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A slice of circular pizza has perimeter 32 inches. Denote the central angle of the slice of pizza by theta radians and the radius by x inches. What is the diameter of the pizza which give maximum area (and hence the most pizza)? Justify your answer. Show a sketch and recall that the area of the sector of a circle with central angle theta radians and radius R is 1/2R2 theta and the length of the arc cut off by such an angle has length R(theta) with the angle measured in radians again.
MATH 54 QUIZ 9. Find a general solution to the differential equation y'' + 8y' + 16y = 0. Solve the initial value problem: {y'' + 2y' + y = 0, y(0) = 1, y'(0) = -3}. Find a general solution to the differential equation y''' - y''+ 2y = 0
Casey earned $5200 last month for selling 12 units of product x and 8 units of product y. Find the commission rates for each product.
A set A is call a partially-ordered set if there is a relation R on A such that R is reflexive and transitive. If A is any set, prove that the power set P(A) is a partially ordered set under the relation "is a subset of".
a plant orders chemical x that is used atnbspa rate of 800 barrels per year. each order placed with the supplier costs
the initial price of a cup of coffee is 1.5 and at that price 200 cups are demanded. if the price falls to 0.90 the
Suppose the monthly total cost for the manufacture of radio is C(x)=1475 + 45x, where x is the number of radios produced each month. What is the marginal cost for the product?
s to manufacture a box with a volume of 24 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Round to the nearest tenth, if necessary.
A point P is moving in the xy-plane. When P is at (4, 3), its distance to the origin is increasing at a rate of √2 cm/sec. Determine the rate of change of the x-coordinate of P at that moment.
A manufacture has been selling 1300 television sets a week at 420 each. A market survey indicates that for each 16 rebate offered to a buyer, the number of sets sold will increase by 160 per week.
Architecture. An architect is designing the floors for a hotel. Each floor is to be rectangular and is allotted 720 ft of security piping around walls outside the rooms. What dimensions of the atrium will allow an atrium at the bottom to have maxi..
question consider quadrilateral abcd with a -34 b 26 c 2-1 and d -3-3. find the area and perimeter of abcd. please
Computing the Volume of a regular tetrahedron of edge length 2(alpha). Explain how to compute the volume of a regular tetrahedron of edge length 2(alpha).
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