Solve the problem.An open-top box is to be made by cutting small identical squares from each corner of a
sheet of tin and bending up the sides. If each corner square is x inches on a side, the volume of the box (in in.3) is given by: V(x) = 144x - 48x2 + 4x3By sketching the graph of V(x), estimate what values of x result in a box with a volume greater than 64 in3.
A. 0.1 in. ? x ? 5.0 in.
B. 0.54 in. ? x ? 4 in.
C. 1.5 in. ? x ? 2.5 in.
D. 1.0 in. ? x ? 3.0 in.
Answer: B
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The salinity S, in parts per thousand of dissolved solids, of a tank is being raised to a target value of 84 parts per thousand. The table below shows the difference ? between the target salinity and the current salinity after t hours.
t 0 2 4 6 D 59.00 38.71 25.40 16.66? A: Find an exponential model for the data. Be careful. The data are given in steps of 2 hours. Round your answer to two decimal places, if necessary.B: Find a formula that gives the salinity S after t hours. Round your answer to two decimal places, if necessary.C: Make a graph ofS versust over the first 10 hours. Include the horizontal line representing the target value.E: According to the model, when does salinity reach 64.00 parts per thousand? Round your answer to two decimal places. What will be an ideal response?
Evaluate the integral.
A.
B.
C.
D.
The question(s) that follow refer to the problem of finding the minimum spanning tree for the weighted network shown below.
Which of the following edges of the given network are not part of the minimum spanning tree?
A. EB B. BD C. AC D. AB E. none of these
Use the commutative and associative properties to simplify the expression.-4 + (4x - 2)
A. -6 + 4x B. -6x - 2 C. -8x D. 8 + 4x