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Answer all the question given below:
1. Given the demand curve D(x) = (x-7)^2 and the supply curve S(x) = x^2 Only consider values in the first quadrant, from x= 0 to 7 Find the following: a) the equilibrium point (as ordered pair) b) the consumers surplus at the equilibrium point c) the producers surplus at the equilibrium point
2.Find fx and fy for f(x) = e^(5x+7y)
3.Find the 2nd derivatives: fxx; fyy; fyx and fxy for f(x,y) = x(^5)y(^3)-2(x^2) y
Mustafa buys a book that costs $12.50. If the sales tax is 8%, what is the total cost of the book?
The derivative from the rate of changes
Find the roots of the characteristic polynomial, r+ and r-, larger and smaller or equal, respectively. Find the real-valued fundamental solutions to the differential equation associated to the roots in part (a).
A rectangular garden plot has dimensions of 15 ft. by 12 ft. A uniform path around the garden increases the total area to 270 sq. ft. What is the width of the larger rectangle?
The bases of an isosceles trapezoid are 18cm and 24cm. If one of the angles of this trapezoid is 120 degrees, find the exact area and perimeter.
Ms.Johnson works a basic week of 35 hours at the rate of $3.76 per hour. Calculate her earnings for a basic week.
Find the probability values based on binomial distribution
a company's total cost in millions of dollars,is given by c(t)=280-30e^-t where t= time in years, find the marginal cost when t=3
A ranger in tower A spots a fire at a direction of 354 degrees. A ranger in tower B located 60 miles aat a direction of 50 degrees from tower A spots fire at 317 degrees. How far is fire from tower A and B.
Suppose there are two events, A and B. A and B are mutually exclusive. P(A)=.4, P(B)=.5. What is P(A'|B)?
Calculate the probability that a randomly chosen U.S. adult does not take a multiple formula. c. If three U.S. adults were chosen at random, compute the probability that only two of them take a multiple formula as their primary source.
A ball is thrown vertically upward with an initial velocity of 48 feet per second. If the ball started its flight at a height of 8 feet, then its height s at time t can be determined by: s(t)=-16t squared +48t+8.
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