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1) You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
2) A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?
3) Determine whether the given ordered pair is a solution of the system.
(8,5)
5x - 4y =20
3 y = 2X + 1
4) Solve by the substitution method.
2X + 5y =1
-x + 6y =8
What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches?
Verify that 18^3 - 1^3 = 17* 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates.
Use a graphing device to graph the polar curve. Choose the parameter interval to make sure that you produce the entire curve.
The average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.
Find whether x=3 is a local maximum or a local minimum and Sketch the graph - Sketch possible graphs for all four cases.
Starbucks cashiers take thousands of orders each day. Samples of the accuracy in the orders are listed below. One hundred orders taken by each cashier were carefully examined and the number of errors counted.
Confidence interval for population proportion of drug test.
Linear Transformations, Rotations, Submodules and Subspaces, (7) Let F=R, let V=R^2 and let T be the linear transformation from V to V which is rotation clockwise about the origin by pi-radians. Show that every subspace of V is an F[X]-submodule f..
Find the second derivative
Normal curve approximation to the binomial distribution, Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent.
Solve equations and systems of equations in two variables, formulate real-world problems in terms of linear equations and solve these systems by several commonly applied methods.
Find the equation of the tangent plane to the ellipsoid 7x2 + 5y2 + 3z2 = 60 which pass through the line 5y - 3z = 0 = 7x + 10y - 30.
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