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Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes.(b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.(c) Write an expression for the volume V in terms of both x and y.V=(d) Use the given information to write an equation that relates the variables x and y.(e) Use part (d) to write the volume as a function of only x. V(x) =(f) Finish solving the problem by finding the largest volume that such a box can have.
Find the volume of the solid obtained by revolving the graph of y=8x*sqrt(16-x^2) over [0,16] about the y-axis.
Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.75, and in January 2006, the price of regular unleaded gasoline was $2.57.
Suppose C(x) = x^3-6X^2+15X where x represents thousands of units. Is there a production level that minimizes average cost? If so what it it?
The temperature T(F) at which water boils at selected pressures p (pounds per square inch) can be modeled. Find the rate of change of the temperature when the pressure is 70 pounds per square inch.
1. in a study of fraternal twins of different genders researchers measured the heights of each twin. the data show that
What does a saddle point or a null point mean? What kind of physical meaning could that correspond to?
which of the following is the solution to system3x 4y 7x 2y 2answerx 6 y -2 x 5 y -2 x 4 y -12 x 3 y
students from four classes are going on a tour to a historical center. the largest class is 29 students. if the
Determine the coefficients of the function if the coordinates of the vertex of the parabola are the ordered pair (-100,-5000) and the fixed cost is $5000. Determine the domain and range of the variables, is the vertix a minimum or a maximum, why?
How many friend samples Sara should have in order to draw the conclusion with 95% confidence interval? Why?How would you explain your conclusion to Sara without using any statistical jargon? Why
A wire lies along the piecewise linear curve extending from the point (2,4) to the point (10,6) to the point (10,9). If the density of the wire is given by p(xy)=2xy+4x , use a line integral to find the mass of the wire. p=rho
Estimate the mean fill amount of a certain bottle-filling machine to within 0.05 liter. Assume that the population standard deviation is 0.17 liters. How large of a sample is needed to estimate the mean with 95% confidence?
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