Suppose you are trying to decide on a price for your latest creation a coffee mug that never tips. Through a survey, you have determined that at a price of $2, you can sell 2100 mugs, but at a price of $12 you can only sell 100 mugs. Furthermore, your supplier can supply you 3500 mugs if you charge your customers $12, but only 500 if you charge $2. What price should you charge so that the supply equals demand, and at that price how many coffee mugs will you be able to sell?
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Step-by-step explanation:
Calculus: Early Transcendentals
(a) For what values of rr does the function y=erxy=erx satisfy the differential equation 2y′′+y′−y=0?2y"+y′−y=0? (b) if r1r1 and r2r2 are the values of rr that you found in part (a), show that every member of the family of functions y=aer1x+ber2xy=aer1x+ber2x is also a solution.

04:15

Physics 2012
The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force F¯¯¯¯ SM F¯ SM that the sun exerts on the moon is perpendicular to the force F→EMF→EM that the earth exerts on the moon. The masses are: mass of sun =1.99×1030kg=1.99×1030kg , mass of earth =5.98×1024kg=5.98×1024kg , mass of moon =7.35×1022kg=7.35×1022kg . The distances shown in the drawing are rSM=1.50×1011mrSM=1.50×1011m and rEM=3.85×108m.rEM=3.85×108m. Determine the magnitude of the net gravitational force on the moon.

03:20

Calculus: Early Transcendentals
Evaluate