Solve the problem.An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc). Each side of the base has length x cm. The box's surface area S is given by S(x) =  + x2. Estimate the minimum surface area and the value of x that will yield it.

A. 256 cm2 when x = 6 cm
B. 192 cm2 when x = 8 cm
C. 207 cm2 when x = 6 cm
D. 256 cm2 when x = 8 cm


Answer: B

Mathematics

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Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x2 + y2 + Dx + Ey + F = 0.Tangent to the x axis, a radius of length 7, and abscissa of center is –8 

A. x2 + y2 - 16x - 14y + 64 = 0 and x2 + y2 - 16x + 14y + 64 = 0 B. x2 + y2 + 16x - 14y + 64 = 0 C. x2 + y2 + 16x - 14y + 64 = 0 and x2 + y2 + 16x + 14y + 64 = 0 D. x2 + y2 + 16x + 14y + 64 = 0 E. x2 + y2 - 16x + 14y + 64 = 0

Mathematics

Choose the best estimate from the list. ? 3 is approximately -4, -3, -2, -1

A. -4 B. -3 C. -1 D. -2

Mathematics

Use transformations to explain how the graph of the given function can be obtained from the graph of the appropriate root function (y =  or y =).f(x) = 

A. Rewrite as 2. Shift the graph of y =  to the left 4 units and stretch vertically by a factor of 2.
B. Rewrite as 2. Shift the graph of y =  to the right 4 units and stretch vertically by a factor of 2.
C. Rewrite as 2. Shift the graph of y =  to the right 2 units and upward 4 units.
D. Rewrite as 2. Shift the graph of y =  upward 4 units and stretch vertically by a factor of 2.

Mathematics

The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a volunteer is given a capsule, blood samples are drawn every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are as follows.

Time t N(t) (hr) (mg) 0 0 0.5 246.5 1 266 1.5 236.9 2 178.1 2.5 115.9 Use the trapezoidal rule to approximate the average number of milligrams in the bloodstream during the first  hours and round your answer to two decimal places. ? A. 433.60 mg B. 197.09 mg C. 123.18 mg D. 256.22 mg E. 335.05 mg

Mathematics