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The purchase price of an acre of land in the Louisiana purchase in 1803 was about 6 cents. Suppose the value of this property grew at an annual rate of 4.6% compounded annually. What would an acre of land be worth in 2016?
Cosider the function f(x,y) = x2 +(y2)/4 and the level curve at z = 1 is the ellipse x2+(y2)/4=1. Find a vector perpendicular to the tangent line of this level curve at (1/(2)(1/2), (2)(1/2)).
a farmer wishes to enclose a rectangular region with 210 m of fencing in such a way that the length is twice the width and the region is divided into two equal parts. What length and width should be used?
Prove, using only the definition of congruence modulo n, that if a ≡ b (mod n) and c ≡ d (mod n), then a+c ≡ b+d (mod n).
a circle with centre o has radius r cm. a sector of the circle which has an angle of radians at o has perimeter 6 cm
Let F be the face of optimal solutions of the linear program max{cx: x ∈ P}, where P={x∈Rn:Ax≤b}. Let MF= be the equality set of F and let u* be any optimal solution of the dual linear program. Show that ui*=0 if i∉MF=.
In rectangle ABDF above, C and E are midpoints of sides BD and DF, respectively. What fraction of the area of the rectangle shaded?
A particular company produces widgets. Each widget sells for $9, and the variable cost of producing each unit is 40% of the selling price. If the monthly fixed costs incurred by the company are $50,000, what is the break-even point?
Tabatha's parents bought a new house in Florida for $110,000. After 10 years, the value was $145,000. Using x as the number of years and y as the house value, graph the two points.
The water from the reservoir is not safe to drink if the bacteria concentration reaches 0.01 g/m3. How many days does it take for the bacteria concentration to reach this level? Express the answer in exact form and to 3 decimal places
A fence around a rectangular corral has a length of 180 feet and a width of 90 feet. What is the perimeter of the fence?
What is the sum of three points on an elliptic curve that lie on a straight line?
Think back to the Getting Started discussion of a math course which is Math Proof/ Problem solving you were asked your thoughts on proof and problem solving. After completing this course
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