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Application of differential calculus: Maximization and Minimization.
You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 300 ordered. What are the largest and smallest revenues your company can make under this deal?
Let u = [2,1,1]^T, v = [1,3,2]^T (i.e. they are column vectors). Caclulate v^Tu and uv^T. Show that u is an eigenvector of the matrix uv^T and calculate its eigenvalue.
Determine the nature of the solutions of the equation. x^2-10=0. Choose the correct nature of the solutions of the equation. Is it a) 1 real solution; b) 2 imaginary solutions; or c) 2 real solutions.
Evaluate the nearest distance between two tunnels using cosine rule. In a mine, two tunnels are dug starting at the same point.
A recepie for muffin mix calls for 8 cups of flour ,2 2/3 of cups of oatmeal ,and 4 tablespoons of baking powder along with other ingridients .If you had only 3 cups of flour , what would be the comparable amounts of oatmeal and baking powder.
A 1.50 103 kg car starts from rest and accelerates uniformly to 19.4 m/s in 12.7 s. Assume that air resistance remains constant at 400 N during this time.
One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations of X and Y.
Using calipers, you find that a copper cylinder has length 8.625 and diameter 1.218 . An electronic pan balance shows that its mass is 89.84 . Find the cylinder's density.
Henry received a 6% raise. If his old monthly salary was $2,250, what is his monthly salary now? (Hint: Find the amount of the raise. The add the raise to the previous monthly salary.)
Probability of Picking Groups of Cards, Find the probability that a hand of 13 cards dealt from a well shuffled pack of 52 contains
If, in a special right triangle the sides are denoted by "a, b, c" and the angles are denoted by "A, B, C" If I knew only C was 90 degrees, that a was 6 units long and b was 13 units long. How would I be able to find the degrees of Angle A and B?
A woman w = 6 ft tall is standing near a street lamp that is s = 14 ft tall. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.
The cost (in dollars) of producing x yards of a certain fabric for wedding dressess is C(x)=1200+12x-.1x^2+.0005x^3. the company finds that id it sells x yards of fabric
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