangle of length 11 and width 1 have the same area by dividing one of them into a fi nite number of triangles and reassembling the triangles to get the other. Can you do so?..
At a local Wendy's, a survey showed that out of 5,500 customers eating lunch, 575 ordered Diet Pepsi with their meal. What percent of customers ordered Diet Pepsi? (Round your answer to the nearest whole percent.
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