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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.
Oil from a ruptured tanker spreads in a circular pattern. If the radius of the circle increases at the constant rate of 1.5 feet per second, how fast is the enclosed area increasing at the end of 2 hours?
suppose the rectangular plot runs along a building, so that you need to fence only three sides. What dimensions will now yield a maximum area with 100 meters of fencing?
A particular test for the presence of steroids is to be used after a professional track meet. If steroids are present, the test will accurately indicate this 95% of the time.
Let S represent the student s score of the final exam. Provide a symbolic rule for the students final percentage score.?
A triangular sail has an area of x^2 + 5x + 6 square meters and a height of x + 3 meters. Find the length of the sail's base.
A piece of wire is 20 cm long. It is to be cut into two pieces (not necessarily of the same length). One piece is ti be bent into a square and the other into a circle. How should this be done so that the resulting sum of the areas of the two objec..
A sky diver in free fall travels at a speed modeled by ft per second after t seconds. How long will it take for the skydiver to attain the speed of 60 mph (note: 60 mph = 88 ft/sec)?
multiply and simplify the given expression.1 simplifynbsp 2x - 32x 3 - 2x 122 multiply and simplifynbsp 3x -
Let's say you hgave an area with 100 feet of fence. Two configurations were a circle and a rectangle. What other possibilities of utilizing other shapes for this fenced in area.
1) Which one is a protease inhibitor ? a) DDT b) Thiourea c) PMSF d) SDS
the restaurant you are working at makes one massive batch of potato salad each day. if yourun out before the end of the
A particle starts from a point 0 with an initial velocity of 2m/s and travels along a straight line with a constant acceleration of 2m/(s*s).
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